Indicators for the characterization of discrete Choquet integrals

Ordered weighted averaging (OWA) operators and their extensions are powerful tools used in numerous decision-making problems. This class of operator belongs to a more general family of aggregation operators, understood as discrete Choquet integrals. Aggregation operators are usually characterized by indicators. In this article four indicators usually associated with the OWA operator are extended to discrete Choquet integrals: namely, the degree of balance, the divergence, the variance indicator and Renyi entropies. All of these indicators are considered from a local and a global perspective. Linearity of indicators for linear combinations of capacities is investigated and, to illustrate the application of results, indicators of the probabilistic ordered weighted averaging -POWA- operator are derived. Finally, an example is provided to show the application to a specific context.

Discrete distributions when modeling the disability severity score of motor victims

Many European states apply score systems to evaluate the disability severity of non-fatal motor victims under the law of third-party liability. The score is a non-negative integer with an upper bound at 100 that increases with severity. It may be automatically converted into financial terms and thus also reflects the compensation cost for disability. In this paper, discrete regression models are applied to analyze the factors that influence the disability severity score of victims. Standard and zero-altered regression models are compared from two perspectives: an interpretation of the data generating process and the level of statistical fit. The results have implications for traffic safety policy decisions aimed at reducing accident severity. An application using data from Spain is provided.

Features extraction based on the Discrete Hartley Transform for closed contour

In this paper the authors propose a new closed contour descriptor that could be seen as a Feature Extractor of closed contours based on the Discrete Hartley Transform (DHT), its main characteristic is that uses only half of the coefficients required by Elliptical Fourier Descriptors (EFD) to obtain a contour approximation with similar error measure. The proposed closed contour descriptor provides an excellent capability of information compression useful for a great number of AI applications. Moreover it can provide scale, position and rotation invariance, and last but not least it has the advantage that both the parameterization and the reconstructed shape from the compressed set can be computed very efficiently by the fast Discrete Hartley Transform (DHT) algorithm. This Feature Extractor could be useful when the application claims for reversible features and when the user needs and easy measure of the quality for a given level of compression, scalable from low to very high quality.

New Distance Transforms for Gray Level Image Compression

This thesis deals with distance transforms which are a fundamental issue in image processing and computer vision. In this thesis, two new distance transforms for gray level images are presented. As a new application for distance transforms, they are applied to gray level image compression. The new distance transforms are both new extensions of the well known distance transform algorithm developed by Rosenfeld, Pfaltz and Lay. With some modification their algorithm which calculates a distance transform on binary images with a chosen kernel has been made to calculate a chessboard like distance transform with integer numbers (DTOCS) and a real value distance transform (EDTOCS) on gray level images. Both distance transforms, the DTOCS and EDTOCS, require only two passes over the graylevel image and are extremely simple to implement. Only two image buffers are needed: The original gray level image and the binary image which defines the region(s) of calculation. No other image buffers are needed even if more than one iteration round is performed. For large neighborhoods and complicated images the two pass distance algorithm has to be applied to the image more than once, typically 3 10 times. Different types of kernels can be adopted. It is important to notice that no other existing transform calculates the same kind of distance map as the DTOCS. All the other gray weighted distance function, GRAYMAT etc. algorithms find the minimum path joining two points by the smallest sum of gray levels or weighting the distance values directly by the gray levels in some manner. The DTOCS does not weight them that way. The DTOCS gives a weighted version of the chessboard distance map. The weights are not constant, but gray value differences of the original image. The difference between the DTOCS map and other distance transforms for gray level images is shown. The difference between the DTOCS and EDTOCS is that the EDTOCS calculates these gray level differences in a different way. It propagates local Euclidean distances inside a kernel. Analytical derivations of some results concerning the DTOCS and the EDTOCS are presented. Commonly distance transforms are used for feature extraction in pattern recognition and learning. Their use in image compression is very rare. This thesis introduces a new application area for distance transforms. Three new image compression algorithms based on the DTOCS and one based on the EDTOCS are presented. Control points, i.e. points that are considered fundamental for the reconstruction of the image, are selected from the gray level image using the DTOCS and the EDTOCS. The first group of methods select the maximas of the distance image to new control points and the second group of methods compare the DTOCS distance to binary image chessboard distance. The effect of applying threshold masks of different sizes along the threshold boundaries is studied. The time complexity of the compression algorithms is analyzed both analytically and experimentally. It is shown that the time complexity of the algorithms is independent of the number of control points, i.e. the compression ratio. Also a new morphological image decompression scheme is presented, the 8 kernels' method. Several decompressed images are presented. The best results are obtained using the Delaunay triangulation. The obtained image quality equals that of the DCT images with a 4 x 4

Modelling syntectonic sedimentation: combining a discrete element model of tectonic. Deformation and process-based sedimentary Model in 3D.

This paper presents a new numerical program able to model syntectonic sedimentation. The new model combines a discrete element model of the tectonic deformation of a sedimentary cover and a process-based model of sedimentation in a single framework. The integration of these two methods allows us to include the simulation of both sedimentation and deformation processes in a single and more effective model. The paper describes briefly the antecedents of the program, Simsafadim-Clastic and a discrete element model, in order to introduce the methodology used to merge both programs to create the new code. To illustrate the operation and application of the program, analysis of the evolution of syntectonic geometries in an extensional environment and also associated with thrust fault propagation is undertaken. Using the new code, much more complex and realistic depositional structures can be simulated together with a more complex analysis of the evolution of the deformation within the sedimentary cover, which is seen to be affected by the presence of the new syntectonic sediments.

An octree isosurface codification based on discrete planes

Describes a method to code a decimated model of an isosurface on an octree representation while maintaining volume data if it is needed. The proposed technique is based on grouping the marching cubes (MC) patterns into five configurations according the topology and the number of planes of the surface that are contained in a cell. Moreover, the discrete number of planes on which the surface lays is fixed. Starting from a complete volume octree, with the isosurface codified at terminal nodes according to the new configuration, a bottom-up strategy is taken for merging cells. Such a strategy allows one to implicitly represent co-planar faces in the upper octree levels without introducing any error. At the end of this merging process, when it is required, a reconstruction strategy is applied to generate the surface contained in the octree intersected leaves. Some examples with medical data demonstrate that a reduction of up to 50% in the number of polygons can be achieved

On convergence of transforms based on parabolic scaling

This thesis studies properties of transforms based on parabolic scaling, like Curvelet-, Contourlet-, Shearlet- and Hart-Smith-transform. Essentially, two di erent questions are considered: How these transforms can characterize H older regularity and how non-linear approximation of a piecewise smooth function converges. In study of Hölder regularities, several theorems that relate regularity of a function f : R2 → R to decay properties of its transform are presented. Of particular interest is the case where a function has lower regularity along some line segment than elsewhere. Theorems that give estimates for direction and location of this line, and regularity of the function are presented. Numerical demonstrations suggest also that similar theorems would hold for more general shape of segment of low regularity. Theorems related to uniform and pointwise Hölder regularity are presented as well. Although none of the theorems presented give full characterization of regularity, the su cient and necessary conditions are very similar. Another theme of the thesis is the study of convergence of non-linear M ─term approximation of functions that have discontinuous on some curves and otherwise are smooth. With particular smoothness assumptions, it is well known that squared L2 approximation error is O(M-2(logM)3) for curvelet, shearlet or contourlet bases. Here it is shown that assuming higher smoothness properties, the log-factor can be removed, even if the function still is discontinuous.

Qualitative Characteristics and Quantitative Measures of Solution's Reliability in Discrete Optimization: Traditional Analytical Approaches, Innovative Computational Methods and Applicability

The purpose of this thesis is twofold. The first and major part is devoted to sensitivity analysis of various discrete optimization problems while the second part addresses methods applied for calculating measures of solution stability and solving multicriteria discrete optimization problems. Despite numerous approaches to stability analysis of discrete optimization problems two major directions can be single out: quantitative and qualitative. Qualitative sensitivity analysis is conducted for multicriteria discrete optimization problems with minisum, minimax and minimin partial criteria. The main results obtained here are necessary and sufficient conditions for different stability types of optimal solutions (or a set of optimal solutions) of the considered problems. Within the framework of quantitative direction various measures of solution stability are investigated. A formula for a quantitative characteristic called stability radius is obtained for the generalized equilibrium situation invariant to changes of game parameters in the case of the H¨older metric. Quality of the problem solution can also be described in terms of robustness analysis. In this work the concepts of accuracy and robustness tolerances are presented for a strategic game with a finite number of players where initial coefficients (costs) of linear payoff functions are subject to perturbations. Investigation of stability radius also aims to devise methods for its calculation. A new metaheuristic approach is derived for calculation of stability radius of an optimal solution to the shortest path problem. The main advantage of the developed method is that it can be potentially applicable for calculating stability radii of NP-hard problems. The last chapter of the thesis focuses on deriving innovative methods based on interactive optimization approach for solving multicriteria combinatorial optimization problems. The key idea of the proposed approach is to utilize a parameterized achievement scalarizing function for solution calculation and to direct interactive procedure by changing weighting coefficients of this function. In order to illustrate the introduced ideas a decision making process is simulated for three objective median location problem. The concepts, models, and ideas collected and analyzed in this thesis create a good and relevant grounds for developing more complicated and integrated models of postoptimal analysis and solving the most computationally challenging problems related to it.

Experimental and discrete element simulation studies of bell-less charging of blast furnace

This thesis presents an experimental study and numerical study, based on the discrete element method (DEM), of bell-less charging in the blast furnace. The numerical models are based on the microscopic interaction between the particles in the blast furnace charging process. The emphasis is put on model validation, investigating several phenomena in the charging process, and on finding factors that influence the results. The study considers and simulates size segregation in the hopper discharging process, particle flow and behavior on the chute, which is the key equipment in the charging system, using mono-size spherical particles, multi-size spheres and nonspherical particles. The behavior of the particles at the burden surface and pellet percolation into a coke layer is also studied. Small-scale experiments are used to validate the DEM models.

Covalidation of Integral Transforms and Method of Lines in Nonlinear Convection-Diffusion with Mathematica

The Mathematica system (version 4.0) is employed in the solution of nonlinear difusion and convection-difusion problems, formulated as transient one-dimensional partial diferential equations with potential dependent equation coefficients. The Generalized Integral Transform Technique (GITT) is first implemented for the hybrid numerical-analytical solution of such classes of problems, through the symbolic integral transformation and elimination of the space variable, followed by the utilization of the built-in Mathematica function NDSolve for handling the resulting transformed ODE system. This approach ofers an error-controlled final numerical solution, through the simultaneous control of local errors in this reliable ODE's solver and of the proposed eigenfunction expansion truncation order. For covalidation purposes, the same built-in function NDSolve is employed in the direct solution of these partial diferential equations, as made possible by the algorithms implemented in Mathematica (versions 3.0 and up), based on application of the method of lines. Various numerical experiments are performed and relative merits of each approach are critically pointed out.

Chronic imipramine treatment-induced changes in acetylcholinesterase (EC 3.1.1.7) activity in discrete rat brain regions

Cholinergic as well as monoaminergic neurotransmission seems to be involved in the etiology of affective disorders. Chronic treatment with imipramine, a classical antidepressant drug, induces adaptive changes in monoaminergic neurotransmission. In order to identify possible changes in cholinergic neurotransmission we measured total, membrane-bound and soluble acetylcholinesterase (Achase) activity in several rat brain regions after chronic imipramine treatment. Changes in Achase activity would indicate alterations in acetylcholine (Ach) availability to bind to its receptors in the synaptic cleft. Male rats were treated with imipramine (20 mg/kg, ip) for 21 days, once a day. Twenty-four hours after the last dose the rats were sacrificed and homogenates from several brain regions were prepared. Membrane-bound Achase activity (nmol thiocholine formed min-1 mg protein-1) after chronic imipramine treatment was significantly decreased in the hippocampus (control = 188.8 ± 19.4, imipramine = 154.4 ± 7.5, P<0.005) and striatum (control = 850.9 ± 59.6, imipramine = 742.5 ± 34.7, P<0.005). A small increase in total Achase activity was observed in the medulla oblongata and pons. No changes in enzyme activity were detected in the thalamus or total cerebral cortex. Since the levels of Achase seem to be enhanced through the interaction between Ach and its receptors, a decrease in Achase activity may indicate decreased Ach release by the nerve endings. Therefore, our data indicate that cholinergic neurotransmission is decreased after chronic imipramine treatment which is consistent with the idea of an interaction between monoaminergic and cholinergic neurotransmission in the antidepressant effect of imipramine

Rapid eye movement sleep deprivation induces an increase in acetylcholinesterase activity in discrete rat brain regions

Some upper brainstem cholinergic neurons (pedunculopontine and laterodorsal tegmental nuclei) are involved in the generation of rapid eye movement (REM) sleep and project rostrally to the thalamus and caudally to the medulla oblongata. A previous report showed that 96 h of REM sleep deprivation in rats induced an increase in the activity of brainstem acetylcholinesterase (Achase), the enzyme which inactivates acetylcholine (Ach) in the synaptic cleft. There was no change in the enzyme's activity in the whole brain and cerebrum. The components of the cholinergic synaptic endings (for example, Achase) are not uniformly distributed throughout the discrete regions of the brain. In order to detect possible regional changes we measured Achase activity in several discrete rat brain regions (medulla oblongata, pons, thalamus, striatum, hippocampus and cerebral cortex) after 96 h of REM sleep deprivation. Naive adult male Wistar rats were deprived of REM sleep using the flower-pot technique, while control rats were left in their home cages. Total, membrane-bound and soluble Achase activities (nmol of thiocholine formed min-1 mg protein-1) were assayed photometrically. The results (mean ± SD) obtained showed a statistically significant (Student t-test) increase in total Achase activity in the pons (control: 147.8 ± 12.8, REM sleep-deprived: 169.3 ± 17.4, N = 6 for both groups, P<0.025) and thalamus (control: 167.4 ± 29.0, REM sleep-deprived: 191.9 ± 15.4, N = 6 for both groups, P<0.05). Increases in membrane-bound Achase activity in the pons (control: 171.0 ± 14.7, REM sleep-deprived: 189.5 ± 19.5, N = 6 for both groups, P<0.05) and soluble enzyme activity in the medulla oblongata (control: 147.6 ± 16.3, REM sleep-deprived: 163.8 ± 8.3, N = 6 for both groups, P<0.05) were also observed. There were no statistically significant differences in the enzyme's activity in the other brain regions assayed. The present findings show that the increase in Achase activity induced by REM sleep deprivation was specific to the pons, a brain region where cholinergic neurons involved in REM generation are located, and also to brain regions which receive cholinergic input from the pons (the thalamus and medulla oblongata). During REM sleep extracellular levels of Ach are higher in the pons, medulla oblongata and thalamus. The increase in Achase activity in these brain areas after REM sleep deprivation suggests a higher rate of Ach turnover.

Stability Analysis in Multicriteria Discrete Portfolio Optimization.

Almost every problem of design, planning and management in the technical and organizational systems has several conflicting goals or interests. Nowadays, multicriteria decision models represent a rapidly developing area of operation research. While solving practical optimization problems, it is necessary to take into account various kinds of uncertainty due to lack of data, inadequacy of mathematical models to real-time processes, calculation errors, etc. In practice, this uncertainty usually leads to undesirable outcomes where the solutions are very sensitive to any changes in the input parameters. An example is the investment managing. Stability analysis of multicriteria discrete optimization problems investigates how the found solutions behave in response to changes in the initial data (input parameters). This thesis is devoted to the stability analysis in the problem of selecting investment project portfolios, which are optimized by considering different types of risk and efficiency of the investment projects. The stability analysis is carried out in two approaches: qualitative and quantitative. The qualitative approach describes the behavior of solutions in conditions with small perturbations in the initial data. The stability of solutions is defined in terms of existence a neighborhood in the initial data space. Any perturbed problem from this neighborhood has stability with respect to the set of efficient solutions of the initial problem. The other approach in the stability analysis studies quantitative measures such as stability radius. This approach gives information about the limits of perturbations in the input parameters, which do not lead to changes in the set of efficient solutions. In present thesis several results were obtained including attainable bounds for the stability radii of Pareto optimal and lexicographically optimal portfolios of the investment problem with Savage's, Wald's criteria and criteria of extreme optimism. In addition, special classes of the problem when the stability radii are expressed by the formulae were indicated. Investigations were completed using different combinations of Chebyshev's, Manhattan and Hölder's metrics, which allowed monitoring input parameters perturbations differently.