This paper describes a new algorithm for estimating the position and orientation of objects. The problem is formulated as an optimization problem using dual number quaternious. The advantage of using this representation is that the method solves for the location estimate by minimizing a single cost function associated with the sum of the orientation and position errors and thus is expected to have a better performance on the estimation, both in accuracy and in speed. Several forms of sensory information can be used by the algorithm. That is, the measured data can be a combination of measured points on an object's surfaces and measured unit direction vectors located on the object. Simulations have been carried out on a Compaq 386/20 computer and the SiIIIUkItiOU reSUltS are analyzed.

Background Molecular descriptors and fingerprints have been routinely used in QSAR/SAR analysis, virtual drug screening, compound search/ranking, drug ADME/T prediction and other drug discovery processes. Since the calculation of such quantitative representations of molecules may require substantial computational skills and efforts, several tools have been previously developed to make an attempt to ease the process. However, there are still several hurdles for users to overcome to fully harness the power of these tools. First, most of the tools are distributed as standalone software or packages that require necessary configuration or programming efforts of users. Second, many of the tools can only calculate a subset of molecular descriptors, and the results from multiple tools need to be manually merged to generate a comprehensive set of descriptors. Third, some packages only provide application programming interfaces and are implemented in different computer languages, which pose additional challenges to the integration of these tools.Results A freely available web-based platform, named ChemDes, is developed in this study. It integrates multiple state-of-the-art packages (i.e., Pybel, CDK, RDKit, BlueDesc, Chemopy, PaDEL and jCompoundMapper) for computing molecular descriptors and fingerprints. ChemDes not only provides friendly web interfaces to relieve users from burdensome programming work, but also offers three useful and convenient auxiliary tools for format converting, MOPAC optimization and fingerprint similarity calculation. Currently, ChemDes has the capability of computing 3679 molecular descriptors and 59 types of molecular fingerprints.ConclusionChemDes provides users an integrated and friendly tool to calculate various molecular descriptors and fingerprints. It is freely available at http://www.scbdd.com/chemdes. The source code of the project is also available as a supplementary file.Graphical abstract:An overview of ChemDes. A platform for computing various molecular descriptors and fingerprints

A shear-improved Smagorinsky model is introduced based on recent results concerning shear effects in wall-bounded turbulence by Toschi et al. (2000). The Smagorinsky eddyviscosity is modified as ν T = (C s ∆) 2 (|S|−| S |): the magnitude of the mean shear | S | is subtracted to the magnitude of the instantaneous resolved strain-rate tensor |S|; here C S is the standard Smagorinsky constant and ∆ denotes the grid spacing. This subgrid-scale model is tested in large-eddy simulations of plane-channel flows at Reynolds numbers Re τ = 395 and Re τ = 590. First comparisons with the dynamic Smagorinsky model and direct numerical simulations, including mean velocity, turbulent kinetic energy and Reynolds stress profiles, are shown to be extremely satisfactory. The proposed model, in addition of being physically sound, has a low computational cost and possesses a high potentiality of generalization to more complex non-homogeneous turbulent flows.

Rotation strongly affects the stability of turbulent flows in the presence of large eddies. In this paper, we examine the applicability of the classic Bradshaw-Richardson criterion to flows more general than a simple combination of rotation and pure shear. Two approaches are used. Firstly the linearized theory is applied to a class of rotating two-dimensional flows having arbitrary rates of strain and vorticity and streamfunctions that are quadratic. This class includes simple shear and elliptic flows as special cases. Secondly, we describe a large-eddy simulation of initially quasi-homogeneous three-dimensional turbulence superimposed on a periodic array of two-dimensional Taylor-Green vortices in a rotating frame.The results of both approaches indicate that, for a large structure of vorticity W and subject to rotation Ω, maximum destabilization is obtained for zero tilting vorticity (½W + 2Ω = 0) whereas stability occurs for zero absolute vorticity (2Ω = 0) These results are consistent with the Bradshaw-Richardson criterion; however the numerical results show that in other cases the Bradshaw-Richardson number $B=2\Omega(W+2\Omega)/W^2$ is not always a good indicator of the flow stability.

The normalized turbulent dissipation rate $C_\epsilon$ is studied in decaying and forced turbulence by direct numerical simulations, large-eddy simulations, and closure calculations. A large difference in the values of $C_\epsilon$ is observed for the two types of turbulence. This difference is found at moderate Reynolds number, and it is shown that it persists at high Reynolds number, where the value of $C_\epsilon$ becomes independent of the Reynolds number, but is still not unique. This difference can be explained by the influence of the nonlinear cascade time that introduces a spectral disequilibrium for statistically nonstationary turbulence. Phenomenological analysis yields simple analytical models that satisfactorily reproduce the numerical results. These simple spectral models also reproduce and explain the increase of $C_\epsilon$ at low Reynolds number that is observed in the simulations

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In multi-objective convex optimization it is necessary to compute an infinite set of nondominated points. We propose a method for approximating the nondominated set of a multi-objective nonlinear programming problem, where the objective functions and the feasible set are convex. This method is an extension of Benson's outer approximation algorithm for multi-objective linear programming problems. We prove that this method provides a set of weakly ε-nondominated points. For the case that the objectives and constraints are differentiable, we describe an efficient way to carry out the main step of the algorithm, the construction of a hyperplane separating an exterior point from the feasible set in objective space. We provide examples that show that this cannot always be done in the same way in the case of non-differentiable objectives or constraints.

The design of an intensity modulated radiotherapy treatment includes the selection of beam angles (geometry problem), the computation of an intensity map for each selected beam angle (intensity problem), and finding a sequence of configurations of a multileaf collimator to deliver the treatment (realization problem). Until the end of the last century research on radiotherapy treatment design has been published almost exclusively in the medical physics literature. However, since then, the attention of researchers in mathematical optimization has been drawn to the area and important progress has been made. In this paper we survey the use of optimization models, methods, and theories in intensity modulated radiotherapy treatment design. This is an updated version of the paper that appeared in 4OR, 6(3), 199-262 (2008).