38 research outputs found
Interval Prediction Based on Expertsâ Statements
In the work [1] we proposed an approach of forming a consensus of expertsâ 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 Expertsâ 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 expertsâ 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
â The work was supported by the RFBR under Grant N04-01-00858.Let Î be a population of elements or objects concerned by the problem of recognition. By assumption,
some experts give probabilistic predictions of unknown belonging classes Îł of objects a â Î , 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 Expertsâ 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 expertsâ statements is suggested. The method of
forming of united expert decision rule is considered
Induced differential forms on manifolds of functions
Differential forms on the Fr\'echet manifold F(S,M) of smooth functions on a
compact k-dimensional manifold S can be obtained in a natural way from pairs of
differential forms on M and S by the hat pairing. Special cases are the
transgression map associating (p-k)-forms on F(S,M) to p-forms on M (hat
pairing with a constant function) and the bar map associating p-forms on F(S,M)
to p-forms on M (hat pairing with a volume form). We develop a hat calculus
similar to the tilda calculus for non-linear Grassmannians.Comment: 17 page
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 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 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 , we find that the amplitudes of our model are related to
Joyce invariants.Comment: 26 page