Multi-model inference ranking and applications to physics at the Large Hadron Collider

In the measurement of the Higgs Boson decaying into two photons the parametrization of an appropriate background model is essential for fitting the Higgs signal mass peak over a continuous background. This diphoton background modeling is crucial in the statistical process of calculating exclusion limits and the significance of observations in comparison to a background-only hypothesis. It is therefore ideal to obtain knowledge of the physical shape for the background mass distribution as the use of an improper function can lead to biases in the observed limits. Using an Information-Theoretic (I-T) approach for valid inference we apply Akaike Information Criterion (AIC) as a measure of the separation for a fitting model from the data. We then implement a multi-model inference ranking method to build a fit-model that closest represents the Standard Model background in 2013 diphoton data recorded by the Compact Muon Solenoid (CMS) experiment at the Large Hadron Collider (LHC). Potential applications and extensions of this model-selection technique are discussed with reference to CMS detector performance measurements as well as in potential physics analyses at future detectors.

Single cell proteomics microchip to profile immune function, with applications in stem cell biology, translational disease mechanism study and clinical therapeutics monitoring

In response to infection or tissue dysfunction, immune cells develop into highly heterogeneous repertoires with diverse functions. Capturing the full spectrum of these functions requires analysis of large numbers of effector molecules from single cells. However, currently only 3-5 functional proteins can be measured from single cells. We developed a single cell functional proteomics approach that integrates a microchip platform with multiplex cell purification. This approach can quantitate 20 proteins from >5,000 phenotypically pure single cells simultaneously. With a 1-million fold miniaturization, the system can detect down to ~100 molecules and requires only ~104 cells. Single cell functional proteomic analysis finds broad applications in basic, translational and clinical studies. In the three studies conducted, it yielded critical insights for understanding clinical cancer immunotherapy, inflammatory bowel disease (IBD) mechanism and hematopoietic stem cell (HSC) biology.

To study phenotypically defined cell populations, single cell barcode microchips were coupled with upstream multiplex cell purification based on up to 11 parameters. Statistical algorithms were developed to process and model the high dimensional readouts. This analysis evaluates rare cells and is versatile for various cells and proteins. (1) We conducted an immune monitoring study of a phase 2 cancer cellular immunotherapy clinical trial that used T-cell receptor (TCR) transgenic T cells as major therapeutics to treat metastatic melanoma. We evaluated the functional proteome of 4 antigen-specific, phenotypically defined T cell populations from peripheral blood of 3 patients across 8 time points. (2) Natural killer (NK) cells can play a protective role in chronic inflammation and their surface receptor – killer immunoglobulin-like receptor (KIR) – has been identified as a risk factor of IBD. We compared the functional behavior of NK cells that had differential KIR expressions. These NK cells were retrieved from the blood of 12 patients with different genetic backgrounds. (3) HSCs are the progenitors of immune cells and are thought to have no immediate functional capacity against pathogen. However, recent studies identified expression of Toll-like receptors (TLRs) on HSCs. We studied the functional capacity of HSCs upon TLR activation. The comparison of HSCs from wild-type mice against those from genetics knock-out mouse models elucidates the responding signaling pathway.

In all three cases, we observed profound functional heterogeneity within phenotypically defined cells. Polyfunctional cells that conduct multiple functions also produce those proteins in large amounts. They dominate the immune response. In the cancer immunotherapy, the strong cytotoxic and antitumor functions from transgenic TCR T cells contributed to a ~30% tumor reduction immediately after the therapy. However, this infused immune response disappeared within 2-3 weeks. Later on, some patients gained a second antitumor response, consisted of the emergence of endogenous antitumor cytotoxic T cells and their production of multiple antitumor functions. These patients showed more effective long-term tumor control. In the IBD mechanism study, we noticed that, compared with others, NK cells expressing KIR2DL3 receptor secreted a large array of effector proteins, such as TNF-α, CCLs and CXCLs. The functions from these cells regulated disease-contributing cells and protected host tissues. Their existence correlated with IBD disease susceptibility. In the HSC study, the HSCs exhibited functional capacity by producing TNF-α, IL-6 and GM-CSF. TLR stimulation activated the NF-κB signaling in HSCs. Single cell functional proteome contains rich information that is independent from the genome and transcriptome. In all three cases, functional proteomic evaluation uncovered critical biological insights that would not be resolved otherwise. The integrated single cell functional proteomic analysis constructed a detail kinetic picture of the immune response that took place during the clinical cancer immunotherapy. It revealed concrete functional evidence that connected genetics to IBD disease susceptibility. Further, it provided predictors that correlated with clinical responses and pathogenic outcomes.

Molecular mechanisms of interleukin-2 gene inducibility: developmental control and combinatorial action of transcription factors

Interleukin-2 is one of the lymphokines secreted by T helper type 1 cells upon activation mediated by T-cell receptor (TCR) and accessory molecules. The ability to express IL-2 is correlated with T-lineage commitment and is regulated during T cell development and differentiation. Understanding the molecular mechanism of how IL-2 gene inducibility is controlled at each transition and each differentiation process of T-cell development is to understand one aspect of T-cell development. In the present study, we first attempted to elucidate the molecular basis for the developmental changes of IL-2 gene inducibility. We showed that IL-2 gene inducibility is acquired early in immature CD4- CD8-TCR- thymocytes prior to TCR gene rearrangement. Similar to mature T cells, a complete set of transcription factors can be induced at this early stage to activate IL-2 gene expression. The progression of these cells to cortical CD4^+CD8^+TCR^(1o) cells is accompanied by the loss of IL-2 gene inducibility. We demonstrated that DNA binding activities of two transcription factors AP-1 and NF-AT are reduced in cells at this stage. Further, the loss of factor binding, especially AP-1, is attributable to the reduced ability to activate expression of three potential components of AP-1 and NF-AT, including c-Fos, FosB, and Fra-2. We next examined the interaction of transcription factors and the IL-2 promoter in vivo by using the EL4 T cell line and two non-T cell lines. We showed an all-or-none phenomenon regarding the factor-DNA interaction, i.e., in activated T cells, the IL-2 promoter is occupied by sequence-specific transcription factors when all the transcription factors are available; in resting T cells or non-T cells, no specific protein-DNA interaction is observed when only a subset of factors are present in the nuclei. Purposefully reducing a particular set of factor binding activities in stimulated T cells using pharmacological agents cyclosporin A or forskolin also abolished all interactions. The results suggest that a combinatorial and coordinated protein-DNA interaction is required for IL-2 gene activation. The thymocyte experiments clearly illustrated that multiple transcription factors are regulated during intrathymic T-cell development, and this regulation in tum controls the inducibility of the lineage-specific IL-2 gene. The in vivo study of protein-DNA interaction stressed the combinatorial action of transcription factors to stably occupy the IL-2 promoter and to initiate its transcription, and provided a molecular mechanism for changes in IL-2 gene inducibility in T cells undergoing integration of multiple environmental signals.

Robot navigation in dense crowds : statistical models and experimental studies of human robot cooperation

This thesis explores the problem of mobile robot navigation in dense human crowds. We begin by considering a fundamental impediment to classical motion planning algorithms called the freezing robot problem: once the environment surpasses a certain level of complexity, the planner decides that all forward paths are unsafe, and the robot freezes in place (or performs unnecessary maneuvers) to avoid collisions. Since a feasible path typically exists, this behavior is suboptimal. Existing approaches have focused on reducing predictive uncertainty by employing higher fidelity individual dynamics models or heuristically limiting the individual predictive covariance to prevent overcautious navigation. We demonstrate that both the individual prediction and the individual predictive uncertainty have little to do with this undesirable navigation behavior. Additionally, we provide evidence that dynamic agents are able to navigate in dense crowds by engaging in joint collision avoidance, cooperatively making room to create feasible trajectories. We accordingly develop interacting Gaussian processes, a prediction density that captures cooperative collision avoidance, and a "multiple goal" extension that models the goal driven nature of human decision making. Navigation naturally emerges as a statistic of this distribution.

Most importantly, we empirically validate our models in the Chandler dining hall at Caltech during peak hours, and in the process, carry out the first extensive quantitative study of robot navigation in dense human crowds (collecting data on 488 runs). The multiple goal interacting Gaussian processes algorithm performs comparably with human teleoperators in crowd densities nearing 1 person/m², while a state of the art noncooperative planner exhibits unsafe behavior more than 3 times as often as the multiple goal extension, and twice as often as the basic interacting Gaussian process approach. Furthermore, a reactive planner based on the widely used dynamic window approach proves insufficient for crowd densities above 0.55 people/m². We also show that our noncooperative planner or our reactive planner capture the salient characteristics of nearly any dynamic navigation algorithm. For inclusive validation purposes, we show that either our non-interacting planner or our reactive planner captures the salient characteristics of nearly any existing dynamic navigation algorithm. Based on these experimental results and theoretical observations, we conclude that a cooperation model is critical for safe and efficient robot navigation in dense human crowds.

Finally, we produce a large database of ground truth pedestrian crowd data. We make this ground truth database publicly available for further scientific study of crowd prediction models, learning from demonstration algorithms, and human robot interaction models in general.

Control of wettability of carbon nanotube array by reversible dry oxidation for superhydrophobic coating and supercapacitor applications

In this thesis, dry chemical modification methods involving UV/ozone, oxygen plasma, and vacuum annealing treatments are explored to precisely control the wettability of CNT arrays. By varying the exposure time of these treatments the surface concentration of oxygenated groups adsorbed on the CNT arrays can be controlled. CNT arrays with very low amount of oxygenated groups exhibit a superhydrophobic behavior. In addition to their extremely high static contact angle, they cannot be dispersed in DI water and their impedance in aqueous electrolytes is extremely high. These arrays have an extreme water repellency capability such that a water droplet will bounce off of their surface upon impact and a thin film of air is formed on their surface as they are immersed in a deep pool of water. In contrast, CNT arrays with very high surface concentration of oxygenated functional groups exhibit an extreme hydrophilic behavior. In addition to their extremely low static contact angle, they can be dispersed easily in DI water and their impedance in aqueous electrolytes is tremendously low. Since the bulk structure of the CNT arrays are preserved during the UV/ozone, oxygen plasma, and vacuum annealing treatments, all CNT arrays can be repeatedly switched between superhydrophilic and superhydrophobic, as long as their O/C ratio is kept below 18%.

The effect of oxidation using UV/ozone and oxygen plasma treatments is highly reversible as long as the O/C ratio of the CNT arrays is kept below 18%. At O/C ratios higher than 18%, the effect of oxidation is no longer reversible. This irreversible oxidation is caused by irreversible changes to the CNT atomic structure during the oxidation process. During the oxidation process, CNT arrays undergo three different processes. For CNT arrays with O/C ratios lower than 40%, the oxidation process results in the functionalization of CNT outer walls by oxygenated groups. Although this functionalization process introduces defects, vacancies and micropores opening, the graphitic structure of the CNT is still largely intact. For CNT arrays with O/C ratios between 40% and 45%, the oxidation process results in the etching of CNT outer walls. This etching process introduces large scale defects and holes that can be obviously seen under TEM at high magnification. Most of these holes are found to be several layers deep and, in some cases, a large portion of the CNT side walls are cut open. For CNT arrays with O/C ratios higher than 45%, the oxidation process results in the exfoliation of the CNT walls and amorphization of the remaining CNT structure. This amorphization process can be implied from the disappearance of C-C sp2 peak in the XPS spectra associated with the pi-bond network.

The impact behavior of water droplet impinging on superhydrophobic CNT arrays in a low viscosity regime is investigated for the first time. Here, the experimental data are presented in the form of several important impact behavior characteristics including critical Weber number, volume ratio, restitution coefficient, and maximum spreading diameter. As observed experimentally, three different impact regimes are identified while another impact regime is proposed. These regimes are partitioned by three critical Weber numbers, two of which are experimentally observed. The volume ratio between the primary and the secondary droplets is found to decrease with the increase of Weber number in all impact regimes other than the first one. In the first impact regime, this is found to be independent of Weber number since the droplet remains intact during and subsequent to the impingement. Experimental data show that the coefficient of restitution decreases with the increase of Weber number in all impact regimes. The rate of decrease of the coefficient of restitution in the high Weber number regime is found to be higher than that in the low and moderate Weber number. Experimental data also show that the maximum spreading factor increases with the increase of Weber number in all impact regimes. The rate of increase of the maximum spreading factor in the high Weber number regime is found to be higher than that in the low and moderate Weber number. Phenomenological approximations and interpretations of the experimental data, as well as brief comparisons to the previously proposed scaling laws, are shown here.

Dry oxidation methods are used for the first time to characterize the influence of oxidation on the capacitive behavior of CNT array EDLCs. The capacitive behavior of CNT array EDLCs can be tailored by varying their oxygen content, represented by their O/C ratio. The specific capacitance of these CNT arrays increases with the increase of their oxygen content in both KOH and Et4NBF4/PC electrolytes. As a result, their gravimetric energy density increases with the increase of their oxygen content. However, their gravimetric power density decreases with the increase of their oxygen content. The optimally oxidized CNT arrays are able to withstand more than 35,000 charge/discharge cycles in Et4NBF4/PC at a current density of 5 A/g while only losing 10% of their original capacitance.

Control of dynamical systems with temporal logic specifications

This thesis is motivated by safety-critical applications involving autonomous air, ground, and space vehicles carrying out complex tasks in uncertain and adversarial environments. We use temporal logic as a language to formally specify complex tasks and system properties. Temporal logic specifications generalize the classical notions of stability and reachability that are studied in the control and hybrid systems communities. Given a system model and a formal task specification, the goal is to automatically synthesize a control policy for the system that ensures that the system satisfies the specification. This thesis presents novel control policy synthesis algorithms for optimal and robust control of dynamical systems with temporal logic specifications. Furthermore, it introduces algorithms that are efficient and extend to high-dimensional dynamical systems.

The first contribution of this thesis is the generalization of a classical linear temporal logic (LTL) control synthesis approach to optimal and robust control. We show how we can extend automata-based synthesis techniques for discrete abstractions of dynamical systems to create optimal and robust controllers that are guaranteed to satisfy an LTL specification. Such optimal and robust controllers can be computed at little extra computational cost compared to computing a feasible controller.

The second contribution of this thesis addresses the scalability of control synthesis with LTL specifications. A major limitation of the standard automaton-based approach for control with LTL specifications is that the automaton might be doubly-exponential in the size of the LTL specification. We introduce a fragment of LTL for which one can compute feasible control policies in time polynomial in the size of the system and specification. Additionally, we show how to compute optimal control policies for a variety of cost functions, and identify interesting cases when this can be done in polynomial time. These techniques are particularly relevant for online control, as one can guarantee that a feasible solution can be found quickly, and then iteratively improve on the quality as time permits.

The final contribution of this thesis is a set of algorithms for computing feasible trajectories for high-dimensional, nonlinear systems with LTL specifications. These algorithms avoid a potentially computationally-expensive process of computing a discrete abstraction, and instead compute directly on the system's continuous state space. The first method uses an automaton representing the specification to directly encode a series of constrained-reachability subproblems, which can be solved in a modular fashion by using standard techniques. The second method encodes an LTL formula as mixed-integer linear programming constraints on the dynamical system. We demonstrate these approaches with numerical experiments on temporal logic motion planning problems with high-dimensional (10+ states) continuous systems.

Temporal and spacial control of RNA stability in the early embryo of Drosophila melanogaster

Early embryogenesis in metazoa is controlled by maternally synthesized products. Among these products, the mature egg is loaded with transcripts representing approximately two thirds of the genome. A subset of this maternal RNA pool is degraded prior to the transition to zygotic control of development. This transfer of control of development from maternal to zygotic products is referred to as the midblastula transition (or MBT). It is believed that the degradation of maternal transcripts is required to terminate maternal control of development and to allow zygotic control of development to begin. Until now this process of maternal transcript degradation and the subsequent timing of the MBT has been poorly understood. I have demonstrated that in the early embryo there are two independent RNA degradation pathways, either of which is sufficient for transcript elimination. However, only the concerted action of both pathways leads to elimination of transcripts with the correct timing, at the MBT. The first pathway is maternally encoded, is triggered by egg activation, and is targeted to specific classes of mRNAs through cis-acting elements in the 3' untranslated region (UTR}. The second pathway is activated 2 hr after fertilization and functions together with the maternal pathway to ensure that transcripts are degraded by the MBT. In addition, some transcripts fail to degrade at select subcellular locations adding an element of spatial control to RNA degradation. The spatial control of RNA degradation is achieved by protecting, or masking, transcripts from the degradation machinery. The RNA degradation and protection events are regulated by distinct cis-elements in the 3' untranslated region (UTR). These results provide the first systematic dissection of this highly conserved process in development and demonstrate that RNA degradation is a novel mechanism used for both temporal and spatial control of development.

Statistical and econometric analysis of the treatment of HIV/AIDS

The epidemic of HIV/AIDS in the United States is constantly changing and evolving, starting from patient zero to now an estimated 650,000 to 900,000 Americans infected. The nature and course of HIV changed dramatically with the introduction of antiretrovirals. This discourse examines many different facets of HIV from the beginning where there wasn't any treatment for HIV until the present era of highly active antiretroviral therapy (HAART). By utilizing statistical analysis of clinical data, this paper examines where we were, where we are and projections as to where treatment of HIV/AIDS is headed.

Chapter Two describes the datasets that were used for the analyses. The primary database utilized was collected by myself from an outpatient HIV clinic. The data included dates from 1984 until the present. The second database was from the Multicenter AIDS Cohort Study (MACS) public dataset. The data from the MACS cover the time between 1984 and October 1992. Comparisons are made between both datasets.

Chapter Three discusses where we were. Before the first anti-HIV drugs (called antiretrovirals) were approved, there was no treatment to slow the progression of HIV. The first generation of antiretrovirals, reverse transcriptase inhibitors such as AZT (zidovudine), DDI (didanosine), DDC (zalcitabine), and D4T (stavudine) provided the first treatment for HIV. The first clinical trials showed that these antiretrovirals had a significant impact on increasing patient survival. The trials also showed that patients on these drugs had increased CD4+ T cell counts. Chapter Three examines the distributions of CD4 T cell counts. The results show that the estimated distributions of CD4 T cell counts are distinctly non-Gaussian. Thus distributional assumptions regarding CD4 T cell counts must be taken, into account when performing analyses with this marker. The results also show the estimated CD4 T cell distributions for each disease stage: asymptomatic, symptomatic and AIDS are non-Gaussian. Interestingly, the distribution of CD4 T cell counts for the asymptomatic period is significantly below that of the CD4 T cell distribution for the uninfected population suggesting that even in patients with no outward symptoms of HIV infection, there exists high levels of immunosuppression.

Chapter Four discusses where we are at present. HIV quickly grew resistant to reverse transcriptase inhibitors which were given sequentially as mono or dual therapy. As resistance grew, the positive effects of the reverse transcriptase inhibitors on CD4 T cell counts and survival dissipated. As the old era faded a new era characterized by a new class of drugs and new technology changed the way that we treat HIV-infected patients. Viral load assays were able to quantify the levels of HIV RNA in the blood. By quantifying the viral load, one now had a faster, more direct way to test antiretroviral regimen efficacy. Protease inhibitors, which attacked a different region of HIV than reverse transcriptase inhibitors, when used in combination with other antiretroviral agents were found to dramatically and significantly reduce the HIV RNA levels in the blood. Patients also experienced significant increases in CD4 T cell counts. For the first time in the epidemic, there was hope. It was hypothesized that with HAART, viral levels could be kept so low that the immune system as measured by CD4 T cell counts would be able to recover. If these viral levels could be kept low enough, it would be possible for the immune system to eradicate the virus. The hypothesis of immune reconstitution, that is bringing CD4 T cell counts up to levels seen in uninfected patients, is tested in Chapter Four. It was found that for these patients, there was not enough of a CD4 T cell increase to be consistent with the hypothesis of immune reconstitution.

In Chapter Five, the effectiveness of long-term HAART is analyzed. Survival analysis was conducted on 213 patients on long-term HAART. The primary endpoint was presence of an AIDS defining illness. A high level of clinical failure, or progression to an endpoint, was found.

Chapter Six yields insights into where we are going. New technology such as viral genotypic testing, that looks at the genetic structure of HIV and determines where mutations have occurred, has shown that HIV is capable of producing resistance mutations that confer multiple drug resistance. This section looks at resistance issues and speculates, ceterus parabis, where the state of HIV is going. This section first addresses viral genotype and the correlates of viral load and disease progression. A second analysis looks at patients who have failed their primary attempts at HAART and subsequent salvage therapy. It was found that salvage regimens, efforts to control viral replication through the administration of different combinations of antiretrovirals, were not effective in 90 percent of the population in controlling viral replication. Thus, primary attempts at therapy offer the best change of viral suppression and delay of disease progression. Documentation of transmission of drug-resistant virus suggests that the public health crisis of HIV is far from over. Drug resistant HIV can sustain the epidemic and hamper our efforts to treat HIV infection. The data presented suggest that the decrease in the morbidity and mortality due to HIV/AIDS is transient. Deaths due to HIV will increase and public health officials must prepare for this eventuality unless new treatments become available. These results also underscore the importance of the vaccine effort.

The final chapter looks at the economic issues related to HIV. The direct and indirect costs of treating HIV/AIDS are very high. For the first time in the epidemic, there exists treatment that can actually slow disease progression. The direct costs for HAART are estimated. It is estimated that the direct lifetime costs for treating each HIV infected patient with HAART is between $353,000 to $598,000 depending on how long HAART prolongs life. If one looks at the incremental cost per year of life saved it is only $101,000. This is comparable with the incremental costs per year of life saved from coronary artery bypass surgery.

Policy makers need to be aware that although HAART can delay disease progression, it is not a cure and HIV is not over. The results presented here suggest that the decreases in the morbidity and mortality due to HIV are transient. Policymakers need to be prepared for the eventual increase in AIDS incidence and mortality. Costs associated with HIV/AIDS are also projected to increase. The cost savings seen recently have been from the dramatic decreases in the incidence of AIDS defining opportunistic infections. As patients who have been on HAART the longest start to progress to AIDS, policymakers and insurance companies will find that the cost of treating HIV/AIDS will increase.

Formal methods for control synthesis in partially observed environments : application to autonomous robotic manipulation

Modern robots are increasingly expected to function in uncertain and dynamically challenging environments, often in proximity with humans. In addition, wide scale adoption of robots requires on-the-fly adaptability of software for diverse application. These requirements strongly suggest the need to adopt formal representations of high level goals and safety specifications, especially as temporal logic formulas. This approach allows for the use of formal verification techniques for controller synthesis that can give guarantees for safety and performance. Robots operating in unstructured environments also face limited sensing capability. Correctly inferring a robot's progress toward high level goal can be challenging.

This thesis develops new algorithms for synthesizing discrete controllers in partially known environments under specifications represented as linear temporal logic (LTL) formulas. It is inspired by recent developments in finite abstraction techniques for hybrid systems and motion planning problems. The robot and its environment is assumed to have a finite abstraction as a Partially Observable Markov Decision Process (POMDP), which is a powerful model class capable of representing a wide variety of problems. However, synthesizing controllers that satisfy LTL goals over POMDPs is a challenging problem which has received only limited attention.

This thesis proposes tractable, approximate algorithms for the control synthesis problem using Finite State Controllers (FSCs). The use of FSCs to control finite POMDPs allows for the closed system to be analyzed as finite global Markov chain. The thesis explicitly shows how transient and steady state behavior of the global Markov chains can be related to two different criteria with respect to satisfaction of LTL formulas. First, the maximization of the probability of LTL satisfaction is related to an optimization problem over a parametrization of the FSC. Analytic computation of gradients are derived which allows the use of first order optimization techniques.

The second criterion encourages rapid and frequent visits to a restricted set of states over infinite executions. It is formulated as a constrained optimization problem with a discounted long term reward objective by the novel utilization of a fundamental equation for Markov chains - the Poisson equation. A new constrained policy iteration technique is proposed to solve the resulting dynamic program, which also provides a way to escape local maxima.

The algorithms proposed in the thesis are applied to the task planning and execution challenges faced during the DARPA Autonomous Robotic Manipulation - Software challenge.

An economic air pollution control model-application : photochemical smog in Los Angeles County in 1975

An economic air pollution control model, which determines the least cost of reaching various air quality levels, is formulated. The model takes the form of a general, nonlinear, mathematical programming problem. Primary contaminant emission levels are the independent variables. The objective function is the cost of attaining various emission levels and is to be minimized subject to constraints that given air quality levels be attained.

The model is applied to a simplified statement of the photochemical smog problem in Los Angeles County in 1975 with emissions specified by a two-dimensional vector, total reactive hydrocarbon, (RHC), and nitrogen oxide, (NO_x), emissions. Air quality, also two-dimensional, is measured by the expected number of days per year that nitrogen dioxide, (NO₂), and mid-day ozone, (O₃), exceed standards in Central Los Angeles.

The minimum cost of reaching various emission levels is found by a linear programming model. The base or "uncontrolled" emission levels are those that will exist in 1975 with the present new car control program and with the degree of stationary source control existing in 1971. Controls, basically "add-on devices", are considered here for used cars, aircraft, and existing stationary sources. It is found that with these added controls, Los Angeles County emission levels [(1300 tons/day RHC, 1000 tons /day NO_x) in 1969] and [(670 tons/day RHC, 790 tons/day NO_x) at the base 1975 level], can be reduced to 260 tons/day RHC (minimum RHC program) and 460 tons/day NO_x (minimum NO_x program).

"Phenomenological" or statistical air quality models provide the relationship between air quality and emissions. These models estimate the relationship by using atmospheric monitoring data taken at one (yearly) emission level and by using certain simple physical assumptions, (e. g., that emissions are reduced proportionately at all points in space and time). For NO₂, (concentrations assumed proportional to NO_x emissions), it is found that standard violations in Central Los Angeles, (55 in 1969), can be reduced to 25, 5, and 0 days per year by controlling emissions to 800, 550, and 300 tons /day, respectively. A probabilistic model reveals that RHC control is much more effective than NO_x control in reducing Central Los Angeles ozone. The 150 days per year ozone violations in 1969 can be reduced to 75, 30, 10, and 0 days per year by abating RHC emissions to 700, 450, 300, and 150 tons/day, respectively, (at the 1969 NO_x emission level).

The control cost-emission level and air quality-emission level relationships are combined in a graphical solution of the complete model to find the cost of various air quality levels. Best possible air quality levels with the controls considered here are 8 O₃ and 10 NO₂ violations per year (minimum ozone program) or 25 O₃ and 3 NO₂ violations per year (minimum NO₂ program) with an annualized cost of $230,000,000 (above the estimated $150,000,000 per year for the new car control program for Los Angeles County motor vehicles in 1975).

Part I - The radiation of elastic waves from a spherical cavity in a half space. Part II - Precision determination of focal depths and epicenters of earthquakes.

Part I: The dynamic response of an elastic half space to an explosion in a buried spherical cavity is investigated by two methods. The first is implicit, and the final expressions for the displacements at the free surface are given as a series of spherical wave functions whose coefficients are solutions of an infinite set of linear equations. The second method is based on Schwarz's technique to solve boundary value problems, and leads to an iterative solution, starting with the known expression for the point source in a half space as first term. The iterative series is transformed into a system of two integral equations, and into an equivalent set of linear equations. In this way, a dual interpretation of the physical phenomena is achieved. The systems are treated numerically and the Rayleigh wave part of the displacements is given in the frequency domain. Several comparisons with simpler cases are analyzed to show the effect of the cavity radius-depth ratio on the spectra of the displacements.

Part II: A high speed, large capacity, hypocenter location program has been written for an IBM 7094 computer. Important modifications to the standard method of least squares have been incorporated in it. Among them are a new way to obtain the depth of shocks from the normal equations, and the computation of variable travel times for the local shocks in order to account automatically for crustal variations. The multiregional travel times, largely based upon the investigations of the United States Geological Survey, are confronted with actual traverses to test their validity.

It is shown that several crustal phases provide control enough to obtain good solutions in depth for nuclear explosions, though not all the recording stations are in the region where crustal corrections are considered. The use of the European travel times, to locate the French nuclear explosion of May 1962 in the Sahara, proved to be more adequate than previous work.

A simpler program, with manual crustal corrections, is used to process the Kern County series of aftershocks, and a clearer picture of tectonic mechanism of the White Wolf fault is obtained.

Shocks in the California region are processed automatically and statistical frequency-depth and energy depth curves are discussed in relation to the tectonics of the area.

Robust Control of Evolutionary Dynamics

The application of principles from evolutionary biology has long been used to gain new insights into the progression and clinical control of both infectious diseases and neoplasms. This iterative evolutionary process consists of expansion, diversification and selection within an adaptive landscape - species are subject to random genetic or epigenetic alterations that result in variations; genetic information is inherited through asexual reproduction and strong selective pressures such as therapeutic intervention can lead to the adaptation and expansion of resistant variants. These principles lie at the center of modern evolutionary synthesis and constitute the primary reasons for the development of resistance and therapeutic failure, but also provide a framework that allows for more effective control.

A model system for studying the evolution of resistance and control of therapeutic failure is the treatment of chronic HIV-1 infection by broadly neutralizing antibody (bNAb) therapy. A relatively recent discovery is that a minority of HIV-infected individuals can produce broadly neutralizing antibodies, that is, antibodies that inhibit infection by many strains of HIV. Passive transfer of human antibodies for the prevention and treatment of HIV-1 infection is increasingly being considered as an alternative to a conventional vaccine. However, recent evolution studies have uncovered that antibody treatment can exert selective pressure on virus that results in the rapid evolution of resistance. In certain cases, complete resistance to an antibody is conferred with a single amino acid substitution on the viral envelope of HIV.

The challenges in uncovering resistance mechanisms and designing effective combination strategies to control evolutionary processes and prevent therapeutic failure apply more broadly. We are motivated by two questions: Can we predict the evolution to resistance by characterizing genetic alterations that contribute to modified phenotypic fitness? Given an evolutionary landscape and a set of candidate therapies, can we computationally synthesize treatment strategies that control evolution to resistance?

To address the first question, we propose a mathematical framework to reason about evolutionary dynamics of HIV from computationally derived Gibbs energy fitness landscapes -- expanding the theoretical concept of an evolutionary landscape originally conceived by Sewall Wright to a computable, quantifiable, multidimensional, structurally defined fitness surface upon which to study complex HIV evolutionary outcomes.

To design combination treatment strategies that control evolution to resistance, we propose a methodology that solves for optimal combinations and concentrations of candidate therapies, and allows for the ability to quantifiably explore tradeoffs in treatment design, such as limiting the number of candidate therapies in the combination, dosage constraints and robustness to error. Our algorithm is based on the application of recent results in optimal control to an HIV evolutionary dynamics model and is constructed from experimentally derived antibody resistant phenotypes and their single antibody pharmacodynamics. This method represents a first step towards integrating principled engineering techniques with an experimentally based mathematical model in the rational design of combination treatment strategies and offers predictive understanding of the effects of combination therapies of evolutionary dynamics and resistance of HIV. Preliminary in vitro studies suggest that the combination antibody therapies predicted by our algorithm can neutralize heterogeneous viral populations despite containing resistant mutations.

The statistical bootstrap model

A review is presented of the statistical bootstrap model of Hagedorn and Frautschi. This model is an attempt to apply the methods of statistical mechanics in high-energy physics, while treating all hadron states (stable or unstable) on an equal footing. A statistical calculation of the resonance spectrum on this basis leads to an exponentially rising level density ρ(m) ~ cm^-3 e^βom at high masses.

In the present work, explicit formulae are given for the asymptotic dependence of the level density on quantum numbers, in various cases. Hamer and Frautschi's model for a realistic hadron spectrum is described.

A statistical model for hadron reactions is then put forward, analogous to the Bohr compound nucleus model in nuclear physics, which makes use of this level density. Some general features of resonance decay are predicted. The model is applied to the process of NN annihilation at rest with overall success, and explains the high final state pion multiplicity, together with the low individual branching ratios into two-body final states, which are characteristic of the process. For more general reactions, the model needs modification to take account of correlation effects. Nevertheless it is capable of explaining the phenomenon of limited transverse momenta, and the exponential decrease in the production frequency of heavy particles with their mass, as shown by Hagedorn. Frautschi's results on "Ericson fluctuations" in hadron physics are outlined briefly. The value of β_o required in all these applications is consistently around [120 MeV]^-1 corresponding to a "resonance volume" whose radius is very close to ƛ_π. The construction of a "multiperipheral cluster model" for high-energy collisions is advocated.