Hasil untuk "Applied mathematics. Quantitative methods"

Bell Dominik, Pinto Martin Campos, Kumozec Davor et al.

The gyro-kinetic model is an approximation of the Vlasov-Maxwell system in a strongly magnetized magnetic field. We propose a new algorithm for solving it combining the Semi-Lagrangian (SL) method and the Arakawa (AKW) scheme with a time-integrator. Both methods are successfully used in practice for different kinds of applications, in our case, we combine them by first decomposing the problem into a fast (parallel) and a slow (perpendicular) dynamical system. The SL approach and the AKW scheme will be used to solve respectively the fast and the slow subsystems. Compared to the scheme in [1], where the entire model is solved using only the SL method, our goal is to replace the method used in the slow subsystem by the AKW scheme, in order to improve the conservation of the physical constants.

Pedro Ramaciotti, Duncan Cassells, Zografoula Vagena et al.

Abstract A growing number of social media studies in the U.S. rely on the characterization of the opinion of individual users, for example, as Democrat- or Republican-leaning, or in continuous scales ranging from most liberal to most conservative. Recent works have shown, however, that additional opinion dimensions, for instance measuring attitudes towards elites, institutions, or cultural change, are also relevant for understanding socio-informational phenomena on social platforms and in politics in general. The study of social networks in high-dimensional opinion spaces remains challenging in the US, both because of the relative dominance of a principal liberal-conservative dimension in observed phenomena, and because two-party political systems structure both the preferences of users and the tools to measure them. This article leverages graph embedding in multi-dimensional latent opinion spaces and text analysis to propose a method to identify additional opinion dimensions linked to cultural, policy, social, and ideological groups and preferences. Using Twitter social graph data we infer the political stance of nearly 2 million users connected to the political debate in the U.S. for several issue dimensions of public debate. We show that it is possible to identify several new dimensions structuring social graphs, non-aligned with the classic liberal-conservative dimension. We also show how the social graph is polarized to different degrees along these newfound dimensions, leveraging multi-modality measures in opinion space. These results shed a new light on ideal point estimation methods gaining attention in social media studies, showing that they cannot always assume to capture liberal-conservative divides in single-dimensional models.

Nawzad Hasan Ali, Sizar Abid Mohammed, Jalil Manafian

This paper is concerned with the traveling wave solutions and analytical treatment of the simplified MCH equation and the combined KdV–mKdV equations. Based on a polynomial about x and t, the rational solutions are investigated. The abundant soliton and periodic wave solutions are obtained by using a direct function. The hyperbolic-type and trigonometric-type solutions are given by utilizing the improved tan(ϕ/2)-expansion method. The dynamic properties of these derived results are shown in some three-dimensional, density and 2D plots. Traveling wave solutions are utilized to depict water waves in the mentioned equations, and that is used in physical science to model quantum field theory, dust-acoustic waves, ion acoustic waves, which is taken into account through the application of the improved tan(ϕ/2)-expansion technique. In addition, the recommended technique allowed us to produce some dynamical wave patterns of kink, kink single soliton, single soliton, compacton, periodic shape and other structures are developed, which are shown using three-dimensional, density and 2D plots to more clearly illustrate the physical layout. The method is one of the proficient and effective approaches which have swiftly developed in order to searching appropriate responses to partial differential equations with nonlinear sciences.

Jagdev Singh, Rashmi Agrawal, Kottakkaran Sooppy Nisar

This paper gives insight on the nonlinear mathematical model of fractional order, which defines the dynamic variation of carbon dioxide gas (CO2) concentration in the atmosphere X(t) and examines its solution by applying an efficient technique, namely the q-homotopy analysis generalized transform method (q-HAGTM). This study also highlights the effects of variations in human population N(t) and forest biomass F(t) on the dynamics of CO2 gas concentration in the atmosphere. This technique combines the q-homotopy analysis method (q-HAM) and the generalization of the Laplace transform (GLT) to provide an accurate approximation result. The results prove that the applied technique is suitable for high approximation of the atmospheric carbon dioxide gas concentration fractional model solution and simultaneously proves the efficiency of the applied method. The fluctuating behavior of carbon dioxide gas, forest biomass, and human population concentration is illustrated by the graphical representation of the fractional derivative with variation in time. The convergence and uniqueness of the obtained solutions are evaluated for the studied fractional model. The objective of this work is to assess the pattern of CO2 and its effects on the human population and ecosystem, such as global warming and biomass variation, which in turn affect the patterns of drought, floods, storms, and the spread of climatic and vector-borne diseases.

Koon S. Wong, Zabidin Salleh, Che M. I. Che Taib

Abstract In this paper, we introduce fuzzy generalized β-F-contractions as a generalization of fuzzy F-contractions with admissible mappings. We deduce sufficient conditions for the existence and uniqueness of fixed points for fuzzy generalized β-F-contractions in complete strong fuzzy metric spaces. Our results generalize several fixed-point results from the literature. We present an application of our main result.

Ahmet Yaşar Özban, Bahar Kaya

A new two-parameter family of fourth-order iterative methods for the numerical solution of nonlinear equations of the form f(x)=0has been introduced and their convergence analysis have been performed. The new methods in the family are optimal in the sense of Kung–Traub conjecture. Numerical tests which are made to support the theoretical results also show that our new family of optimal fourth order methods perform well and in many cases some members of the family are superior to other well-known and recent fourth order optimal methods in the literature.

Huafei Di, Zefang Song

Considered herein is the global existence and non-global existence of the initial-boundary value problem for a quasilinear viscoelastic equation with strong damping and source terms. Firstly, we introduce a family of potential wells and give the invariance of some sets, which are essential to derive the main results. Secondly, we establish the existence of global weak solutions under the low initial energy and critical initial energy by the combination of the Galerkin approximation and improved potential well method involving with \(t\). Thirdly, we obtain the finite time blow-up result for certain solutions with the non-positive initial energy and positive initial energy, and then give the upper bound for the blow-up time \(T^\ast\). Especially, the threshold result between global existence and non-global existence is given under some certain conditions. Finally, a lower bound for the life span \(T^\ast\) is derived by the means of integro-differential inequality techniques.

Retno Maharesi

The study discusses problems related to the formation of a decision tree based on a collection of evaluation data records obtained from a number of car buyers. This secondary data was obtained from the UCL machine learning website. The purpose of this research is to produce a prototype algorithm for obtaining an inductive decision tree based on Chi-square statistics. An inductive decision tree formation method based on the Chi-square contingency test was compared with a decision tree obtained using a machine learning algorithm which was done using RapidMiner5 software. The work to produce an inductive decision tree was carried out by first processing data using Microsoft excel and next processed using SPSS software, on the crosstabs descriptive menu. The results of the two methods provide some kind of similar rules, in terms of the order of priority of the variables that most influencing people's decision to accept an automotive product. The formation of the decision tree uses a random sampling of size 300 data records among 1729 respondent data records in the car evaluation database. The resulting decision tree should have a minimal structure like a binary tree. This is possible because its formation is based on the statistical inferential method, so it does not require a separate pruning process as an addition step in the C4.5 algorithm, which actually this algorithm also considers aspects of the statistical significance.

S.H.A.M. Shah, M. Suleman, Umair Khan

In this paper, the steady-state two-dimensional incompressible, magnetohydrodynamics, stagnation point flow and heat transfer of viscous fluid having mixed convection over the linearly shrinking porous sheet is studied. The governing non-linear partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) by exercising the pertinent similarity variables. Numerical results are obtained by using the bvp4c solver in MATLAB to solve the resulting ODEs. The dual solution is obtained for a certain range of shrinking and mass suction parameters. The resulting dual solution projects that local skin friction coefficient and Nusselt number escalates in the upper branch solution and decelerates in the lower branch solution with the increase in the mass suction and magnetic parameter. However, the heat transfer rate is diminishing in both the upper and lower branch solutions due to an escalation of the radiation parameter. In addition, temporal stability analysis has been performed by which the upper branch solution is physically trustworthy and stable while the lower branch solution is not physically stable (unstable).

Pankaj Topiwala, Wei Dai, Jiangfeng Pian et al.

Video quality assessment (VQA) is now a fast-growing field, maturing in the full reference (FR) case, yet challenging in the exploding no reference (NR) case. In this paper, we investigate some variants of the popular FR VMAF video quality assessment algorithm, using both support vector regression and feedforward neural networks. We also extend it to the NR case, using different features but similar learning, to develop a partially unified framework for VQA. When fully trained, FR algorithms such as VMAF perform very well on test datasets, reaching a 90%+ match in the popular correlation coefficients PCC and SRCC. However, for predicting performance in the wild, we train/test them individually for each dataset. With an 80/20 train/test split, we still achieve about 90% performance on average in both PCC and SRCC, with up to 7–9% gains over VMAF, using an improved motion feature and better regression. Moreover, we even obtain good performance (about 75%) if we ignore the reference, treating FR as NR, partly justifying our attempts at unification. In the true NR case, typically with amateur user-generated data, we avail of many more features, but still reduce complexity vs. recent algorithms VIDEVAL and RAPIQUE, while achieving performance within 3–5% of them. Moreover, we develop a method to analyze the saliency of features, and conclude that for both VIDEVAL and RAPIQUE, a small subset of their features provide the bulk of the performance. We also touch upon the current best NR methods: MDT-VSFA, and PVQ which reach above 80% performance. In short, we identify encouraging improvements in trainability in FR, while constraining training complexity against leading methods in NR, elucidating the saliency of features for feature selection.

Su Jiang, Mun-Hong Hui, Louis J. Durlofsky

Data-space inversion (DSI) is a data assimilation procedure that directly generates posterior flow predictions, for time series of interest, without calibrating model parameters. No forward flow simulation is performed in the data assimilation process. DSI instead uses the prior data generated by performing O(1000) simulations on prior geomodel realizations. Data parameterization is useful in the DSI framework as it enables representation of the correlated time-series data quantities in terms of low-dimensional latent-space variables. In this work, a recently developed parameterization based on a recurrent autoencoder (RAE) is applied with DSI for a real naturally fractured reservoir. The parameterization, involving the use of a recurrent neural network and an autoencoder, is able to capture important correlations in the time-series data. RAE training is accomplished using flow simulation results for 1,350 prior model realizations. An ensemble smoother with multiple data assimilation (ESMDA) is applied to provide posterior DSI data samples. The modeling in this work is much more complex than that considered in previous DSI studies as it includes multiple 3D discrete fracture realizations, three-phase flow, tracer injection and production, and complicated field-management logic leading to frequent well shut-in and reopening. Results for the reconstruction of new simulation data (not seen in training), using both the RAE-based parameterization and a simpler approach based on principal component analysis (PCA) with histogram transformation, are presented. The RAE-based procedure is shown to provide better accuracy for these data reconstructions. Detailed posterior DSI results are then presented for a particular “true” model (which is outside the prior ensemble), and summary results are provided for five additional “true” models that are consistent with the prior ensemble. These results again demonstrate the advantages of DSI with RAE-based parameterization for this challenging fractured reservoir case.

Zhenhai Yan, Guojun Yan, Ikudol Miyamoto

The Editors-in-Chief have retracted this article [1] because it showed evidence of peer review manipulation. In addition, the identity of the corresponding author could not be verified: Nagoya University have confirmed that Ikudol Miyamato has not been affiliated with their Graduate School of Mathematics. The authors have not responded to any correspondence regarding this retraction.

Arie Wahyu Wijayanto, Tsuyoshi Murata

Abstract Dynamic networks are networks with temporal relationship features which evolve over time by the inclusion and deletion of nodes and edges. Suppressing the epidemic spreading in such networks is quite challenging. The problem of protecting a limited number of nodes to restrain the spreading of malicious attacks or dangerous rumor in the networks is called graph protection problem. However, most of existing strategies only consider to protect at once regardless the evolving network structure and incoming attacks over time, i.e., these strategies either pre-protect important nodes before the epidemic starts or post-allocate the protection while the attacks have already spread over the network. In this paper, we introduce multiple-turns protection strategies, which divide the size of protection budget into several turns and protect nodes according to the currently observed temporal snapshot of dynamic networks. We construct a minimum vertex cover of the input network efficiently using reinforcement learning approach. To capture the state of the input network, a feature-based representation of each node is constructed using a graph embedding technique. Experimental evaluations show that our proposed methods, namely ReProtect and ReProtect-p effectively restrain epidemic propagation in synthetic and real-world network datasets. By protecting about 15% of nodes, our methods can obtain up to 84% of surviving nodes and outperform other baseline methods on two popular epidemic models: SIS and SIR.

Ramos Ruiz, José, Polo Otero, José, Arrieta Barcasnegras, Aquiles et al.

En esta investigación, se estudia el impacto que tiene la realización de innovaciones en mercadotecnia sobre la conducta de exportación, soportada en la estructura panel ofrecida por el Panel de Innovación Tecnológica (PITEC). Para ello, se hizo uso del método Propensity Score Matching combinado con el método de diferencias en diferencias, propio de los análisis de evaluación de impacto. Los resultados de la aproximación econométrica muestran un impacto negativo y significativo de la innovación en marketing sobre la realización de exportaciones en el sector agroindustrial de España. || This research studies the impact that marketing innovation entails for exporting behavior, supported by the panel data structure given by the Panel of Technological Innovation. To do so, Propensity Score Matching method has been combined with the method of difference in differences, which is usual for impact evaluation analysis. The results from econometric estimations show the existence of a significative, negative impact of marketing innovation on exporting performance for Spanish agro-industry sector.

Erisnaldo Francisco Reis, Marli Teresinha Quartieri, Andreia A. Guimarães Strohschoen

Neste artigo faz-se o relato de dados decorrentes de uma pesquisa desenvolvida por meio de prática pedagógica envolvendo a utilização da Modelagem Matemática e o tema leishmaniose, como proposta de ensino e de aprendizagem. O objetivo é identificar e explorar relações entre Biologia e Matemática, existentes no tema leishmaniose a partir do desenvolvimento de atividades pedagógicas por meio da Modelagem Matemática. A pesquisa foi qualitativa e um estudo de caso que envolveu alunos do 2º ano do Ensino Médio. Os instrumentos para coleta de dados utilizados foram o diário de campo do professor, gravações de aula em vídeo, áudio e questionários aplicados aos alunos. Os dados foram analisados seguindo a abordagem textual discursiva de Moraes e Galiazzi (2006). As atividades foram realizadas em grupo, envolvendo a questão da ocorrência da leishmaniose no município de Rubim-MG, que foi estudada por meio da metodologia Modelagem Matemática relacionando Biologia e Matemática. Os resultados apontam que a utilização da Modelagem Matemática nos processos de ensino e de aprendizagem acerca da Leishmaniose no Ensino Médio possibilita o estabelecimento de uma relação relevante entre Biologia e Matemática, que tem implicações importantes, tais como: relacionar o tema com o cotidiano do aluno; fazer utilização de conhecimentos matemáticos, dentre outras.

Andrzej Katunin, Kamil Fedio

S. Iwami, Benjamin P. Holder, C. Beauchemin et al.

BackgroundDeveloping a quantitative understanding of viral kinetics is useful for determining the pathogenesis and transmissibility of the virus, predicting the course of disease, and evaluating the effects of antiviral therapy. The availability of data in clinical, animal, and cell culture studies, however, has been quite limited. Many studies of virus infection kinetics have been based solely on measures of total or infectious virus count. Here, we introduce a new mathematical model which tracks both infectious and total viral load, as well as the fraction of infected and uninfected cells within a cell culture, and apply it to analyze time-course data of an SHIV infection in vitro.ResultsWe infected HSC-F cells with SHIV-KS661 and measured the concentration of Nef-negative (target) and Nef-positive (infected) HSC-F cells, the total viral load, and the infectious viral load daily for nine days. The experiments were repeated at four different MOIs, and the model was fitted to the full dataset simultaneously. Our analysis allowed us to extract an infected cell half-life of 14.1 h, a half-life of SHIV-KS661 infectiousness of 17.9 h, a virus burst size of 22.1 thousand RNA copies or 0.19 TCID50, and a basic reproductive number of 62.8. Furthermore, we calculated that SHIV-KS661 virus-infected cells produce at least 1 infectious virion for every 350 virions produced.ConclusionsOur method, combining in vitro experiments and a mathematical model, provides detailed quantitative insights into the kinetics of the SHIV infection which could be used to significantly improve the understanding of SHIV and HIV-1 pathogenesis. The method could also be applied to other viral infections and used to improve the in vitro determination of the effect and efficacy of antiviral compounds.

Z. Liang, Xiaochu Liu, B. Ye et al.

Because the application of surface fitting algorithms exerts a considerable fuzzy influence on the mathematical features of kinetic energy distribution, their relation mechanism in different external conditional parameters must be quantitatively analyzed. Through determining the kinetic energy value of each selected representative position coordinate point by calculating kinetic energy parameters, several typical algorithms of complicated surface fitting are applied for constructing microkinetic energy distribution surface models in the objective turbulence runner with those obtained kinetic energy values. On the base of calculating the newly proposed mathematical features, we construct fuzzy evaluation data sequence and present a new three-dimensional fuzzy quantitative evaluation method; then the value change tendencies of kinetic energy distribution surface features can be clearly quantified, and the fuzzy performance mechanism discipline between the performance results of surface fitting algorithms, the spatial features of turbulence kinetic energy distribution surface, and their respective environmental parameter conditions can be quantitatively analyzed in detail, which results in the acquirement of final conclusions concerning the inherent turbulence kinetic energy distribution performance mechanism and its mathematical relation. A further turbulence energy quantitative study can be ensured.

P. Tran, Pavan K. Bendapudi, H. J. Lin et al.

S. Olyaee, S. Hamedi