We study numerical stability for interior-point methods applied to Linear Programming, LP, and Semidefinite Programming, SDP. We analyze the difficulties inherent in current methods and present robust algorithms. <br /><br /> We start with the error bound analysis of the search directions for the normal equation approach for LP. Our error analysis explains the surprising fact that the ill-conditioning is not a significant problem for the normal equation system. We also explain why most of the popular LP solvers have a default stop tolerance of only 10^-8 when the machine precision on a 32-bit computer is approximately 10^-16. <br /><br /> We then propose a simple alternative approach for the normal equation based interior-point method. This approach has better numerical stability than the normal equation based method. Although, our approach is not competitive in terms of CPU time for the NETLIB problem set, we do obtain higher accuracy. In addition, we obtain significantly smaller CPU times compared to the normal equation based direct solver, when we solve well-conditioned, huge, and sparse problems by using our iterative based linear solver. Additional techniques discussed are: crossover; purification step; and no backtracking. <br /><br /> Finally, we present an algorithm to construct SDP problem instances with prescribed strict complementarity gaps. We then introduce two <em>measures of strict complementarity gaps</em>. We empirically show that: (i) these measures can be evaluated accurately; (ii) the size of the strict complementarity gaps correlate well with the number of iteration for the SDPT3 solver, as well as with the local asymptotic convergence rate; and (iii) large strict complementarity gaps, coupled with the failure of Slater's condition, correlate well with loss of accuracy in the solutions. In addition, the numerical tests show that there is no correlation between the strict complementarity gaps and the geometrical measure used in [31], or with Renegar's condition number.

Bakgrunden till min studie kommer ursprungligen från mitt eget intresse att diskutera ämnesintegrerad undervisnings betydelse i skola och samhälle. Syftet med föreliggande studie är att utifrån ett multimodalt perspektiv ta reda på hur en musiklärare och en specialpedagog i matematik samarbetar för att integrera matematik och musik i sin undervisning i årskurs 1-3. Jag har använt mig av observationer och samtal för att ta reda på hur de arbetar, vilka redskap de använder sig av samt varför de arbetar som de gör.     Den undervisning jag har observerat kallas mattemusik och är en utarbetad metod för ämnesintegrerat lärande. I resultatet visas att det är läroplanens mål och kunskapskrav i matematik och musik som styr undervisningen och att de två lärarna anser att det sätt som undervisningen bedrivs på även uppfyller många sociala mål som till exempel samarbetsförmåga, hänsynstagande och turtagning. Lektionerna i mattemusik utgick från ett tema och sedan arbetade lärarna tillsammans med eleverna mot den nya kunskapen ifrån många olika håll och med flera sinnen involverade. Undervisningen var i många avseenden multimodal då även momenten under lektionerna i sig själva var det.     Det jag tar upp i diskussionen är bland annat avsaknaden av det taktila sinnet som inte fanns representerat i lika stor utsträckning som de visuella, auditiva och kinestetiska sinnena. / The background of my study is originally my own interest in discussing the role of crossover teaching in school and society. The purpose of this study is to discern how one music teacher and one special education teacher in mathematics work to integrate mathematics and music in their teaching in grades 1-3 from a multimodal perspective. I have used observations and conversations to determine how the teachers work, why they work the way they do, and what tools they are using.     The teaching I have observed is called math-music and it is an elaborate method of crossover teaching in mathematics and music. The result shows that it is the curriculum goals and knowledge in mathematics and music that governs the teaching and that the two teachers believe that the way teaching is carried on also fulfills many social goals such as teamwork, consideration and turn-taking. The classes in math-music were based on one theme, with  teachers and students working together from different perspectives, involving multiple senses. In many respects the teaching was multimodal, in which even different parts of the teaching, one by one, was multimodal in themselves.     What I discuss includes the lack of the tactile sense, which was not represented as much as the visual, auditory and kinesthetic senses.

We study numerical stability for interior-point methods applied to Linear Programming, LP, and Semidefinite Programming, SDP. We analyze the difficulties inherent in current methods and present robust algorithms. <br /><br /> We start with the error bound analysis of the search directions for the normal equation approach for LP. Our error analysis explains the surprising fact that the ill-conditioning is not a significant problem for the normal equation system. We also explain why most of the popular LP solvers have a default stop tolerance of only 10^-8 when the machine precision on a 32-bit computer is approximately 10^-16. <br /><br /> We then propose a simple alternative approach for the normal equation based interior-point method. This approach has better numerical stability than the normal equation based method. Although, our approach is not competitive in terms of CPU time for the NETLIB problem set, we do obtain higher accuracy. In addition, we obtain significantly smaller CPU times compared to the normal equation based direct solver, when we solve well-conditioned, huge, and sparse problems by using our iterative based linear solver. Additional techniques discussed are: crossover; purification step; and no backtracking. <br /><br /> Finally, we present an algorithm to construct SDP problem instances with prescribed strict complementarity gaps. We then introduce two <em>measures of strict complementarity gaps</em>. We empirically show that: (i) these measures can be evaluated accurately; (ii) the size of the strict complementarity gaps correlate well with the number of iteration for the SDPT3 solver, as well as with the local asymptotic convergence rate; and (iii) large strict complementarity gaps, coupled with the failure of Slater's condition, correlate well with loss of accuracy in the solutions. In addition, the numerical tests show that there is no correlation between the strict complementarity gaps and the geometrical measure used in [31], or with Renegar's condition number.

This thesis focuses on the analysis of Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) evolution in ultracold superfluid Fermi gases when the interaction between atoms is varied. The tuning of attractive interactions permits the ground state of the system to evolve from a weak fermion attraction BCS limit of loosely bound and largely overlapping Cooper pairs to a strong fermion attraction limit of tightly bound small bosonic molecules which undergo BEC. This evolution is accompanied by anomalous behavior of many superfluid properties, and reveals several quantum phase transitions. This thesis has two parts: In the first part, I analyze zero and nonzero orbital angular momentum pairing effects, and show that a quantum phase transition occurs for nonzero angular momentum pairing, unlike the $s$-wave case where the BCS to BEC evolution is just a crossover. In the second part, I analyze two-species fermion mixtures with mass and population imbalance in continuum, trap and lattice models. In contrast with the crossover physics found in the mass and population balanced mixtures, I demonstrate the existence of phase transitions between normal and superfluid phases, as well as phase separation between superfluid (paired) and normal (excess) fermions in imbalanced mixtures as a function of scattering parameter and mass and population imbalance.

In this thesis, a long-term operation direct methanol fuel cell (DMFC) stack is developed. In order to reach this goal required in many ways, including select highly chemical stability materials, operating conditions must also be stable, and avoid changing the MEA structure when preserved, then can cause the DMFC to maintain stable operation for a long time. First of all, in order to avoid contaminating electrode, this study find out the chemical instability materials. Second, this study design a device which does not require power then can stability supply consumption fuel, and apply this device in 16-cell DMFC. Finally compare with continuous fuel supply and without fuel supply, two operating conditions performance stability. From these experiments can find out, the DMFC indeed in stable operation for a long time under the appropriate supplement. Traditional fuel supply systems typically using the pump fuel recycling, so the structure is more complex, difficult to reduce the volume, and not conducive to carry. If using a passive operation, fuel completely stored in the reaction Chamber, even though the structure is simple there will be a problem with fuel supply. In recent years, someone use vapors of methanol to supply the fuel, although can use high concentration methanol to extend operating time, but the evaporation rate is difficult to control, the fuel can¡¦t be supplied in time, especially when the large current is needed, and CROSSOVER issues would be difficult to overcome. In our 16-cell DMFC, continues to add appropriate amount of fuel consumed which according to the different current. The fuel supply device with a sliding control plate which can control methanol and water diffusion rate respectively. This device only to provide consumed by reaction and leaked fuel in anode chamber, so that the methanol concentration can maintained in the proper range at anode chamber. This device only use diffusion and gravity effects, don't use a fuel pump, so will not consume DMFC power.

Abstract A one-watt portable air-breathing direct methanol fuel cell stack (called DMFC), which can supply fuel passively and operate steadily, is developed in this thesis. A DMFC to maintain its performance stable, the most important strategy is to keep the methanol concentration in reacting chamber to be proper and stable. A fuel supplying system will be in accordance with the depletion of chemical reaction and the leakage of fuel under different circuit current to supplying fuel. To regulate the methanol and water supplying, a fuel supplying system by gravitation and diffusion forces deliver methanol and water to fill up the consumed fuel to maintain the concentration of methanol solution in anode reaction chamber, by adjusting a sliding gate to control the area of a diffusive membrane and utilizing three cotton threads and hoses to distribute the fuel to proper location. In doing so, the methanol concentration in the anode chamber can keep within an appropriate range, so that the DMFC stack can operate stably for a longer period. Yet the diffusivity of the diffusive membrane is comparatively less, the supply system is not easy to downsize. To reduce the size of portable DMFC, we make use of a fuel plug tank to combine the supply tank and reacting chamber, and thus the cell package is more portable. Between the plug tank and the reacting chamber, the three cotton threads are used to distribute the fuel to proper location. The above two design with no extra auxiliary device; therefore, no extra energy will be consumed. To reduce the fuel leakage, and make more use of fuel, four block films is pasted on the bare area of the nafion membranes in a 16-cell DMFC stack. If no fuel is fed into reaction chamber, this will prolong the cell operation time. Under the condition of 3.7 V (cell phone rated voltage) and the operating current 225 mA, our experiments display that the stacks with the two fuel supplying systems can continuously operate for more than 3 hours with no obvious change in methanol concentration within reaction chamber. The experimental results show that this simple passive fuel supplemental system can really keep the DMFC stack operating stably for a sufficient long period.

A genetic algorithm using conventional heuristics as operators is considered in this study for the traveling salesman problem with backhauls (TSPB). Properties of a crossover operator (Nearest Neighbor Crossover, NNX) based on the nearest neighbor heuristic and the idea of using more than two parents are investigated in a series of experiments. Different parent selection and replacement strategies and generation of multiple children are tried as well. Conventional improvement heuristics are also used as mutation operators. It has been observed that 2-edge exchange and node insertion heuristics work well with NNX using only two parents. The best settings among different alternatives experimented are applied on traveling salesman problem with backhauls (TSPB). TSPB is a problem in which there are two groups of customers. The aim is to minimize the distance traveled visiting all the cities, where the second group can be visited only after all cities in the first group are already visited. The approach we propose shows very good performance on randomly generated TSPB instances.

The increasing performance of computers, reduced prices and ability to connect systems with low cost gigabit ethernet LAN and ATM WAN networks make distributed database systems an attractive research area. However, the complexity of distributed database query optimization is still a limiting factor. Optimal techniques, such as dynamic programming, used in centralized database query optimization are not feasible because of the increased problem size. The recently developed genetic algorithm (GA) based optimization techniques presents a promising alternative. We compared the best known GA with a random algorithm and showed that it achieves almost no improvement over the random search algorithm generating an equal number of random solutions. Then, we analyzed a set of possible GA parameters and determined that two-point truncate technique using GA gives the best results. New mutation and crossover operators defined in our GA are experimentally analyzed within a synthetic distributed database having increasing the numbers of relations and nodes. The designed synthetic database replicated relations, but there was no horizontal/vertical fragmentation. We can translate a select-project-join query including a fragmented relation with N fragments into a corresponding query with N relations. Comparisons with optimal results found by exhaustive search are only 20% off the results produced by our new GA formulation showing a 50% improvement over the previously known GA based algorithm.

When a liquid is cooled below its equilibrium freezing temperature, it becomes supercooled and the molecular motions slow down until the system becomes kinetically arrested, forming a glass, at the glass transition temperature. These amorphous materials have the mechanical properties of a solid while retaining the structural properties of a liquid, but do not exhibit the usual features of a thermodynamic phase transition. As such, they present a number of important challenges to our understanding of the dynamics and thermodynamics of condensed phases. For example, supercooled liquids are classified on the basis of the temperature dependence of their transport properties and structural relaxations times. Strong liquids display an Arrhenius behavior, with the logarithm of their viscosity growing linearly with inverse temperature. Fragile liquids behave in a super-Arrhenius manner, where the viscosity appears to diverge at temperatures above absolute zero, suggesting the possibility of an underlying thermodynamic origin to the glass transition. Some complex, network forming liquids, such as water and silica have also been shown to have a dynamical crossover from fragile to strong liquid behavior as the temperature is decreased. The potential energy landscape paradigm, combined with inherent structure formalism, provide a framework for connecting the way particles pack together with the thermodynamics and dynamics of the liquid and glassy phases. However, the complexity of this multi-dimensional surface makes it difficult to fully characterize and rigorous relationships between the nature of particle packing and glass forming properties have not been established. The goal of this thesis is to study some of the general features of glass transition and find the connection between the dynamics and the thermodynamics of glass forming liquids. To this end, the packing landscapes of quasi-one-dimensional hard discs and hard spheres are studied. A two dimensional system of hard discs with diameter σ, confined between two hard walls (lines) of length L, separated by a distance 1<Hd/σ< 1+√(3/4), is studied by using the Transfer Matrix (TM) method and Molecular Dynamics (MD) simulations. The complete packing landscape is characterized in terms of the density distribution of inherent structures and the number of local defect states. It is shown that this model exhibits a dynamic fragile-strong liquid crossover at the maximum in the constant pressure heat capacity (Cp) for the system, similar to that observed in anomalous network forming liquids such as water and silica. Furthermore, we find that rescaling the relaxation times of systems with different channel widths by the relaxation time at the Cp maximum causes all the data to collapse on a single master curve. The Cp maximum occurs at a critical value of the defect concentration. At high defect concentrations, where the defects interact, the fluid is fragile. When the defect concentration is low, relaxation appears to occur through the hopping of isolated defects, leading to Arrhenius dynamics. This suggests the thermodynamics associated with the Cp maximum is intimately related to the dynamic crossover. A system of three-dimensional hard spheres confined in a narrow channel was used to study the effect of a more complicated landscape on the dynamics of the system. For this system, the thermodynamic and dynamic properties of the system were studied for two different channel diameters, the 1<Hd/σ<1+√(3/4) case, which only allows first neighbors contact for the spheres and, 1+√(3/4)< Hd/σ < 1.98, which allows second neighbors contact to exist. For the first case, the TM method was implemented to obtain the thermodynamic properties and MD simulation was used to measure the dynamics. For the case that the second neighbor contact is allowed 1+√(3/4)< Hd/σ < 1.98. The thermodynamic and dynamic properties were obtained using MD simulations. In this channel diameter range, the system creates chiral helical jammed packings and defect states appear where sections of helices with different local chiralities come into contact. The equation of state (EOS) shows the presence of two heat capacity maxima. The high density Cp maximum is linked to fragile strong crossover. Finite size scaling analysis shows that the low density Cp maximum is related to an orientational order transition stabilized by the presence of the defects. This type of transition has been shown to exist in bulk two-dimensional systems but this work is the first study that provides strong evidence of the existence of this transition in a quasi-one-dimensional system in a system with short-range interactions.

Demographic researchers have identified a crossover pattern between the mortality rates of the Caucasian-American and African-American oldest-old (80+) populations for over a century. Debate has centered on whether the crossover effect is due to age misreporting or the heterogeneity hypothesis or if it continues beyond age 99. This thesis addresses these issues by using new data from the SSA’s study of supercentenarians. The study identified 355 persons aged 110 or older whose ages could be verified, creating the first reliable American dataset for this population group. Analysis of the data has indicated that mortality rates at ages 110-115 were significantly lower for African-American supercentenarians than for their Caucasian-American counterparts, and that the African-American proportion of the population increased steadily with age. The results of this analysis show that the crossover phenomenon is multicausal and cannot be fully accounted for by age misreporting, suggesting a need to consider genetic and environmental impacts on racial variations in maximum human longevity.