Splitting of operations for alternative and Malcev structures

In this paper, we define pre-Malcev algebras and alternative quadri-algebras and prove that they generalize pre-Lie algebras and quadri-algebras, respectively, to the alternative setting. We use the results and techniques from [4 Bai, C., Bellier, O., Guo, L., Ni, X. (2013). Splitting of operations, Manin products, and Rota-Baxter operators. Int. Math. Res. Not. 2013(3):485–524. [Google Scholar], 14 Gubarev, V. Y., Kolesnikov, P. S. (2013). Embedding of dendriform algebras into Rota-Baxter algebras. Cent. Eur. J. Math. 11(2):226–245.[Crossref], [Web of Science ®] , [Google Scholar]] to discuss and give explicit computations of different constructions in terms of bimodules, splitting of operations, and Rota–Baxter operators.     

Bayesian analysis of quantile regression for censored dynamic panel data

This paper develops a Bayesian approach to analyzing quantile regression models for censored dynamic panel data. We employ a likelihood-based approach using the asymmetric Laplace error distribution and introduce lagged observed responses into the conditional quantile function. We also deal with the initial conditions problem in dynamic panel data models by introducing correlated random effects into the model. For posterior inference, we propose a Gibbs sampling algorithm based on a location-scale mixture representation of the asymmetric Laplace distribution. It is shown that the mixture representation provides fully tractable conditional posterior densities and considerably simplifies existing estimation procedures for quantile regression models. In addition, we explain how the proposed Gibbs sampler can be utilized for the calculation of marginal likelihood and the modal estimation. Our approach is illustrated with real data on medical expenditures.     

Static and dynamic analysis of cracked or weakened structures

Stiffness modifications in engineering structures, for example due to damage and cracking, will inevitably also lead to changes in deformations, internal forces, natural frequencies and mode shapes of the structures. In this paper, an efficient and simple method for sensitivity analysis of cracked or weakened structures under time-harmonic loading is presented. The method is based on a comparison between the strain energy and the kinetic energy of an uncracked structure and that of a cracked structure in conjunction with the application of exact or approximate Green's functions as described in [3] for the static case. The present analysis enables the prediction of any changes in the displacements and stresses and has a lower computational effort as compared to available classical methods, because only the damaged region has to be re-considered in the method. Green's functions are taken as a basis of the approach, which have the ability to weight the influence of the stiffness modifications in a region of a structure and show how sensitive other regions respond to the stiffness modifications. Based on linear elastic fracture mechanics, cracked or damaged regions are approximated by spring models in the analytical solution of some simple beam problems, while cracked finite elements are used for complicated cases where analytical solutions cannot be obtained. Sensitivity analysis with Green's functions (SAGF) approach is applied to static and dynamic analysis of cracked and weakened structures, which consist of homogeneous materials or fiber reinforced composites like reinforced concretes. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Efficiency analysis in two-stage structures using fuzzy data envelopment analysis

Two-stage data envelopment analysis (TsDEA) models evaluate the performance of a set of production systems in which each system includes two operational stages. Taking into account the internal structures is commonly found in many situations such as seller-buyer supply chain, health care provision and environmental management. Contrary to conventional DEA models as a black-box structure, TsDEA provides further insight into sources of inefficiencies and a more informative basis for performance evaluation. In addition, ignoring the qualitative and imprecise data leads to distorted evaluations, both for the subunits and the system efficiency. We present the fuzzy input and output-oriented TsDEA models to calculate the global and pure technical efficiencies of a system and sub-processes when some data are fuzzy. To this end, we propose a possibilistic programming problem and then convert it into a deterministic interval programming problem using the α-level based method. The proposed method preserves the link between two stages in the sense that the total efficiency of the system is equal to the product of the efficiencies derived from two stages. In addition to the study of technical efficiency, this research includes two further contributions to the ancillary literature; firstly, we minutely discuss the efficiency decompositions to indicate the sources of inefficiency and secondly, we present a method for ranking the efficient units in a fuzzy environment. An empirical illustration is also utilised to show the applicability of the proposed technique.     

Some operations research methods for analyzing protein sequences and structures

The operations research is probably one of the most successful field of applied mathematics used in economics, physics, chemistry, almost everywhere where one has to analyze huge amounts of data. Lately, these techniques of operations research were introduced in biology, especially in the protein analysis area to support biologists. The fast growth of protein data makes operations research an important issue in bioinformatics, a science which lays on the border between computer science and biology. This paper gives a short overview of the operations research techniques currently used to support structural and functional analysis of proteins.     

Some operations research methods for analyzing protein sequences and structures

Operations Research is probably one of the most successful fields of applied mathematics used in Economics, Physics, Chemistry, almost everywhere one has to analyze huge amounts of data. Lately, these techniques were introduced in biology, especially in the protein analysis area to support biologists. The fast growth of protein data makes operations research an important issue in bioinformatics, a science which lays on the border between computer science and biology. This paper gives a short overview of the operations research techniques currently used to support structural and functional analysis of proteins. Received: February 2006, Revised: May 2006     

Examination of the dynamic software-supported learning environment in data analysis

The Fatih Project in Turkey has improved software in mathematics teaching such as data analysis software. As a result, the need to inquire into the efficiency of computer-supported learning environments has emerged. This study aims to examine the effect of dynamic data analysis software-supported learning environments on secondary school students’ achievement and attitude. The research method employs a quasi-experimental design with a pre-test, post-test control group. Basic topics related to data analysis were introduced through dynamic statistics software in the experimental group while the students were taught with the help of smart boards, course books and exercises in the control group. Data were collected with an achievement test, attitude scale and semi-structured interviews. Also, interviews were conducted with four students from the experimental group in order to get more detailed information from students. The data gained in the study were analysed both quantitatively and qualitatively. The findings revealed that statistics teaching through statistics software is more efficient than the one with the traditional method on achievement and attitudes. In accordance with this result, it is suggested that computer-supported statistics software should be used in statistics teaching.     

On dynamic finite element analysis of viscoplastic thin-walled structures with non-local damage

In this article we propose a non-local damage model for dynamic finite element computation of viscoplastic thin-shell structures. To take void nucleation and growth into account, the free energy function is enhanced phenomenologically in terms of a non-local damage variable and its gradient on the mid-surface of shell structures. The dynamic thin-shell elastic theory including large rotations proposed by Simo and Tarnow (1994) is used to capture finite deformation. Local constitutive laws considering viscoplastic behaviour, isotropic hardening and isotropic ductile damage leading to softening in Velde et al. (2009) are employed. The performance of the proposed approach is demonstrated through the preliminary numerical simulations of shock-wave loaded structures, which are validated by comparision with the experimental results. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An equilibrium-correction model for dynamic network data

We propose a two-stage MRQAP to analyze dynamic network data within the framework of an equilibrium-correction (EC) model. Extensive simulation results indicate practical relevance of our method and its improvement over standard OLS. In addition, empirical illustration shows that the EC-model yields interpretable parameters, in contrast to an unrestricted dynamic model.     

Adaptive finite element analysis of structures under transient dynamic loading using modal superposition

In this paper, the error estimation and adaptive strategy developed for the linear elastodynamic problem under transient dynamic loading based on the Z–Z criterion is utilized for 2D and plate bending problems. An automatic mesh generator based on “growth meshing” is utilized effectively for adaptive mesh refinement. Optimal meshes are obtained iteratively corresponding to the prescribed domain discretization error limit and for a chosen number of basis modes satisfying modal truncation errors. Numerous examples show the effectiveness of the integrated approach in achieving the target accuracy in finite element transient dynamic analysis.     

Union and split operations on dynamic trapezoidal maps

We propose algorithms to perform two new operations on an arrangement of line segments in the plane, represented by a trapezoidal map: the split of the map along a given vertical line D, and the union of two trapezoidal maps computed in two vertical slabs of the plane that are adjacent through a vertical line D. The data structure we use is a modified Influence Graph, still allowing dynamic insertions and deletions of line segments in the map. The algorithms for both operations run in O(s_D logn+log²n) time, where n is the number of line segments in the map, and s_D is the number of line segments intersected by D.     

Non-linear dynamic contact of thin-walled structures

In many areas of mechanical engineering contact problems of thin–walled structures play a crucial role. Car crash tests and incremental sheet metal forming can be named as examples. But also in civil engineering, for instance when determining the moment–rotation characteristics of a bolted beam–column joint, contact occurs. Effective simulation of these and other contact problems, especially in three–dimensional non–linear implicit structural mechanic is still a challenging task. Modelling of those problems needs a robust method, which takes the thin–walled character and dynamic effects into account. We use a segment–to–segment approach for discretization of the contact and introduce Lagrange Multipliers, which physically represent the contact pressure. The geometric impenetrability condition is formulated in a weak, integral sense. Choosing dual shape functions for the interpolation of the Lagrange Multipliers, we obtain decoupled nodal constraint conditions. Combining this with an active set strategy, an elimination of the Lagrange multipliers is easily possible, so that the size of the resulting system of equations remains constant. Discretization in time is done with the implicit Generalized-α Method and the Generalized Energy–Momentum Method. Using the “Velocity–Update” Method, the total energy is conserved for frictionless contact. Various examples show the performance of the presented strategies. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A perceptual mapping procedure for analysis of proximity data to determine common and unique product-market structures

Traditional techniques of perceptual mapping hypothesize that products are differentiated in a common perceptual space of attributes. This paper suggests that each product is differentiated not only in a common perceptual space, but also a unique perceptual space consisting of as many dimensions as the number of products. It provides a model and estimation procedure based on alternating least squares for estimating the model parameters.     

Succinct data structures for flexible text retrieval systems

We propose succinct data structures for text retrieval systems supporting document listing queries and ranking queries based on the tf*idf (term frequency times inverse document frequency) scores of documents. Traditional data structures for these problems support queries only for some predetermined keywords. Recently Muthukrishnan proposed a data structure for document listing queries for arbitrary patterns at the cost of data structure size. For computing the tf*idf scores there has been no efficient data structures for arbitrary patterns.Our new data structures support these queries using small space. The space is only 2/ times the size of compressed documents plus 10n bits for a document collection of length n, for any 0<1. This is much smaller than the previous O(nlogn) bit data structures. Query time is O(m+qlogn) for listing and computing tf*idf scores for all q documents containing a given pattern of length m. Our data structures are flexible in a sense that they support queries for arbitrary patterns.     

On data reduction for dynamic vector bin packing

We study a dynamic vector bin packing (DVBP) problem. We show hardness for shrinking arbitrary DVBP instances to size polynomial in the number of request types or in the maximal number of requests overlapping in time. We also present a simple polynomial-time data reduction algorithm that allows to recover $(1+\epsilon )$-approximate solutions for arbitrary $\epsilon >0$. It shrinks instances from Microsoft Azure and Huawei Cloud by an order of magnitude for $\epsilon =0.02$.     

Heuristics for selecting robust database structures with dynamic query patterns

The success of a company increasingly depends on timely information (internal or external) being available to the right person at the right time for crucial managerial decision-making. Achieving such a “right time/right place” duet depends directly on database performance. A database system has been a core component that supports modern business system such as enterprise resource planning (ERP) system that integrates and supports all enterprise processes including product designing and engineering, manufacturing, and other business functions to achieve highest efficiency and effectiveness of operations. We develop and demonstrate through a proof-of-concept case study, a new “query-driven” heuristics for database design that seeks to identify database structures that perform robustly in dynamic settings with dynamic queries. Our focus is the design of efficient structures to process read-only queries in complex environments. Our heuristics begins with detailed analysis of relationships between diverse queries and the performance of different database structures. These relationships are then used in a series of steps that identify “robust” database structures that maintain high performance levels for a wide range of query patterns. We conjecture that our heuristics can facilitate efficient operations and effective decision-making of companies in today’s dynamic environment.