Blood pressure measurement has been and continues to be one of the most important measurements in clinical practice and yet, it remains one of the most inaccurately performed. The use of oscillometric blood pressure measurement monitors has become common in hospitals, clinics and even homes. Typically, these monitors assume that the heartbeat rate remains stable, which is contrary to what happens in atrial fibrillation. In this thesis, a new method that provides a more precise estimate of Mean Arterial Pressure (MAP) is proposed using anon-invasive oscillometric blood pressure monitor. The proposed method is based on calculating a ratio of peak amplitude to trough amplitude for every pulse, then identifying where the ratio first reaches a value of 2. The performance of the proposed method is assessed by comparing the accuracy and variability of the readings against reference monitors -first in healthy subjects, then in atrial fibrillation patients. In healthy subjects and in atrial fibrillation patients, the proposed method achieved a performance accuracy that is well within the ANSI/AAMI SP10 protocol requirements of the reference monitors. The presence of atrial fibrillation diminished the performance of the reference monitor by increasing the variability of the reference readings. The proposed algorithm, on the other hand, performed better by achieving substantially lower variability in the readings than the reference device.

An optical study of Mn and Mo isotopes has been performed in two contrasting regions of the nuclear chart. Collinear laser spectroscopic methods were employed using the Ion Guide Separator On-Line (IGISOL) at the University of Jyväskylä, Finland. Optical pumping in an ion-trap with the use of frequency quadrupled titanium sapphire lasers, greatly improved the efficiency of the spectroscopy performed.For the first time, the change in mean-square charge radius was determined for ground and isomeric states in 50-56Mn with a sharp shell closure seen across N = 28. Nuclear quadrupole moments in 50m,53,54,56Mn were also extracted, displaying trends similar to those of the charge radii. Newly extracted hyperfine structures and isotope shifts of 90-92,94-98,100,102-106,108Mo span the N = 50 shell closure and well-known N = 60 shape change. Unlike the Z = 38 - 41 isotopic chains, Mo exhibits a smooth increase in mean-square charge radius, with no sudden onset of deformation at N = 60. These measurements signify the end point of this strongly deformed A ~ 100 region in both Z and N. In the Z ~ 40 region, the charge radii follow the trends in the mass measurements near perfectly. However, in the Mn measurements a clear disparity between the mass and charge radii measurements is seen across the N = 28 magic shell closure. The absence of any shell effects in the Mn mass measurements show the importance of charge radii measurements, with pertinent implications for future investigations in the N = 40 region. Additionally, a portable data acquisition system for laser spectroscopy has been successfully tested. It is based on the LabJack system which will directly interface to a USB connection. It is able to register individual photons from amplified and converted photomultiplier tube signals (with bunched or continuous ion beams). The device drives a Cooknell voltage supply, which steps the voltage across the laser-ion interaction region. The introduction of an accurate 100 ms time window into the LabJack system has enabled a precise photon detection system for future off-line testing and on-line use. Further to this, a new method of locating hyperfine resonances has been introduced into our spectroscopy.

In this dissertation, I study critical phenomena and phase transitions in systems with long-range interactions, in particular, the ferromagnetic Ising model with quenched site dilution and the asset exchange model with growth. In the site-diluted Ising model, I focus on the effects of quenched disorder on both critical phenomena and nucleation. For critical phenomena, I generalize the Harris criterion for the mean-field critical point and the spinodal, and find that they are not affected by dilution, whereas pseudospinodals are smeared out. For nucleation, I find that dilution reduces the lifetime of the metastable state. I also investigate the structure of nucleating droplets in both nearest-neighbor and long-range Ising models. In both cases, nucleating droplets are more likely to occur in spatially more dilute regions. I also modify the asset exchange model to include different types of economic growth, such as constant growth and geometric growth. For constant growth, one agent eventually gets almost all the wealth regardless of the growth rate. For geometric growth, the wealth distribution depends on the way that the growth is distributed among agents, which is represented by the parameter 𝛾. For the evenly distributed growth, 𝛾=0, and as 𝛾 increases, the growth in the total wealth is distributed preferentially to richer agents. For 𝛾=1, the wealth of every agent grows at a rate that is linearly proportional to his/her wealth. I find a phase transition at 𝛾=1. For 𝛾<1, there is an rescaled steady state wealth distribution and the system is effectively ergodic. In this state, the wealth at all ranks grows exponentially in time and inequality stays constant. For 𝛾>1, one agent eventually obtains almost all the wealth, and the system is not ergodic. For 𝛾=1$, the dynamics of the poor agents' wealth is similar to that of a geometric random walk. In addition, I elucidate the effects of unfair trading, inhomogeneity in agents, modified growth which only depends on richest $1% agents' wealth, and a finite range of wealth exchange.

abstract: This dissertation studies the scheduling in two stochastic networks, a co-located wireless network and an outpatient healthcare network, both of which have a cyclic planning horizon and a deadline-related performance metric. For the co-located wireless network, a time-slotted system is considered. A cycle of planning horizon is called a frame, which consists of a fixed number of time slots. The size of the frame is determined by the upper-layer applications. Packets with deadlines arrive at the beginning of each frame and will be discarded if missing their deadlines, which are in the same frame. Each link of the network is associated with a quality of service constraint and an average transmit power constraint. For this system, a MaxWeight-type problem for which the solutions achieve the throughput optimality is formulated. Since the computational complexity of solving the MaxWeight-type problem with exhaustive search is exponential even for a single-link system, a greedy algorithm with complexity O(nlog(n)) is proposed, which is also throughput optimal. The outpatient healthcare network is modeled as a discrete-time queueing network, in which patients receive diagnosis and treatment planning that involves collaboration between multiple service stations. For each patient, only the root (first) appointment can be scheduled as the following appointments evolve stochastically. The cyclic planing horizon is a week. The root appointment is optimized to maximize the proportion of patients that can complete their care by a class-dependent deadline. In the optimization algorithm, the sojourn time of patients in the healthcare network is approximated with a doubly-stochastic phase-type distribution. To address the computational intractability, a mean-field model with convergence guarantees is proposed. A linear programming-based policy improvement framework is developed, which can approximately solve the original large-scale stochastic optimization in queueing networks of realistic sizes. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2020

Mean-field games (MFG) are models of large populations of rational agents who seek to optimize an objective function that takes into account their state variables and the distribution of the state variable of the remaining agents. MFG with congestion model problems where the agents’ motion is hampered in high-density regions. First, we study radial solutions for first- and second-order stationary MFG with congestion on Rd. The radial case, which is one of the simplest non one-dimensional MFG, is relatively tractable. As we observe, the Fokker-Planck equation is integrable with respect to one of the unknowns. Consequently, we obtain a single equation substituting this solution into the Hamilton-Jacobi equation. For the first-order case, we derive explicit formulas; for the elliptic case, we study a variational formulation of the resulting equation. For the first case, we use our approach to compute numerical approximations to the solutions of the corresponding MFG systems. Next, we consider second-order stationary MFG with congestion and prove the existence of stationary solutions. Because moving in congested areas is difficult, agents prefer to move in non-congested areas. As a consequence, the model becomes singular near the zero density. The existence of stationary solutions was previously obtained for MFG with quadratic Hamiltonians thanks to a very particular identity. Here, we develop robust estimates that give the existence of a solution for general subquadratic Hamiltonians. Additionally, we study first-order stationary MFG with congestion with quadratic or power-like Hamiltonians. Using explicit examples, we illustrate two key difficulties: the lack of classical solutions and the existence of areas with vanishing densities. Our main contribution is a new variational formulation for MFG with congestion. With this formulation, we prove the existence and uniqueness of solutions. Finally, we devise a discretization that is combined with optimization algorithms to numerically solve various MFG with congestion.

A plot that includes multiple location and spread statistics can provide useful information about the shape of a distribution, not only with respect to location and variability but also with respect to skewness and kurtosis. We propose a plot containing the interquartile range, mean absolute deviation, standard deviation, and range of a dataset. The comparison of the spread statistics gives information about kurtosis and the comparison of the location statistics gives information about skewness. After the distribution has been divided into two parts by the median, the interquartile range can be thought of as the distance between the medians in each half of the distribution. We explain how the mean absolute deviation with respect to the median can similarly be visualized as half the distance between the means in each half of the distribution. An R function to produce the polyplot is available as an online supplement.

A new confidence interval for the coefficient of dispersion (mean absolute deviation from the median divided by median) is proposed and is shown to perform better than the BCa bootstrap confidence interval.

In this dissertation, new theoretical results are obtained for bounding convergence and mean-square error in conditional coding. Further new statistical methods for the practical application of conditional coding are developed. Criteria for the uniform convergence are first examined. Conditional coding Markov chains are aperiodic, π-irreducible, and Harris recurrent. By applying the general theories of uniform ergodicity of Markov chains on genera l state space, one can conclude that conditional coding Markov cha ins are uniformly ergodic and further, theoretical convergence rates based on Doeblin's condition can be found. Conditional coding Markov chains can be also viewed as having finite state space. This allows use of techniques to get bounds on the second largest eigenvalue which lead to bounds on convergence rate and the mean-square error of sample averages. The results are applied in two examples showing that these bounds are useful in practice. Next some algorithms for perfect sampling in conditional coding are studied. An application of exact sampling to the independence sampler is shown to be equivalent to standard rejection sampling. In case of single-site updating, traditional perfect sampling is not directly applicable when the state space has large cardinality and is not stochastically ordered, so a new procedure is developed that gives perfect samples at a predetermined confidence interval. In last chapter procedures and possibilities of applying conditional coding to mixture models are explored. Conditional coding can be used for analysis of a finite mixture model. This methodology is general and easy to use.

The purpose of this thesis was to compare two estimation procedures, the method of least squares and the method of maximum likelihood, on sample data obtained from a Poisson distribution. Point estimates of the slope and intercept of the regression line and point estimates of the mean squared error for both the slope and intercept were obtained. It is shown that least squares, the preferred method due to its simplicity, does yield results as good as maximum likelihood. Also, confidence intervals were computed by Monte Carlo techniques and then were tested for accuracy. For the method of least squares, confidence bands for the regression line were computed under two different assumptions concerning the variance. It is shown that the assumption of constant variance produces false confidence bands. However, the assumption of the variance equal to the mean yielded accurate results.

We use a combination of Density Functional Theory and Dynamical Mean Field Theory (DFT+DMFT) to study electronic correlations in unconventional superconductors, with a focus on nickelate analogs of cuprate superconductors. We study the infinite layer nickelate superconductor NdNiO₂ in parallel with the isostructural CaCuO₂. Our results point to superconductivity in the nickelate being cupratelike, with correlations dominated by a hybrid Ni-𝑑_{𝑥²-𝑦²} and O-𝑝 band, and with the extra bands not contributing substantially to the superconducting state. We find that the infinite layer nickelate NdNiO₂ and the trilayer nickelate Pr₄Ni₃O₈ are virtually identical in terms of correlation physics when compared at the same chemical doping, despite the differences in Fermiology, indicating that the number of layers can stand in for chemical doping for some properties related to electronic correlations. We find that as opposed to in narrow window DFT+DMFT, in wide window DFT+DMFT the choice of downfolding procedure leads to very different results. This is an important ambiguity in the method that must be resolved or the method is incomplete by itself. We also study Sr₂MoO₄ in parallel with the Hund's superconductor Sr₂RuO₄, and find that Sr₂MoO₄ is a particle-hole dual of Sr₂RuO₄ but without the van Hove singularity at the Fermi level, which disentangles the influence of the van Hove singularity from Hund's physics. We show that Sr₂MoO₄ has a characteristic Hund's peak on the occupied of the spectral function, indicating that the peak should be observable by photoemission experiments.