New Class Of Methods Research Articles

Modeling methods and characteristic analysis of new Hamiltonian and non-Hamiltonian conservative chaotic systems

Recently, more and more researches on conservative system have become the focus of scholars’ research. In this paper, we propose a new class of methods for constructing Hamiltonian and non-Hamiltonian conservative chaotic systems, which are suitable for constructing three-dimensional, four-dimensional and higher-dimensional conservative chaotic systems. The non-Hamiltonian conservative chaotic systems can show manifest properties such as hyperchaos and multistability with symmetry. To confirm the correctness of the modeling methods, we construct a five-dimensional system using the above methods and analyze the dynamics by means of phase diagram, Lyapunov exponent spectrum, bifurcation diagram and complexity analysis. Finally, the hardware implementation of the system is carried out by the DSP platform. The results prove the effectiveness of the conservative chaotic system modeling approaches.

Numerical investigation of fractional-order Kersten\u2013Krasil\u2019shchik coupled KdV\u2013mKdV system with Atangana\u2013Baleanu derivative

In this article, we present a fractional Kersten–Krasil’shchik coupled KdV-mKdV nonlinear model associated with newly introduced Atangana–Baleanu derivative of fractional order which uses Mittag-Leffler function as a nonsingular and nonlocal kernel. We investigate the nonlinear behavior of multi-component plasma. For this effective approach, named homotopy perturbation, transformation approach is suggested. This scheme of nonlinear model generally occurs as a characterization of waves in traffic flow, multi-component plasmas, electrodynamics, electromagnetism, shallow water waves, elastic media, etc. The main objective of this study is to provide a new class of methods, which requires not using small variables for finding estimated solution of fractional coupled frameworks and unrealistic factors and eliminate linearization. Analytical simulation represents that the suggested method is effective, accurate, and straightforward to use to a wide range of physical frameworks. This analysis indicates that analytical simulation obtained by the homotopy perturbation transform method is very efficient and precise for evaluation of the nonlinear behavior of the scheme. This result also suggests that the homotopy perturbation transform method is much simpler and easier, more convenient and effective than other available mathematical techniques.

Concept of the course "Numerical methods in object methodology"

The tasks for which computers were created - routine calculations of an industrial, scientific and military nature - required the creation of a whole class of new methods focused not on manual but on machine calculations. The first programming languages did not have convenient means for reflecting such objects often used in computational mathematics as matrices, vectors, polynomials, etc. Further development of programming languages followed the path of embedding mathematical objects into languages as data types, which led to their complication. So, for example, an attempt to make a universal language Ada, in which there are even such data types as dictionaries and queues, led to the fact that the number of keywords in it exceeded 350, making it almost unusable for learning and use. The compromise solution between these two extremes can be the following: let the programmer himself create the data types that he needs in his professional work. Programming languages that implement this approach are called object-oriented. This, on the one hand, makes it possible to make the language quite easy by reducing the number of keywords, and on the other, expandable, adapting to specific tasks by introducing keywords for creating and using new data types.

A Similarity-based Framework for Classification Task

Similarity-based method gives rise to a new class of methods for multi-label learning and also achieves promising performance. In this paper, we generalize this method, resulting in a new framework for classification task. Specifically, we unite similarity-based learning and generalized linear models to achieve the best of both worlds. This allows us to capture interdependencies between classes and prevent from impairing performance of noisy classes. Each learned parameter of the model can reveal the contribution of one class to another, providing interpretability to some extent. Experiment results show the effectiveness of the proposed approach on multi-class and multi-label datasets

Sensitivity‐Based Soil Moisture Assimilation for Improved Streamflow Forecast Using a Novel Forward Sensitivity Method (FSM) Approach

AbstractThe need for and the use of different data assimilation techniques to improve the quality of streamflow forecast is now well established. In this paper, the goal is to demonstrate the power of a new class of methods known as the forward sensitivity method (FSM) which is based on the temporal evolution of model sensitivities with respect to the control variables consisting of initial conditions and parameters. FSM operates in two phases: the first phase provides a simple algorithm for placing observations at or near where the square of forward sensitivities attains their maximum values. Using only this selected subset of observations in a weighted least squares method, the second phase then provides an estimate of the unknown elements of the control variables. In this paper, FSM based assimilation is applied to a simple class of two parameter model in a medium‐sized agriculture dominant watershed lying in the Krishna River Basin, India. Four assimilation scenarios were tested to determine the effect of assimilating only sensitive observations as well as the impact of temporally evolving initial condition sensitivity. Sensitivity results showed that observations during the monsoon time alone are enough for assimilation purposes, which has helped in reducing the computational time greatly. Assimilation and forecast results also indicated that the scenarios which assimilated only sensitive observations are better in estimating daily streamflow. From the obtained results, it is concluded that FSM based assimilation has significant potential to improve the streamflow simulations, especially in places where data availability remains a major challenge.

Rosenbrock Type Methods for Solving Non-Linear Second-Order in Time Problems

In this work, we develop a new class of methods which have been created in order to numerically solve non-linear second-order in time problems in an efficient way. These methods are of the Rosenbrock type, and they can be seen as a generalization of these methods when they are applied to second-order in time problems which have been previously transformed into first-order in time problems. As they also follow the ideas of Runge–Kutta–Nyström methods when solving second-order in time problems, we have called them Rosenbrock–Nyström methods. When solving non-linear problems, Rosenbrock–Nyström methods present less computational cost than implicit Runge–Kutta–Nyström ones, as the non-linear systems which arise at every intermediate stage when Runge–Kutta–Nyström methods are used are replaced with sequences of linear ones.

The Inter-modal Pre-Construction Method (IMPreC): Exploring Hyper-Generalization

In this article, we present the blueprint for a new class of methods—inter-modal pre-constructive methods—uniting the value of moving across modalities of understanding (poetry, drawing, music, etc.) in a scheme of microgenetic construction of affective fields. For this purpose, the historical roots of this class of methods were reviewed, and two empirical demonstrations are provided. In the demonstration, the possibility of exploring hyper-generalized feelings was opened up by repeatedly producing the feelings while transforming the modality step by step. In addition, it was suggested that the modality of music could be used as the next possibility. The inter-modal pre-constructive methods are ways of triggering and increasing the difficulty of expression of the original feelings. The difficulty of switching the modality is a new synthesis while keeping attention to the feeling once felt. Alternatively, we felt the feeling of “understanding” about others’ poetry. This implied that poetry, like painting, allowed for a new synthesis of the reader’s experiences. The multiplicity of the synthesis through a particular medium can be called “pluri-synthesis.” While such syntheses are unique to each person, we found that this diversity of meaning-making can be a catalyst for pleromatization through the communication of others’ feelings.

A New Class of A Stable Summation by Parts Time Integration Schemes with Strong Initial Conditions

Since integration by parts is an important tool when deriving energy or entropy estimates for differential equations, one may conjecture that some form of summation by parts (SBP) property is involved in provably stable numerical methods. This article contributes to this topic by proposing a novel class of A stable SBP time integration methods which can also be reformulated as implicit Runge-Kutta methods. In contrast to existing SBP time integration methods using simultaneous approximation terms to impose the initial condition weakly, the new schemes use a projection method to impose the initial condition strongly without destroying the SBP property. The new class of methods includes the classical Lobatto IIIA collocation method, not previously formulated as an SBP scheme. Additionally, a related SBP scheme including the classical Lobatto IIIB collocation method is developed.

A class of computationally efficient numerical algorithms for locating multiple zeros

In recent times, many iterative methods for computing multiple zeros of nonlinear functions have been appeared in literature. Different from these existing methods, here we propose a new class of methods with eighth order convergence for multiple zeros. With four evaluations per iteration, the methods satisfy the criterion of attaining optimal convergence of eighth order. Applicability is demonstrated on different examples that illustrates the computational efficiency of novel methods. Comparison of numerical results shows that the proposed techniques possess good convergence compared to existing optimal order techniques. Besides, the accuracy of existing techniques is also challenged which is the main advantage.

Transformed Subspace Clustering

Subspace clustering assumes that the data is separable into separate subspaces. Such a simple assumption, does not always hold. We assume that, even if the raw data is not separable into subspaces, one can learn a representation (transform coefficients) such that the learnt representation is separable into subspaces. To achieve the intended goal, we embed subspace clustering techniques (locally linear manifold clustering, sparse subspace clustering and low rank representation) into transform learning. The entire formulation is jointly learnt; giving rise to a new class of methods called transformed subspace clustering (TSC). In order to account for non-linearity, kernelized extensions of TSC are also proposed. To test the performance of the proposed techniques, benchmarking is performed on image clustering and document clustering datasets. Comparison with state-of-the-art clustering techniques shows that our formulation improves upon them.

Scalable machine learning-assisted model exploration and inference using Sciope.

SummaryDiscrete stochastic models of gene regulatory networks are fundamental tools for in silico study of stochastic gene regulatory networks. Likelihood-free inference and model exploration are critical applications to study a system using such models. However, the massive computational cost of complex, high-dimensional and stochastic modelling currently limits systematic investigation to relatively simple systems. Recently, machine-learning-assisted methods have shown great promise to handle larger, more complex models. To support both ease-of-use of this new class of methods, as well as their further development, we have developed the scalable inference, optimization and parameter exploration (Sciope) toolbox. Sciope is designed to support new algorithms for machine-learning-assisted model exploration and likelihood-free inference. Moreover, it is built ground up to easily leverage distributed and heterogeneous computational resources for convenient parallelism across platforms from workstations to clouds.Availability and implementationThe Sciope Python3 toolbox is freely available on https://github.com/Sciope/Sciope, and has been tested on Linux, Windows and macOS platforms.Supplementary information Supplementary information is available at Bioinformatics online.

Improving Faceted Search Results for Web-based Information Exploration

The World Wide Web (WWW), a fast-growing store, contains a significant portion of human knowledge. However, the sheer scale of the Web, along with the fact that it is decentralized, highly redundant, and largely inaccurate, causes the use of the knowledge is quite cumbersome. The present search engines (SEs) use the query, and the response lookup process is incapable of producing a precise result. Thus, researchers work beyond this paradigm to explore a new class of methods to seek information, which known as an exploratory search (ES). This ES is open-ended, and its faceted search (FS) improves the overall search process. The search engine presented in this study is running in the cloud computing platform environment. Its development is based on the idea of improving visual ES while exploring information on the Web. This notion reflects the process of seeking and combing the vast information by using the coordinated visualization method, apart from minimizing the effort spent in seeking information per query. Finally, we evaluate the proposed prototype against the Internet Movie Database (IMDb) search engine, an online database of information related to films, television programs, home videos, video games, and streaming content online including cast, production crew, and personal biographies, plot summaries, trivia, fan, and critical reviews, and ratings. The results show that the proposed search engine gives more relevant search results as compared with the others.

Compositions of pseudo-symmetric integrators with complex coefficients for the numerical integration of differential equations

In this paper, we are concerned with the construction and analysis of a new class of methods obtained as double jump compositions with complex coefficients and projection on the real axis. It is shown in particular that the new integrators are symmetric and symplectic up to high orders if one uses a symmetric and symplectic basic method. In terms of efficiency, the aforementioned technique requires fewer stages than standard compositions of the same orders and is thus expected to lead to faster methods.

Demystifying a class of multiply robust estimators

Summary For estimating the population mean of a response variable subject to ignorable missingness, a new class of methods, called multiply robust procedures, has been proposed. The advantage of multiply robust procedures over the traditional doubly robust methods is that they permit the use of multiple candidate models for both the propensity score and the outcome regression, and they are consistent if any one of the multiple models is correctly specified, a property termed multiple robustness. This paper shows that, somewhat surprisingly, multiply robust estimators are special cases of doubly robust estimators, where the final propensity score and outcome regression models are certain combinations of the candidate models. To further improve model specifications in the doubly robust estimators, we adapt a model mixing procedure as an alternative method for combining multiple candidate models. We show that multiple robustness and asymptotic normality can also be achieved by our mixing-based doubly robust estimator. Moreover, our estimator and its theoretical properties are not confined to parametric models. Numerical examples demonstrate that the proposed estimator is comparable to and can even outperform existing multiply robust estimators.

Generalized Second Derivative Linear Multistep Methods Based on the Methods of Enright

The Adams-type second derivative multistep methods of W. H. Enright is generalized to a class of boundary value methods for the numerical solution of initial value problems in ordinary differential equations. The root distribution of the stability polynomials of the new class of methods are given for the purpose of their correct implementation as boundary value methods. Computational results on some stiff problems are compared with those from some existing methods, while ODE15s of MATLAB is used as a reference numerical solution.

Deeply transformed subspace clustering

Subspace clustering assumes that the data is separable into separate subspaces; this assumption may not always hold. For such cases, we assume that, even if the raw data is not separable into subspaces, one can learn a deep representation such that the learnt representation is separable into subspaces. To achieve the intended goal, we propose to embed subspace clustering techniques (locally linear manifold clustering, sparse subspace clustering and low rank representation) into deep transform learning. The entire formulation is jointly learnt; giving rise to a new class of methods called deeply transformed subspace clustering (DTSC). To test the performance of the proposed techniques, benchmarking is performed on image clustering problems. Comparison with state-of-the-art clustering techniques shows that our formulation improves upon them.

Application of spline to approximate the solution of singularly perturbed boundary-value problems

We develop a class of new methods based on modification of polynomial spline function for the numerical solution of singularly perturbed boundary-value problems. The modified spline contains the exponential terms and named by tension spline, which is infinity smooth. Tension spline contain parameter, by choosing arbitrary values of such parameters the various classes of spline can be obtained. The proposed methods are accurate for solution of linear and non-linear singularly perturbed boundary-value problems. Boundary formulas are developed to associate with spline methods. These methods are converging. The analysis of convergence is shown to yield up to O(h^8 ) approximation to the solution of singularly perturbed boundary-value problems. Comparison are carried out, numerical examples are given to showing the efficiency of our methods

Efficient variants of the CMRH method for solving a sequence of multi-shifted non-Hermitian linear systems simultaneously

Multi-shifted linear systems with non-Hermitian coefficient matrices arise in numerical solutions of time-dependent partial/fractional differential equations (PDEs/FDEs), in control theory, PageRank problems, and other research fields. We derive efficient variants of the restarted Changing Minimal Residual method based on the cost-effective Hessenberg procedure (CMRH) for this problem class. Then, we introduce a flexible variant of the algorithm that allows to use variable preconditioning at each iteration to further accelerate the convergence of shifted CMRH. We analyse the performance of the new class of methods in the numerical solution of PDEs and FDEs, also against other multi-shifted Krylov subspace methods.

Optical Methods of Diagnostics of the Isotopic Composition of Natural and Technological Media: A Review

The studies of the isotope ratios of earth-abundant stable elements by the classical and laser optical methods are reviewed. These methods have been actively developed in recent years. Supplementing the well-known mass-spectrometric and chromatographic techniques, they are in some respects simpler, more efficient, and not inferior in accuracy. Actually, the case in point is a new class of methods of spectral analysis for gases of complex composition, with enhanced requirements for the selectivity, accuracy, and dynamic range. The technique and results of studying the isotope ratios are discussed. Examples of real applications of these methods are presented, which demonstrate their efficiency in the fields of environmental protection, geophysics, physics of plasma, power engineering, commercial production monitoring, and medical diagnostics.

An Instrumental Variable Approach to Dynamic Models

We present a new class of methods for identification and inference in dynamic models with serially correlated unobservables, which typically imply that state variables are econometrically endogenous. In the context of Industrial Organization, these state variables often reflect econometrically endogenous market structure. We propose the use of Generalized Instrument Variables methods to identify those dynamic policy functions that are consistent with instrumental variable (IV) restrictions. Extending popular “two-step†methods, these policy functions then identify a set of structural parameters that are consistent with the dynamic model, the IV restrictions and the data. We provide computed illustrations to both single-agent and oligopoly examples. We also present a simple empirical analysis that, among other things, supports the counterfactual study of an environmental policy entailing an increase in sunk costs.