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Alicia Cordero, Jai P. Jaiswal and Juan R. Torregrosa

Abstract

The use of complex dynamics tools in order to deepen the knowledge of qualitative behaviour of iterative methods for solving non-linear equations is a growing area of research in the last few years with fruitful results. Most of the studies dealt with the analysis of iterative schemes for solving non-linear equations with simple roots; however, the case involving multiple roots remains almost unexplored. The main objective of this paper was to discuss the dynamical analysis of the rational map associated with an existing class of iterative procedures for multiple roots. This study was performed for cases of double and triple multiplicities, giving as a conjecture that the wideness of the convergence regions of the multiple roots increases when the multiplicity is higher and also that this family of parametric methods includes some specially fast and stable elements with global convergence.

Open access

M. Ćwiklińska-Jurkowska

Summary

The usefulness of combining methods is examined using the example of microarray cancer data sets, where expression levels of huge numbers of genes are reported. Problems of discrimination into two groups are examined on three data sets relating to the expression of huge numbers of genes. For the three examined microarray data sets, the cross-validation errors evaluated on the remaining half of the whole data set, not used earlier for the selection of genes, were used as measures of classifier performance. Common single procedures for the selection of genes—Prediction Analysis of Microarrays (PAM) and Significance Analysis of Microarrays (SAM)—were compared with the fusion of eight selection procedures, or of a smaller subset of five of them, excluding SAM or PAM. Merging five or eight selection methods gave similar results. Based on the misclassification rates for the three examined microarray data sets, for any examined ensemble of classifiers, the combining of gene selection methods was not superior to single PAM or SAM selection for two of the examined data sets. Additionally, the procedure of heterogeneous combining of five base classifiers—k-nearest neighbors, SVM linear and SVM radial with parameter c=1, shrunken centroids regularized classifier (SCRDA) and nearest mean classifier—proved to significantly outperform resampling classifiers such as bagging decision trees. Heterogeneously combined classifiers also outperformed double bagging for some ranges of gene numbers and data sets, but merging is generally not superior to random forests. The preliminary step of combining gene rankings was generally not essential for the performance for either heterogeneously or homogeneously combined classifiers.

Open access

Agata Savary, Silvio Ricardo Cordeiro, Timm Lichte, Carlos Ramisch, Uxoa Iñurrieta and Voula Giouli

Abstract

Multiword expressions can have both idiomatic and literal occurrences. For instance pulling strings can be understood either as making use of one’s influence, or literally. Distinguishing these two cases has been addressed in linguistics and psycholinguistics studies, and is also considered one of the major challenges in MWE processing. We suggest that literal occurrences should be considered in both semantic and syntactic terms, which motivates their study in a treebank. We propose heuristics to automatically pre-identify candidate sentences that might contain literal occurrences of verbal VMWEs, and we apply them to existing treebanks in five typologically different languages: Basque, German, Greek, Polish and Portuguese. We also perform a linguistic study of the literal occurrences extracted by the different heuristics. The results suggest that literal occurrences constitute a rare phenomenon. We also identify some properties that may distinguish them from their idiomatic counterparts. This article is a largely extended version of Savary and Cordeiro (2018).

Open access

Koji Arikawa

Abstract

Graph theory, which quantitatively measures the precise structure and complexity of any network, uncovers an optimal force balance in sentential graphs generated by the computational procedures of human natural language (CHL). It provides an alternative way to evaluate grammaticality by calculating ‘feature potential’ of nodes and ‘feature current’ along edges. An optimal force balance becomes visible by expressing ‘feature current’ through different point sizes of lines. Graph theory provides insights into syntax and contradicts Chomsky’s current proposal to discard tree notations. We propose an error minimization hypothesis for CHL: a good sentential network possesses an error-free self-organized force balance. CHL minimizes errors by (a) converting bottom-up flow (structure building) to top-down flow (parsing), (b) removing head projection edges, (c) preserving edges related to feature checking, (d) deleting DPmovement trajectories headed by an intermediate copy, (e) ensuring that covert wh-movement trajectories have infinitesimally small currents and conserving flow directions, and (f) robustly remedying a gap in wh-loop by using infinitesimally inexpensive wh-internally-merged (wh- IM) edge with the original flow direction. The CHL compels the sensorimotor (SM) interface to ground nodes so that Kirchhoff’s current law (a fundamental balance law) is satisfied. Internal merges are built-in grounding operations at the CHL–SM interface that generate loops and optimal force balance in sentential networks.

Open access

Pavel Vondřička

Abstract

The paper proposes design of a generic database for multiword expressions (MWE), based on the requirements for implementation of the lexicon of Czech MWEs. The lexicon is aimed at different goals concerning lexicography, teaching Czech as a foreign language, and theoretical issues of MWEs as entities standing between lexicon and grammar, as well as for NLP tasks such as tagging and parsing, identification and search of MWEs, or word sense and semantic disambiguation. The database is designed to account for flexibility in morphology and word order, syntactic and lexical variants and even creatively used fragments. Current state of implementation is presented together with some emerging issues, problems and solutions.

Open access

Asıf Yokuş and Sema Gülbahar

Abstract

In this study, numerical solutions of the fractional Harry Dym equation are investigated. Linearization techniques are utilized for non-linear terms existing in the fractional Harry Dym equation. The error norms L 2 and L are computed. Stability of the finite difference method is studied with the aid of Von Neumann stabity analysis.

Open access

Juan Pedro Ruiz-Fernández, Javier Benlloch, Miguel A. López and Nelia Valverde-Gascueña

Abstract

The objectives in each construction process can be multiple. However, the constructions have to be carried out under some restrictions concerning price and terms. They constitute some strategic and interdependent goals. In other words, “time is money”. Several papers support that seasonal effects influence the execution rate of construction. Thus, most of them try to improve the forecasts by evaluating and joining them to the planning, although always measuring their influence indirectly. In this paper, we suggest a methodology to directly measure the influence of the seasonal factors as a whole over the earned value of construction. Additionally, we apply it to a certain case study regarding the subsidised housing of public promotion in the Castilla-La Mancha region (Spain). It is worth mentioning that our results are clarified: we have calculated the average monthly production for each month a year with respect to the annual monthly mean. Moreover, the differences regarding the average monthly production we have contributed are quite significant, and hence they have to be taken into account for each earned value forecast so that a project becomes reliable.

Open access

Sadibou Aidara

Abstract

In this work, we deal with a new type of differential equations called anticipated backward doubly stochastic differential equations. We establish existence and uniqueness of solution in the case of non-Lipschitz coefficients.

Open access

Shiyong Li, Yue Zhang, Yan Wang and Wei Sun

Abstract

This paper considers reasonable bandwidth allocation for multiclass services in peer-to-peer (P2P) networks, measures the satisfaction of each peer as a customer by a utility function when acquiring one service, and develops an optimization model for bandwidth allocation with the objective of utility maximization. Elastic services with concave utilities are first considered and the exact expression of optimal bandwidth allocation for each peer is deduced. In order to obtain an optimum in distributed P2P networks, we develop a gradient-based bandwidth allocation scheme and illustrate the performance with numerical examples. Then we investigate bandwidth allocation for inelastic services with sigmoidal utilities, which is a nonconvex optimization problem. In order to solve it, we analyze provider capacity provisioning for bandwidth allocation of inelastic services and modify the update rule for prices that service customers should pay. Numerical examples are finally given to illustrate that the improved scheme can also efficiently converge to the global optimum.

Open access

Said Djennoune, Maamar Bettayeb and Ubaid Muhsen Al-Saggaf

Abstract

This paper deals with the synchronization of fractional-order chaotic discrete-time systems. First, some new concepts regarding the output-memory observability of non-linear fractional-order discrete-time systems are developed. A rank criterion for output-memory observability is derived. Second, a dead-beat observer which recovers exactly the true state system from the knowledge of a finite number of delayed inputs and delayed outputs is proposed. The case of the presence of an unknown input is also studied. Third, secure data communication based on a generalized fractional-order Hénon map is proposed. Numerical simulations and application to secure speech communication are presented to show the efficiency of the proposed approach.