Interval Prediction Based on Experts’ Statements

In the work [1] we proposed an approach of forming a consensus of experts’ statements in pattern recognition. In this paper, we present a method of aggregating sets of individual statements into a collective one for the case of forecasting of quantitative variable

Multidimensional Heterogeneous Variable Prediction Based on Experts’ Statements

* The work was supported by the RFBR under Grant N07-01-00331a.In the works [1, 2] we proposed an approach of forming a consensus of experts’ statements for the case of forecasting of qualitative and quantitative variable. In this paper, we present a method of aggregating sets of individual statements into a collective one for the general case of forecasting of multidimensional heterogeneous variable

Constructing of a Consensus of Several Experts Statements

∗ The work was supported by the RFBR under Grant N04-01-00858.Let Γ be a population of elements or objects concerned by the problem of recognition. By assumption, some experts give probabilistic predictions of unknown belonging classes γ of objects a ∈ Γ , being already aware of their description X (a ) . In this paper, we present a method of aggregating sets of individual statements into a collective one using distances / similarities between multidimensional sets in heterogeneous feature space

On Coordination of Experts’ Estimations of Quantitative Variable

* The work was supported by the RFBR under Grants N07-01-00331a, 08-07-00136aIn this paper, we consider some problems related to forecasting of quantitative feature. We assume that decision rule is constructed on the base of analysis of empirical information represented in the form of statements from several experts. The criterion of a quality of experts’ statements is suggested. The method of forming of united expert decision rule is considered

Bone Stress-Strain State Evaluation Using CT Based FEM

Nowadays, the use of a digital prototype in numerical modeling is one of the main approaches to calculating the elements of an inhomogeneous structure under the influence of external forces. The article considers a finite element analysis method based on computed tomography data. The calculations used a three-dimensional isoparametric finite element of a continuous medium developed by the authors with a linear approximation, based on weighted integration of the local stiffness matrix. The purpose of this study is to describe a general algorithm for constructing a numerical model that allows static calculation of objects with a porous structure according to its computed tomography data. Numerical modeling was carried out using kinematic boundary conditions. To evaluate the results obtained, computational and postprocessor grids were introduced. The qualitative assessment of the modeling data was based on the normalized error. Three-point bending of bone specimens of the pig forelimbs was considered as a model problem. The numerical simulation results were compared with the data obtained from a physical experiment. The relative error ranged from 3 to 15%, and the crack location, determined by the physical experiment, corresponded to the area where the ultimate strength values were exceeded, determined by numerical modeling. The results obtained reflect not only the effectiveness of the proposed approach, but also the agreement with experimental data. This method turned out to be relatively non-resource-intensive and time-efficient

Computing Amplitudes in topological M-theory

We define a topological quantum membrane theory on a seven dimensional manifold of $G_2$ holonomy. We describe in detail the path integral evaluation for membrane geometries given by circle bundles over Riemann surfaces. We show that when the target space is $CY_3\times S^1$ quantum amplitudes of non-local observables of membranes wrapping the circle reduce to the A-model amplitudes. In particular for genus zero we show that our model computes the Gopakumar-Vafa invariants. Moreover, for membranes wrapping calibrated homology spheres in the $CY_3$, we find that the amplitudes of our model are related to Joyce invariants.Comment: 26 page