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.

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.

Analytical modelling of bacterial migration and accumulation with rate-limited sorption in discrete fractures

An analytical model for bacterial accumulation in a discrete fractllre has been developed. The transport and accumlllation processes incorporate into the model include advection, dispersion, rate-limited adsorption, rate-limited desorption, irreversible adsorption, attachment, detachment, growth and first order decay botl1 in sorbed and aqueous phases. An analytical solution in Laplace space is derived and nlln1erically inverted. The model is implemented in the code BIOFRAC vvhich is written in Fortran 99. The model is derived for two phases, Phase I, where adsorption-desorption are dominant, and Phase II, where attachment-detachment are dominant. Phase I ends yvhen enollgh bacteria to fully cover the substratllm have accllillulated. The model for Phase I vvas verified by comparing to the Ogata-Banks solution and the model for Phase II was verified by comparing to a nonHomogenous version of the Ogata-Banks solution. After verification, a sensitiv"ity analysis on the inpllt parameters was performed. The sensitivity analysis was condllcted by varying one inpllt parameter vvhile all others were fixed and observing the impact on the shape of the clirve describing bacterial concentration verSllS time. Increasing fracture apertllre allovvs more transport and thus more accllffilliation, "Vvhich diminishes the dllration of Phase I. The larger the bacteria size, the faster the sllbstratum will be covered. Increasing adsorption rate, was observed to increase the dllration of Phase I. Contrary to the aSSllmption ofllniform biofilm thickness, the accllffilliation starts frOll1 the inlet, and the bacterial concentration in aqlleous phase moving towards the olitiet declines, sloyving the accumulation at the outlet. Increasing the desorption rate, redllces the dliration of Phase I, speeding IIp the accllmlilation. It was also observed that Phase II is of longer duration than Phase I. Increasing the attachment rate lengthens the accliffililation period. High rates of detachment speeds up the transport. The grovvth and decay rates have no significant effect on transport, althollgh increases the concentrations in both aqueous and sorbed phases are observed. Irreversible adsorption can stop accllillulation completely if the vallIes are high.

A composite discrete traction vector.

Tesis (Maestría en Ciencias con Orientación en Ingeniería Estructural) UANL, 2013.

A Representation Theorem for Domains with Discrete and Continuous Variables.

This paper proves a new representation theorem for domains with both discrete and continuous variables. The result generalizes Debreu's well-known representation theorem on connected domains. A strengthening of the standard continuity axiom is used in order to guarantee the existence of a representation. A generalization of the main theorem and an application of the more general result are also presented.

Exact Nonparametric Two-Sample Homogeneity Tests for Possibly Discrete Distributions.

In this paper, we study several tests for the equality of two unknown distributions. Two are based on empirical distribution functions, three others on nonparametric probability density estimates, and the last ones on differences between sample moments. We suggest controlling the size of such tests (under nonparametric assumptions) by using permutational versions of the tests jointly with the method of Monte Carlo tests properly adjusted to deal with discrete distributions. We also propose a combined test procedure, whose level is again perfectly controlled through the Monte Carlo test technique and has better power properties than the individual tests that are combined. Finally, in a simulation experiment, we show that the technique suggested provides perfect control of test size and that the new tests proposed can yield sizeable power improvements.

Aumann-Shapley Pricing : A Reconsideration of the Discrete Case

We reconsider the following cost-sharing problem: agent i = 1,...,n demands a quantity xi of good i; the corresponding total cost C(x1,...,xn) must be shared among the n agents. The Aumann-Shapley prices (p1,...,pn) are given by the Shapley value of the game where each unit of each good is regarded as a distinct player. The Aumann-Shapley cost-sharing method assigns the cost share pixi to agent i. When goods come in indivisible units, we show that this method is characterized by the two standard axioms of Additivity and Dummy, and the property of No Merging or Splitting: agents never find it profitable to split or merge their demands.

The dynamics of sustained reentry in a loop model with discrete gap junction resistance

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal.

Special functions of Weyl groups and their continuous and discrete orthogonality

Cette thèse s'intéresse à l'étude des propriétés et applications de quatre familles des fonctions spéciales associées aux groupes de Weyl et dénotées $C$, $S$, $S^s$ et $S^l$. Ces fonctions peuvent être vues comme des généralisations des polynômes de Tchebyshev. Elles sont en lien avec des polynômes orthogonaux à plusieurs variables associés aux algèbres de Lie simples, par exemple les polynômes de Jacobi et de Macdonald. Elles ont plusieurs propriétés remarquables, dont l'orthogonalité continue et discrète. En particulier, il est prouvé dans la présente thèse que les fonctions $S^s$ et $S^l$ caractérisées par certains paramètres sont mutuellement orthogonales par rapport à une mesure discrète. Leur orthogonalité discrète permet de déduire deux types de transformées discrètes analogues aux transformées de Fourier pour chaque algèbre de Lie simple avec racines des longueurs différentes. Comme les polynômes de Tchebyshev, ces quatre familles des fonctions ont des applications en analyse numérique. On obtient dans cette thèse quelques formules de <>, pour des fonctions de plusieurs variables, en liaison avec les fonctions $C$, $S^s$ et $S^l$. On fournit également une description complète des transformées en cosinus discrètes de types V--VIII à $n$ dimensions en employant les fonctions spéciales associées aux algèbres de Lie simples $B_n$ et $C_n$, appelées cosinus antisymétriques et symétriques. Enfin, on étudie quatre familles de polynômes orthogonaux à plusieurs variables, analogues aux polynômes de Tchebyshev, introduits en utilisant les cosinus (anti)symétriques.