Improving minimax disparity model to determine the OWA operator weights

Determining the Ordered Weighted Averaging (OWA) operator weights is important in decision making applications. Several approaches have been proposed in the literature to obtain the associated weights. This paper provides an alternative disparity model to identify the OWA operator weights. The proposed mathematical model extends the existing disparity approaches by minimizing the sum of the deviation between two distinct OWA weights. The proposed disparity model can be used for a preference ranking aggregation. A numerical example in preference ranking and an application in search engines prove the usefulness of the generated OWA weights.

About Methods of Mathematical Modelling in the Development of Information Systems

This article describes the approach, which allows to develop information systems without taking into consideration details of physical storage of the relational model and type database management system. Described in terms of graph model, this approach allows to construct several algorithms, for example, for verification application domain. This theory was introduced into operation testing as a part of CASE-system METAS.

Mathematical Models of Domain Ontologies

* This paper was made according to the program No 14 of fundamental scientific research of the Presidium of the Russian Academy of Sciences, the project "Intellectual Systems Based on Multilevel Domain Models".

An Information Model for Pension Fund Management

In this paper the issues of Ukrainian new three-level pension system are discussed. First, the paper presents the mathematical model that allows calculating the optimal size of contributions to the non-state pension fund. Next, the non-state pension fund chooses an Asset Management Company. To do so it is proposed to use an approach based on Kohonen networks to classify asset management companies that work in Ukrainian market. Further, when the asset management company is chosen, it receives the pension contributions of the participants of the non-pension fund. Asset Management Company has to invest these contributions profitably. This paper proposes an approach for choosing the most profitable investment project using decision trees. The new pension system has been lawfully ratified only four years ago and is still developing, that is why this paper is very important.

Improving the predictability of time series by chaotic parameter estimation

Limited literature regarding parameter estimation of dynamic systems has been identified as the central-most reason for not having parametric bounds in chaotic time series. However, literature suggests that a chaotic system displays a sensitive dependence on initial conditions, and our study reveals that the behavior of chaotic system: is also sensitive to changes in parameter values. Therefore, parameter estimation technique could make it possible to establish parametric bounds on a nonlinear dynamic system underlying a given time series, which in turn can improve predictability. By extracting the relationship between parametric bounds and predictability, we implemented chaos-based models for improving prediction in time series. ^ This study describes work done to establish bounds on a set of unknown parameters. Our research results reveal that by establishing parametric bounds, it is possible to improve the predictability of any time series, although the dynamics or the mathematical model of that series is not known apriori. In our attempt to improve the predictability of various time series, we have established the bounds for a set of unknown parameters. These are: (i) the embedding dimension to unfold a set of observation in the phase space, (ii) the time delay to use for a series, (iii) the number of neighborhood points to use for avoiding detection of false neighborhood and, (iv) the local polynomial to build numerical interpolation functions from one region to another. Using these bounds, we are able to get better predictability in chaotic time series than previously reported. In addition, the developments of this dissertation can establish a theoretical framework to investigate predictability in time series from the system-dynamics point of view. ^ In closing, our procedure significantly reduces the computer resource usage, as the search method is refined and efficient. Finally, the uniqueness of our method lies in its ability to extract chaotic dynamics inherent in non-linear time series by observing its values. ^

A non-linear discrete stochastic optimization model for Advanced Access patient appointment scheduling

Access to healthcare is a major problem in which patients are deprived of receiving timely admission to healthcare. Poor access has resulted in significant but avoidable healthcare cost, poor quality of healthcare, and deterioration in the general public health. Advanced Access is a simple and direct approach to appointment scheduling in which the majority of a clinic's appointments slots are kept open in order to provide access for immediate or same day healthcare needs and therefore, alleviate the problem of poor access the healthcare. This research formulates a non-linear discrete stochastic mathematical model of the Advanced Access appointment scheduling policy. The model objective is to maximize the expected profit of the clinic subject to constraints on minimum access to healthcare provided. Patient behavior is characterized with probabilities for no-show, balking, and related patient choices. Structural properties of the model are analyzed to determine whether Advanced Access patient scheduling is feasible. To solve the complex combinatorial optimization problem, a heuristic that combines greedy construction algorithm and neighborhood improvement search was developed. The model and the heuristic were used to evaluate the Advanced Access patient appointment policy compared to existing policies. Trade-off between profit and access to healthcare are established, and parameter analysis of input parameters was performed. The trade-off curve is a characteristic curve and was observed to be concave. This implies that there exists an access level at which at which the clinic can be operated at optimal profit that can be realized. The results also show that, in many scenarios by switching from existing scheduling policy to Advanced Access policy clinics can improve access without any decrease in profit. Further, the success of Advanced Access policy in providing improved access and/or profit depends on the expected value of demand, variation in demand, and the ratio of demand for same day and advanced appointments. The contributions of the dissertation are a model of Advanced Access patient scheduling, a heuristic to solve the model, and the use of the model to understand the scheduling policy trade-offs which healthcare clinic managers must make. ^

An experimental and theoretical analysis of nitric oxide availability in the microcirculation

Nitric Oxide (NO) is produced in the vascular endothelium where it then diffuses to the adjacent smooth muscle cells (SMC) activating agents known to regulate vascular tone. The close proximity of the site of NO production to the red blood cells (RBC) and its known fast consumption by hemoglobin, suggests that the blood will scavenge most of the NO produced. Therefore, it is unclear how NO is able to play its role in accomplishing vasodilation. Investigation of NO production and consumption rates will allow insight into this paradox. DAF-FM is a sensitive NO fluorescence probe widely used for qualitative assessment of cellular NO production. With the aid of a mathematical model of NO/DAF-FM reaction kinetics, experimental studies were conducted to calibrate the fluorescence signal showing that the slope of fluorescent intensity is proportional to [NO]2 and exhibits a saturation dependence on [DAF-FM]. In addition, experimental data exhibited a Km dependence on [NO]. This finding was incorporated into the model elucidating NO 2 as the possible activating agent of DAF-FM. A calibration procedure was formed and applied to agonist stimulated cells, providing an estimated NO release rate of 0.418 ± 0.18 pmol/cm2s. To assess NO consumption by RBCs, measurements of the rate of NO consumption in a gas stream flowing on top of an RBC solution of specified Hematocrit (Hct) was performed. The consumption rate constant (kbl)in porcine RBCs at 25°C and 45% Hct was estimated to be 3500 + 700 s-1. kbl is highly dependent on Hct and can reach up to 9900 + 4000 s-1 for 60% Hct. The nonlinear dependence of kbl on Hct suggests a predominant role for extracellular diffusion in limiting NO uptake. Further simulations showed a linear relationship between varying NO production rates and NO availability in the SMCs utilizing the estimated NO consumption rate. The corresponding SMC [NO] level for the average NO production rate estimated was approximately 15.1 nM. With the aid of experimental and theoretical methods we were able to examine the NO paradox and exhibit that endothelial derived NO is able to escape scavenging by RBCs to diffuse to the SMCs.

Influence of hydrobiogeochemistry on transport of chromium through manganese -containing sediments: Experimental and modeling approaches

Chromium (Cr) is a metal of particular environmental concern, owing to its toxicity and widespread occurrence in groundwater, soil, and soil solution. A combination of hydrological, geochemical, and microbiological processes governs the subsurface migration of Cr. Little effort has been devoted to examining how these biogeochemical reactions combine with hydrologic processes influence Cr migration. This study has focused on the complex problem of predicting the Cr transport in laboratory column experiments. A 1-D reactive transport model was developed and evaluated against data obtained from laboratory column experiments. ^ A series of dynamic laboratory column experiments were conducted under abiotic and biotic conditions. Cr(III) was injected into columns packed with β-MnO 2-coated sand at different initial concentrations, variable flow rates, and at two different pore water pH (3.0 and 4.0). In biotic anaerobic column experiments Cr(VI) along with lactate was injected into columns packed with quartz sand or β-MnO2-coated sand and bacteria, Shewanella alga Simidu (BrY-MT). A mathematical model was developed which included advection-dispersion equations for the movement of Cr(III), Cr(VI), dissolved oxygen, lactate, and biomass. The model included first-order rate laws governing the adsorption of each Cr species and lactate. The equations for transport and adsorption were coupled with nonlinear equations for rate-limited oxidation-reduction reactions along with dual-monod kinetic equations. Kinetic batch experiments were conducted to determine the reduction of Cr(VI) by BrY-MT in three different substrates. Results of the column experiments with Cr(III)-containing influent solutions demonstrate that β-MnO2 effectively catalyzes the oxidation of Cr(III) to Cr(VI). For a given influent concentration and pore water velocity, oxidation rates are higher, and hence effluent concentrations of Cr(VI) are greater, at pH 4 relative to pH 3. Reduction of Cr(VI) by BrY-MT was rapid (within one hour) in columns packed with quartz sand, whereas Cr(VI) reduction by BrY-MT was delayed (57 hours) in presence of β-MnO 2-coated sand. BrY-MT grown in BHIB (brain heart infusion broth) reduced maximum amount of Cr(VI) to Cr(III) followed by TSB (tryptic soy broth) and M9 (minimum media). The comparisons of data and model results from the column experiments show that the depths associated with Cr(III) oxidation and transport within sediments of shallow aquatic systems can strongly influence trends in surface water quality. The results of this study suggests that carefully performed, laboratory column experiments is a useful tool in determining the biotransformation of redox-sensitive metals even in the presence of strong oxidant, like β-MnO2. ^

Mathematical Modeling of Perifusion Cell Culture Experiments

In perifusion cell cultures, the culture medium flows continuously through a chamber containing immobilized cells and the effluent is collected at the end. In our main applications, gonadotropin releasing hormone (GnRH) or oxytocin is introduced into the chamber as the input. They stimulate the cells to secrete luteinizing hormone (LH), which is collected in the effluent. To relate the effluent LH concentration to the cellular processes producing it, we develop and analyze a mathematical model consisting of coupled partial differential equations describing the intracellular signaling and the movement of substances in the cell chamber. We analyze three different data sets and give cellular mechanisms that explain the data. Our model indicates that two negative feedback loops, one fast and one slow, are needed to explain the data and we give their biological bases. We demonstrate that different LH outcomes in oxytocin and GnRH stimulations might originate from different receptor dynamics. We analyze the model to understand the influence of parameters, like the rate of the medium flow or the fraction collection time, on the experimental outcomes. We investigate how the rate of binding and dissociation of the input hormone to and from its receptor influence its movement down the chamber. Finally, we formulate and analyze simpler models that allow us to predict the distortion of a square pulse due to hormone-receptor interactions and to estimate parameters using perifusion data. We show that in the limit of high binding and dissociation the square pulse moves as a diffusing Gaussian and in this limit the biological parameters can be estimated.

Extended nonlinear analytical models of compliant parallelogram mechanisms: third-order models

This paper proposes extended nonlinear analytical models, third-order models, of compliant parallelogram mechanisms. These models are capable of capturing the accurate effects from the very large axial force within the transverse motion range of 10% of the beam length through incorporating the terms associated with the high-order (up to third-order) axial force. Firstly, the free-body diagram method is employed to derive the nonlinear analytical model for a basic compliant parallelogram mechanism based on load-displacement relations of a single beam, geometry compatibility conditions, and load-equilibrium conditions. The procedures for the forward solutions and inverse solutions are described. Nonlinear analytical models for guided compliant multi-beam parallelogram mechanisms are then obtained. A case study of the compound compliant parallelogram mechanism, composed of two basic compliant parallelogram mechanisms in symmetry, is further implemented. This work intends to estimate the internal axial force change, the transverse force change, and the transverse stiffness change with the transverse motion using the proposed third-order model in comparison with the first-order model proposed in the prior art. In addition, FEA (finite element analysis) results validate the accuracy of the third-order model for a typical example. It is shown that in the case study the slenderness ratio affects the result discrepancy between the third-order model and the first-order model significantly, and the third-order model can illustrate a non-monotonic transverse stiffness curve if the beam is thin enough.

Development of An Enhanced Oil Sands Fluid Tailings Generation Model

Bitumen extraction from surface-mined oil sands results in the production of large volumes of Fluid Fine Tailings (FFT). Through Directive 085, the Province of Alberta has signaled that oil sands operators must improve and accelerate the methods by which they deal with FFT production, storage and treatment. This thesis aims to develop an enhanced method to forecast FFT production based on specific ore characteristics. A mass relationship and mathematical model to modify the Forecasting Tailings Model (FTM) by using fines and clay boundaries, as the two main indicators in FFT accumulation, has been developed. The modified FTM has been applied on representative block model data from an operating oil sands mining venture. An attempt has been made to identify order-of-magnitude associated tailings treatment costs, and to improve financial performance by not processing materials that have ultimate ore processing and tailings storage and treatment costs in excess of the value of bitumen they produce. The results on the real case study show that there is a 53% reduction in total tailings accumulations over the mine life by selectively processing only lower tailings generating materials through eliminating 15% of total mined ore materials with higher potential of fluid fines inventory. This significant result will assess the impact of Directive 082 on mining project economic and environmental performance towards the sustainable development of mining projects.

Mathematical Modeling to Assess the Drivers of the Recent Emergence of Typhoid Fever in Blantyre, Malawi

BACKGROUND: Multiyear epidemics of Salmonella enterica serovar Typhi have been reported from countries across eastern and southern Africa in recent years. In Blantyre, Malawi, a dramatic increase in typhoid fever cases has recently occurred, and may be linked to the emergence of the H58 haplotype. Strains belonging to the H58 haplotype often exhibit multidrug resistance and may have a fitness advantage relative to other Salmonella Typhi strains.

METHODS: To explore hypotheses for the increased number of typhoid fever cases in Blantyre, we fit a mathematical model to culture-confirmed cases of Salmonella enterica infections at Queen Elizabeth Central Hospital, Blantyre. We explored 4 hypotheses: (1) an increase in the basic reproductive number (R0) in response to increasing population density; (2) a decrease in the incidence of cross-immunizing infection with Salmonella Enteritidis; (3) an increase in the duration of infectiousness due to failure to respond to first-line antibiotics; and (4) an increase in the transmission rate following the emergence of the H58 haplotype.

RESULTS: Increasing population density or decreasing cross-immunity could not fully explain the observed pattern of typhoid emergence in Blantyre, whereas models allowing for an increase in the duration of infectiousness and/or the transmission rate of typhoid following the emergence of the H58 haplotype provided a good fit to the data.

CONCLUSIONS: Our results suggest that an increase in the transmissibility of typhoid due to the emergence of drug resistance associated with the H58 haplotype may help to explain recent outbreaks of typhoid in Malawi and similar settings in Africa.

Symmetries and exact solutions of KP equation with an arbitrary nonlinear term

The generalized KP (GKP) equations with an arbitrary nonlinear term model and characterize many nonlinear physical phenomena. The symmetries of GKP equation with an arbitrary nonlinear term are obtained. The condition that must satisfy for existence the symmetries group of GKP is derived and also the obtained symmetries are classified according to different forms of the nonlinear term. The resulting similarity reductions are studied by performing the bifurcation and the phase portrait of GKP and also the corresponding solitary wave solutions of GKP
equation are constructed.

The use of mathematical modelling in fire safety engineering

Fire is a form of uncontrolled combustion which generates heat, smoke, toxic and irritant gases. All of these products are harmful to man and account for the heavy annual cost of 800 lives and £1,000,000,000 worth of property damage in Britain alone. The new discipline of Fire Safety Engineering has developed as a means of reducing these unacceptable losses. One of the main tools of Fire Safety Engineering is the mathematical model and over the past 15 years a number of mathematical models have emerged to cater for the needs of this discipline. Part of the difficulty faced by the Fire Safety Engineer is the selection of the most appropriate modelling tool to use for the job. To make an informed choice it is essential to have a good understanding of the various modelling approaches, their capabilities and limitations. In this paper some of the fundamental modelling tools used to predict fire and evacuation are investigated as are the issues associated with their use and recent developments in modelling technology.

Hybrid mathematical and informational modeling of beam-to-column connections

The analysis of steel and composite frames has traditionally been carried out by idealizing beam-to-column connections as either rigid or pinned. Although some advanced analysis methods have been proposed to account for semi-rigid connections, the performance of these methods strongly depends on the proper modeling of connection behavior. The primary challenge of modeling beam-to-column connections is their inelastic response and continuously varying stiffness, strength, and ductility. In this dissertation, two distinct approaches—mathematical models and informational models—are proposed to account for the complex hysteretic behavior of beam-to-column connections. The performance of the two approaches is examined and is then followed by a discussion of their merits and deficiencies. To capitalize on the merits of both mathematical and informational representations, a new approach, a hybrid modeling framework, is developed and demonstrated through modeling beam-to-column connections. Component-based modeling is a compromise spanning two extremes in the field of mathematical modeling: simplified global models and finite element models. In the component-based modeling of angle connections, the five critical components of excessive deformation are identified. Constitutive relationships of angles, column panel zones, and contact between angles and column flanges, are derived by using only material and geometric properties and theoretical mechanics considerations. Those of slip and bolt hole ovalization are simplified by empirically-suggested mathematical representation and expert opinions. A mathematical model is then assembled as a macro-element by combining rigid bars and springs that represent the constitutive relationship of components. Lastly, the moment-rotation curves of the mathematical models are compared with those of experimental tests. In the case of a top-and-seat angle connection with double web angles, a pinched hysteretic response is predicted quite well by complete mechanical models, which take advantage of only material and geometric properties. On the other hand, to exhibit the highly pinched behavior of a top-and-seat angle connection without web angles, a mathematical model requires components of slip and bolt hole ovalization, which are more amenable to informational modeling. An alternative method is informational modeling, which constitutes a fundamental shift from mathematical equations to data that contain the required information about underlying mechanics. The information is extracted from observed data and stored in neural networks. Two different training data sets, analytically-generated and experimental data, are tested to examine the performance of informational models. Both informational models show acceptable agreement with the moment-rotation curves of the experiments. Adding a degradation parameter improves the informational models when modeling highly pinched hysteretic behavior. However, informational models cannot represent the contribution of individual components and therefore do not provide an insight into the underlying mechanics of components. In this study, a new hybrid modeling framework is proposed. In the hybrid framework, a conventional mathematical model is complemented by the informational methods. The basic premise of the proposed hybrid methodology is that not all features of system response are amenable to mathematical modeling, hence considering informational alternatives. This may be because (i) the underlying theory is not available or not sufficiently developed, or (ii) the existing theory is too complex and therefore not suitable for modeling within building frame analysis. The role of informational methods is to model aspects that the mathematical model leaves out. Autoprogressive algorithm and self-learning simulation extract the missing aspects from a system response. In a hybrid framework, experimental data is an integral part of modeling, rather than being used strictly for validation processes. The potential of the hybrid methodology is illustrated through modeling complex hysteretic behavior of beam-to-column connections. Mechanics-based components of deformation such as angles, flange-plates, and column panel zone, are idealized to a mathematical model by using a complete mechanical approach. Although the mathematical model represents envelope curves in terms of initial stiffness and yielding strength, it is not capable of capturing the pinching effects. Pinching is caused mainly by separation between angles and column flanges as well as slip between angles/flange-plates and beam flanges. These components of deformation are suitable for informational modeling. Finally, the moment-rotation curves of the hybrid models are validated with those of the experimental tests. The comparison shows that the hybrid models are capable of representing the highly pinched hysteretic behavior of beam-to-column connections. In addition, the developed hybrid model is successfully used to predict the behavior of a newly-designed connection.