On the Mathematical Modelling of Microbial Growth: Some Computational Aspects

We propose a new approach to the mathematical modelling of microbial growth. Our approach differs from familiar Monod type models by considering two phases in the physiological states of the microorganisms and makes use of basic relations from enzyme kinetics. Such an approach may be useful in the modelling and control of biotechnological processes, where microorganisms are used for various biodegradation purposes and are often put under extreme inhibitory conditions. Some computational experiments are performed in support of our modelling approach.

Integer Programming Approach to HP Folding

One of the most widely studied protein structure prediction models is the hydrophobic-hydrophilic (HP) model, which explains the hydrophobic interaction and tries to maximize the number of contacts among hydrophobic amino-acids. In order to find a lower bound for the number of contacts, a number of heuristics have been proposed, but finding the optimal solution is still a challenge. In this research, we focus on creating a new integer programming model which is capable to provide tractable input for mixed-integer programming solvers, is general enough and allows relaxation with provable good upper bounds. Computational experiments using benchmark problems show that our formulation achieves these goals.

A Variable Neighborhood Search Approach for Solving the Maximum Set Splitting Problem

This paper presents a Variable neighbourhood search (VNS) approach for solving the Maximum Set Splitting Problem (MSSP). The algorithm forms a system of neighborhoods based on changing the component for an increasing number of elements. An efficient local search procedure swaps the components of pairs of elements and yields a relatively short running time. Numerical experiments are performed on the instances known in the literature: minimum hitting set and Steiner triple systems. Computational results show that the proposed VNS achieves all optimal or best known solutions in short times. The experiments indicate that the VNS compares favorably with other methods previously used for solving the MSSP. ACM Computing Classification System (1998): I.2.8.

Theory of hybrid computational and physical measurement-based integration of thermal and dimensional measurement

In dimensional metrology, often the largest source of uncertainty of measurement is thermal variation. Dimensional measurements are currently scaled linearly, using ambient temperature measurements and coefficients of thermal expansion, to ideal metrology conditions at 20˚C. This scaling is particularly difficult to implement with confidence in large volumes as the temperature is unlikely to be uniform, resulting in thermal gradients. A number of well-established computational methods are used in the design phase of product development for the prediction of thermal and gravitational effects, which could be used to a greater extent in metrology. This paper outlines the theory of how physical measurements of dimension and temperature can be combined more comprehensively throughout the product lifecycle, from design through to the manufacturing phase. The Hybrid Metrology concept is also introduced: an approach to metrology, which promises to improve product and equipment integrity in future manufacturing environments. The Hybrid Metrology System combines various state of the art physical dimensional and temperature measurement techniques with established computational methods to better predict thermal and gravitational effects.

An unsupervised Bayesian modelling approach to storyline detection from news articles

Storyline detection from news articles aims at summarizing events described under a certain news topic and revealing how those events evolve over time. It is a difficult task because it requires first the detection of events from news articles published in different time periods and then the construction of storylines by linking events into coherent news stories. Moreover, each storyline has different hierarchical structures which are dependent across epochs. Existing approaches often ignore the dependency of hierarchical structures in storyline generation. In this paper, we propose an unsupervised Bayesian model, called dynamic storyline detection model, to extract structured representations and evolution patterns of storylines. The proposed model is evaluated on a large scale news corpus. Experimental results show that our proposed model outperforms several baseline approaches.

Physical dynamic simulation of shipboard power system components in a distributed computational environment

Shipboard power systems have different characteristics than the utility power systems. In the Shipboard power system it is crucial that the systems and equipment work at their peak performance levels. One of the most demanding aspects for simulations of the Shipboard Power Systems is to connect the device under test to a real-time simulated dynamic equivalent and in an environment with actual hardware in the Loop (HIL). The real time simulations can be achieved by using multi-distributed modeling concept, in which the global system model is distributed over several processors through a communication link. The advantage of this approach is that it permits the gradual change from pure simulation to actual application. In order to perform system studies in such an environment physical phase variable models of different components of the shipboard power system were developed using operational parameters obtained from finite element (FE) analysis. These models were developed for two types of studies low and high frequency studies. Low frequency studies are used to examine the shipboard power systems behavior under load switching, and faults. High-frequency studies were used to predict abnormal conditions due to overvoltage, and components harmonic behavior. Different experiments were conducted to validate the developed models. The Simulation and experiment results show excellent agreement. The shipboard power systems components behavior under internal faults was investigated using FE analysis. This developed technique is very curial in the Shipboard power systems faults detection due to the lack of comprehensive fault test databases. A wavelet based methodology for feature extraction of the shipboard power systems current signals was developed for harmonic and fault diagnosis studies. This modeling methodology can be utilized to evaluate and predicate the NPS components future behavior in the design stage which will reduce the development cycles, cut overall cost, prevent failures, and test each subsystem exhaustively before integrating it into the system.

Optimization of transit transfer times: A system-wide approach

This dissertation presents a system-wide approach, based on genetic algorithms, for the optimization of transfer times for an entire bus transit system. Optimization of transfer times in a transit system is a complicated problem because of the large set of binary and discrete values involved. The combinatorial nature of the problem imposes a computational burden and makes it difficult to solve by classical mathematical programming methods. ^ The genetic algorithm proposed in this research attempts to find an optimal solution for the transfer time optimization problem by searching for a combination of adjustments to the timetable for all the routes in the system. It makes use of existing scheduled timetables, ridership demand at all transfer locations, and takes into consideration the randomness of bus arrivals. ^ Data from Broward County Transit are used to compute total transfer times. The proposed genetic algorithm-based approach proves to be capable of producing substantial time savings compared to the existing transfer times in a reasonable amount of time. ^ The dissertation also addresses the issues related to spatial and temporal modeling, variability in bus arrival and departure times, walking time, as well as the integration of scheduling and ridership data. ^

A quantitative approach to the organizational design problem

The span of control is the most discussed single concept in classical and modern management theory. In specifying conditions for organizational effectiveness, the span of control has generally been regarded as a critical factor. Existing research work has focused mainly on qualitative methods to analyze this concept, for example heuristic rules based on experiences and/or intuition. This research takes a quantitative approach to this problem and formulates it as a binary integer model, which is used as a tool to study the organizational design issue. This model considers a range of requirements affecting management and supervision of a given set of jobs in a company. These decision variables include allocation of jobs to workers, considering complexity and compatibility of each job with respect to workers, and the requirement of management for planning, execution, training, and control activities in a hierarchical organization. The objective of the model is minimal operations cost, which is the sum of supervision costs at each level of the hierarchy, and the costs of workers assigned to jobs. The model is intended for application in the make-to-order industries as a design tool. It could also be applied to make-to-stock companies as an evaluation tool, to assess the optimality of their current organizational structure. Extensive experiments were conducted to validate the model, to study its behavior, and to evaluate the impact of changing parameters with practical problems. This research proposes a meta-heuristic approach to solving large-size problems, based on the concept of greedy algorithms and the Meta-RaPS algorithm. The proposed heuristic was evaluated with two measures of performance: solution quality and computational speed. The quality is assessed by comparing the obtained objective function value to the one achieved by the optimal solution. The computational efficiency is assessed by comparing the computer time used by the proposed heuristic to the time taken by a commercial software system. Test results show the proposed heuristic procedure generates good solutions in a time-efficient manner.

Evaluation of wind-induced internal pressure in low-rise buildings: A multi scale experimental and numerical approach

Hurricane is one of the most destructive and costly natural hazard to the built environment and its impact on low-rise buildings, particularity, is beyond acceptable. The major objective of this research was to perform a parametric evaluation of internal pressure (IP) for wind-resistant design of low-rise buildings and wind-driven natural ventilation applications. For this purpose, a multi-scale experimental, i.e. full-scale at Wall of Wind (WoW) and small-scale at Boundary Layer Wind Tunnel (BLWT), and a Computational Fluid Dynamics (CFD) approach was adopted. This provided new capability to assess wind pressures realistically on internal volumes ranging from small spaces formed between roof tiles and its deck to attic to room partitions. Effects of sudden breaching, existing dominant openings on building envelopes as well as compartmentalization of building interior on the IP were systematically investigated. Results of this research indicated: (i) for sudden breaching of dominant openings, the transient overshooting response was lower than the subsequent steady state peak IP and internal volume correction for low-wind-speed testing facilities was necessary. For example a building without volume correction experienced a response four times faster and exhibited 30–40% lower mean and peak IP; (ii) for existing openings, vent openings uniformly distributed along the roof alleviated, whereas one sided openings aggravated the IP; (iii) larger dominant openings exhibited a higher IP on the building envelope, and an off-center opening on the wall exhibited (30–40%) higher IP than center located openings; (iv) compartmentalization amplified the intensity of IP and; (v) significant underneath pressure was measured for field tiles, warranting its consideration during net pressure evaluations. The study aimed at wind driven natural ventilation indicated: (i) the IP due to cross ventilation was 1.5 to 2.5 times higher for Ainlet/Aoutlet>1 compared to cases where Ainlet/Aoutlet<1, this in effect reduced the mixing of air inside the building and hence the ventilation effectiveness; (ii) the presence of multi-room partitioning increased the pressure differential and consequently the air exchange rate. Overall good agreement was found between the observed large-scale, small-scale and CFD based IP responses. Comparisons with ASCE 7-10 consistently demonstrated that the code underestimated peak positive and suction IP.

Computational evaluation of wind loads on low- and highrise buildings

Buildings and other infrastructures located in the coastal regions of the US have a higher level of wind vulnerability. Reducing the increasing property losses and causalities associated with severe windstorms has been the central research focus of the wind engineering community. The present wind engineering toolbox consists of building codes and standards, laboratory experiments, and field measurements. The American Society of Civil Engineers (ASCE) 7 standard provides wind loads only for buildings with common shapes. For complex cases it refers to physical modeling. Although this option can be economically viable for large projects, it is not cost-effective for low-rise residential houses. To circumvent these limitations, a numerical approach based on the techniques of Computational Fluid Dynamics (CFD) has been developed. The recent advance in computing technology and significant developments in turbulence modeling is making numerical evaluation of wind effects a more affordable approach. The present study targeted those cases that are not addressed by the standards. These include wind loads on complex roofs for low-rise buildings, aerodynamics of tall buildings, and effects of complex surrounding buildings. Among all the turbulence models investigated, the large eddy simulation (LES) model performed the best in predicting wind loads. The application of a spatially evolving time-dependent wind velocity field with the relevant turbulence structures at the inlet boundaries was found to be essential. All the results were compared and validated with experimental data. The study also revealed CFD's unique flow visualization and aerodynamic data generation capabilities along with a better understanding of the complex three-dimensional aerodynamics of wind-structure interactions. With the proper modeling that realistically represents the actual turbulent atmospheric boundary layer flow, CFD can offer an economical alternative to the existing wind engineering tools. CFD's easy accessibility is expected to transform the practice of structural design for wind, resulting in more wind-resilient and sustainable systems by encouraging optimal aerodynamic and sustainable structural/building design. Thus, this method will help ensure public safety and reduce economic losses due to wind perils.

Branch and price solution approach for order acceptance and capacity planning in make -to -order operations

The increasing emphasis on mass customization, shortened product lifecycles, synchronized supply chains, when coupled with advances in information system, is driving most firms towards make-to-order (MTO) operations. Increasing global competition, lower profit margins, and higher customer expectations force the MTO firms to plan its capacity by managing the effective demand. The goal of this research was to maximize the operational profits of a make-to-order operation by selectively accepting incoming customer orders and simultaneously allocating capacity for them at the sales stage. ^ For integrating the two decisions, a Mixed-Integer Linear Program (MILP) was formulated which can aid an operations manager in an MTO environment to select a set of potential customer orders such that all the selected orders are fulfilled by their deadline. The proposed model combines order acceptance/rejection decision with detailed scheduling. Experiments with the formulation indicate that for larger problem sizes, the computational time required to determine an optimal solution is prohibitive. This formulation inherits a block diagonal structure, and can be decomposed into one or more sub-problems (i.e. one sub-problem for each customer order) and a master problem by applying Dantzig-Wolfe’s decomposition principles. To efficiently solve the original MILP, an exact Branch-and-Price algorithm was successfully developed. Various approximation algorithms were developed to further improve the runtime. Experiments conducted unequivocally show the efficiency of these algorithms compared to a commercial optimization solver.^ The existing literature addresses the static order acceptance problem for a single machine environment having regular capacity with an objective to maximize profits and a penalty for tardiness. This dissertation has solved the order acceptance and capacity planning problem for a job shop environment with multiple resources. Both regular and overtime resources is considered. ^ The Branch-and-Price algorithms developed in this dissertation are faster and can be incorporated in a decision support system which can be used on a daily basis to help make intelligent decisions in a MTO operation.^

Branch and Price Solution Approach for Order Acceptance and Capacity Planning in Make-to-Order Operations

The increasing emphasis on mass customization, shortened product lifecycles, synchronized supply chains, when coupled with advances in information system, is driving most firms towards make-to-order (MTO) operations. Increasing global competition, lower profit margins, and higher customer expectations force the MTO firms to plan its capacity by managing the effective demand. The goal of this research was to maximize the operational profits of a make-to-order operation by selectively accepting incoming customer orders and simultaneously allocating capacity for them at the sales stage. For integrating the two decisions, a Mixed-Integer Linear Program (MILP) was formulated which can aid an operations manager in an MTO environment to select a set of potential customer orders such that all the selected orders are fulfilled by their deadline. The proposed model combines order acceptance/rejection decision with detailed scheduling. Experiments with the formulation indicate that for larger problem sizes, the computational time required to determine an optimal solution is prohibitive. This formulation inherits a block diagonal structure, and can be decomposed into one or more sub-problems (i.e. one sub-problem for each customer order) and a master problem by applying Dantzig-Wolfe’s decomposition principles. To efficiently solve the original MILP, an exact Branch-and-Price algorithm was successfully developed. Various approximation algorithms were developed to further improve the runtime. Experiments conducted unequivocally show the efficiency of these algorithms compared to a commercial optimization solver. The existing literature addresses the static order acceptance problem for a single machine environment having regular capacity with an objective to maximize profits and a penalty for tardiness. This dissertation has solved the order acceptance and capacity planning problem for a job shop environment with multiple resources. Both regular and overtime resources is considered. The Branch-and-Price algorithms developed in this dissertation are faster and can be incorporated in a decision support system which can be used on a daily basis to help make intelligent decisions in a MTO operation.

Physical dynamic simulation of shipboard power system components in a distributed computational environment

Shipboard power systems have different characteristics than the utility power systems. In the Shipboard power system it is crucial that the systems and equipment work at their peak performance levels. One of the most demanding aspects for simulations of the Shipboard Power Systems is to connect the device under test to a real-time simulated dynamic equivalent and in an environment with actual hardware in the Loop (HIL). The real time simulations can be achieved by using multi-distributed modeling concept, in which the global system model is distributed over several processors through a communication link. The advantage of this approach is that it permits the gradual change from pure simulation to actual application. In order to perform system studies in such an environment physical phase variable models of different components of the shipboard power system were developed using operational parameters obtained from finite element (FE) analysis. These models were developed for two types of studies low and high frequency studies. Low frequency studies are used to examine the shipboard power systems behavior under load switching, and faults. High-frequency studies were used to predict abnormal conditions due to overvoltage, and components harmonic behavior. Different experiments were conducted to validate the developed models. The Simulation and experiment results show excellent agreement. The shipboard power systems components behavior under internal faults was investigated using FE analysis. This developed technique is very curial in the Shipboard power systems faults detection due to the lack of comprehensive fault test databases. A wavelet based methodology for feature extraction of the shipboard power systems current signals was developed for harmonic and fault diagnosis studies. This modeling methodology can be utilized to evaluate and predicate the NPS components future behavior in the design stage which will reduce the development cycles, cut overall cost, prevent failures, and test each subsystem exhaustively before integrating it into the system.

Generalized atoms in molecules approach (GAIM approach)

This thesis involves two parts. The first is a new-proposed theoretical approach called generalized atoms in molecules (GAIM). The second is a computational study on the deamination reaction of adenine with OH⁻/nH₂O (n=0, 1, 2, 3) and 3H₂O. The GAIM approach aims to solve the energy of each atom variationally in the first step and then to build the energy of a molecule from each atom. Thus the energy of a diatomic molecule (A-B) is formulated as a sum of its atomic energies, EA and EB. Each of these atomic energies is expressed as, EA = Hᴬ + Vₑₑᴬᴬ + 1/2Vₑₑᴬ<>ᴮ EB = Hᴮ + Vₑₑᴮᴮ + 1/2Vₑₑᴬ<>ᴮ where; Hᴬ and Hᴮ are the kinetic and nuclear attraction energy of electrons of atoms A and B, respectively; Vₑₑᴬᴬ and Vₑₑᴮᴮ are the interaction energy between the electrons on atoms A and B, respectively; and Vₑₑᴬ<>ᴮ is the interaction energy between the electrons of atom A with the electrons of atom B. The energy of the molecule is then minimized subject to the following constraint, |ρA(r)dr + |ρB(r)dr = N where ρA(r) and ρB(r) are the electron densities of atoms A and B, respectively, and N is the number of electrons. The initial testing of the performance of GAIM was done through calculating dissociation curves for H₂, LiH, Li₂, BH, HF, HCl, N₂, F₂, and Cl₂. The numerical results show that GAIM performs very well with H₂, LiH, Li₂, BH, HF, and HCl. GAIM shows convergence problems with N₂, F₂, and Cl₂ due to difficulties in reordering the degenerate atomic orbitals Pₓ, Py, and Pz in N, F, and Cl atoms. Further work for the development of GAIM is required. Deamination of adenine results in one of several forms of premutagenic lesions occurring in DNA. In this thesis, mechanisms for the deamination reaction of adenine with OH⁻/nH₂O, (n = 0, 1, 2, 3) and 3H₂O were investigated. HF/6-31G(d), B3LYP/6-31G(d), MP2/6-31G(d), and B3LYP/6-31+G(d) levels of theory were employed to optimize all the geometries. Energies were calculated at the G3MP2B3 and CBS-QB3 levels of theory. The effect of solvent (water) was computed using the polarizable continuum model (PCM). Intrinsic reaction coordinate (IRC) calculations were performed for all transition states. Five pathways were investigated for the deamination reaction of adenine with OH⁻/nH₂O and 3H₂O. The first four pathways (A-D) begin with by deprotonation at the amino group of adenine by OH⁻, while pathway E is initiated by tautomerization of adenine. For all pathways, the next two steps involve the formation of a tetrahedral intermediate followed by dissociation to yield products via a 1,3-hydrogen shift. Deamination with a single OH⁻ has a high activation barrier (190 kJ mol⁻¹ using G3MP2B3 level) for the rate-determining step. Addition of one water molecule reduces this barrier by 68 kJ mol⁻¹ calculated at G3MP2B3 level. Adding more water molecules decreases the overall activation energy of the reaction, but the effect becomes smaller with each additional water molecule. The most plausible mechanism is pathway E, the deamination reaction of adenine with 3H₂O, which has an overall G3MP2B3 activation energy of 139 and 137 kJ mol⁻¹ in the gas phase and PCM, respectively. This barrier is lower than that for the deamination with OH⁻/3H₂O by 6 and 2 kJ mol⁻¹ in the gas phase and PCM, respectively.

Informal Qualitative Models: A Systematic Approach to their Generation

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