A geometric analysis of convex demixing

Demixing is the task of identifying multiple signals given only their sum and prior information about their structures. Examples of demixing problems include (i) separating a signal that is sparse with respect to one basis from a signal that is sparse with respect to a second basis; (ii) decomposing an observed matrix into low-rank and sparse components; and (iii) identifying a binary codeword with impulsive corruptions. This thesis describes and analyzes a convex optimization framework for solving an array of demixing problems.

Our framework includes a random orientation model for the constituent signals that ensures the structures are incoherent. This work introduces a summary parameter, the statistical dimension, that reflects the intrinsic complexity of a signal. The main result indicates that the difficulty of demixing under this random model depends only on the total complexity of the constituent signals involved: demixing succeeds with high probability when the sum of the complexities is less than the ambient dimension; otherwise, it fails with high probability.

The fact that a phase transition between success and failure occurs in demixing is a consequence of a new inequality in conic integral geometry. Roughly speaking, this inequality asserts that a convex cone behaves like a subspace whose dimension is equal to the statistical dimension of the cone. When combined with a geometric optimality condition for demixing, this inequality provides precise quantitative information about the phase transition, including the location and width of the transition region.

Anatomical and developmental patterns of interleukin-2 gene expression in the mouse: analysis of IL-2 expressing cells and partial characterization of interactions involved in mediating IL-2 gene expression in vivo

Interleukin-2 (IL-2) is an important mediator in the vertebrate immune system. IL-2 is a potent growth factor that mature T lymphocytes use as a proliferation signal and the production of IL-2 is crucial for the clonal expansion of antigen-specific T cells in the primary immune response. IL-2 driven proliferation is dependent on the interaction of the lymphokine with its cognate multichain receptor. IL-2 expression is induced only upon stimulation and transcriptional activation of the IL-2 gene relies extensively on the coordinate interaction of numerous inducible and constitutive trans-acting factors. Over the past several years, thousands of papers have been published regarding molecular and cellular aspects of IL-2 gene expression and IL-2 function. The vast majority of these reports describe work that has been carried out in vitro. However, considerably less is known about control of IL-2 gene expression and IL-2 function in vivo.

To gain new insight into the regulation of IL-2 gene expression in vivo, anatomical and developmental patterns of IL-2 gene expression in the mouse were established by employing in situ hybridization and immunohistochemical staining methodologies to tissue sections generated from normal mice and mutant animals in which T -cell development was perturbed. Results from these studies revealed several interesting aspects of IL-2 gene expression, such as (1) induction of IL-2 gene expression and protein synthesis in the thymus, the primary site of T-cell development in the body, (2) cell-type specificity of IL-2 gene expression in vivo, (3) participation of IL-2 in the extrathymic expansion of mature T cells in particular tissues, independent of an acute immune response to foreign antigen, (4) involvement of IL-2 in maintaining immunologic balance in the mucosal immune system, and (5) potential function of IL-2 in early events associated with hematopoiesis.

Extensive analysis of IL-2 mRNA accumulation and protein production in the murine thymus at various stages of development established the existence of two classes of intrathymic IL-2 producing cells. One class of intrathymic IL-2 producers was found exclusively in the fetal thymus. Cells belonging to this subset were restricted to the outermost region of the thymus. IL-2 expression in the fetal thymus was highly transient; a dramatic peak ofiL-2 mRNA accumulation was identified at day 14.5 of gestation and maximal IL-2 protein production was observed 12 hours later, after which both IL-2 mRNA and protein levels rapidly decreased. Significantly, the presence of IL-2 expressing cells in the day 14-15 fetal thymus was not contingent on the generation of T-cell receptor (TcR) positive cells. The second class of IL-2 producing cells was also detectable in the fetal thymus (cells found in this class represented a minority subset of IL-2 producers in the fetal thymus) but persist in the thymus during later stages of development and after birth. Intrathymic IL-2 producers in postnatal animals were located in the subcapsular region and cortex, indicating that these cells reside in the same areas where immature T cells are consigned. The frequency of IL-2 expressing cells in the postnatal thymus was extremely low, indicating that induction of IL-2 expression and protein synthesis are indicative of a rare activation event. Unlike the fetal class of intrathymic IL-2 producers, the presence of IL-2 producing cells in the postnatal thymus was dependent on to the generation of TcR+ cells. Subsequent examination of intrathymic IL-2 production in mutant postnatal mice unable to produce either αβ or γδ T cells showed that postnatal IL-2 producers in the thymus belong to both αβ and γδ lineages. Additionally, further studies indicated that IL-2 synthesis by immature αβ -T cells depends on the expression of bonafide TcR αβ-heterodimers. Taken altogether, IL-2 production in the postnatal thymus relies on the generation of αβ or γδ-TcR^+ cells and induction of IL-2 protein synthesis can be linked to an activation event mediated via the TcR.

With regard to tissue specificity of IL-2 gene expression in vivo, analysis of whole body sections obtained from normal neonatal mouse pups by in situ hybridization demonstrated that IL-2 mRNA^+ cells were found in both lymphoid and nonlymphoid tissues with which T cells are associated, such as the thymus (as described above), dermis and gut. Tissues devoid of IL-2 mRNA^+ cells included brain, heart, lung, liver, stomach, spine, spinal cord, kidney, and bladder. Additional analysis of isolated tissues taken from older animals revealed that IL-2 expression was undetectable in bone marrow and in nonactivated spleen and lymph nodes. Thus, it appears that extrathymic IL-2 expressing cells in nonimmunologically challenged animals are relegated to particular epidermal and epithelial tissues in which characterized subsets of T cells reside and thatinduction of IL-2 gene expression associated with these tissues may be a result of T-cell activation therein.

Based on the neonatal in situ hybridization results, a detailed investigation into possible induction of IL-2 expression resulting in IL-2 protein synthesis in the skin and gut revealed that IL-2 expression is induced in the epidermis and intestine and IL-2 protein is available to drive cell proliferation of resident cells and/or participate in immune function in these tissues. Pertaining to IL-2 expression in the skin, maximal IL-2 mRNA accumulation and protein production were observed when resident Vγ_3^+ T-cell populations were expanding. At this age, both IL-2 mRNA^+ cells and IL-2 protein production were intimately associated with hair follicles. Likewise, at this age a significant number of CD3ε^+ cells were also found in association with follicles. The colocalization of IL-2 expression and CD3ε^+ cells suggests that IL-2 expression is induced when T cells are in contact with hair follicles. In contrast, neither IL-2 mRNA nor IL-2 protein were readily detected once T-cell density in the skin reached steady-state proportions. At this point, T cells were no longer found associated with hair follicles but were evenly distributed throughout the epidermis. In addition, IL-2 expression in the skin was contingent upon the presence of mature T cells therein and induction of IL-2 protein synthesis in the skin did not depend on the expression of a specific TcR on resident T cells. These newly disclosed properties of IL-2 expression in the skin indicate that IL-2 may play an additional role in controlling mature T-cell proliferation by participating in the extrathymic expansion of T cells, particularly those associated with the epidermis.

Finally, regarding IL-2 expression and protein synthesis in the gut, IL-2 producing cells were found associated with the lamina propria of neonatal animals and gut-associated IL-2 production persisted throughout life. In older animals, the frequency of IL-2 producing cells in the small intestine was not identical to that in the large intestine and this difference may reflect regional specialization of the mucosal immune system in response to enteric antigen. Similar to other instances of IL-2 gene expression in vivo, a failure to generate mature T cells also led to an abrogation of IL-2 protein production in the gut. The presence of IL-2 producing cells in the neonatal gut suggested that these cells may be generated during fetal development. Examination of the fetal gut to determine the distribution of IL-2 producing cells therein indicated that there was a tenfold increase in the number of gut-associated IL-2 producers at day 20 of gestation compared to that observed four days earlier and there was little difference between the frequency of IL-2 producing cells in prenatal versus neonatal gut. The origin of these fetally-derived IL-2 producing cells is unclear. Prior to the immigration of IL-2 inducible cells to the fetal gut and/or induction of IL-2 expression therein, IL-2 protein was observed in the fetal liver and fetal omentum, as well as the fetal thymus. Considering that induction of IL-2 protein synthesis may be an indication of future functional capability, detection of IL-2 producing cells in the fetal liver and fetal omentum raises the possibility that IL-2 producing cells in the fetal gut may be extrathymic in origin and IL-2 producing cells in these fetal tissues may not belong solely to the T lineage. Overall, these results provide increased understanding of the nature of IL-2 producing cells in the gut and how the absence of IL-2 production therein and in fetal hematopoietic tissues can result in the acute pathology observed in IL-2 deficient animals.

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.

Technology for Single Cell Protein Analysis in Immunology and Cancer Prognostics

The first chapter of this thesis deals with automating data gathering for single cell microfluidic tests. The programs developed saved significant amounts of time with no loss in accuracy. The technology from this chapter was applied to experiments in both Chapters 4 and 5.

The second chapter describes the use of statistical learning to prognose if an anti-angiogenic drug (Bevacizumab) would successfully treat a glioblastoma multiforme tumor. This was conducted by first measuring protein levels from 92 blood samples using the DNA-encoded antibody library platform. This allowed the measure of 35 different proteins per sample, with comparable sensitivity to ELISA. Two statistical learning models were developed in order to predict whether the treatment would succeed. The first, logistic regression, predicted with 85% accuracy and an AUC of 0.901 using a five protein panel. These five proteins were statistically significant predictors and gave insight into the mechanism behind anti-angiogenic success/failure. The second model, an ensemble model of logistic regression, kNN, and random forest, predicted with a slightly higher accuracy of 87%.

The third chapter details the development of a photocleavable conjugate that multiplexed cell surface detection in microfluidic devices. The method successfully detected streptavidin on coated beads with 92% positive predictive rate. Furthermore, chambers with 0, 1, 2, and 3+ beads were statistically distinguishable. The method was then used to detect CD3 on Jurkat T cells, yielding a positive predictive rate of 49% and false positive rate of 0%.

The fourth chapter talks about the use of measuring T cell polyfunctionality in order to predict whether a patient will succeed an adoptive T cells transfer therapy. In 15 patients, we measured 10 proteins from individual T cells (~300 cells per patient). The polyfunctional strength index was calculated, which was then correlated with the patient's progress free survival (PFS) time. 52 other parameters measured in the single cell test were correlated with the PFS. No statistical correlator has been determined, however, and more data is necessary to reach a conclusion.

Finally, the fifth chapter talks about the interactions between T cells and how that affects their protein secretion. It was observed that T cells in direct contact selectively enhance their protein secretion, in some cases by over 5 fold. This occurred for Granzyme B, Perforin, CCL4, TNFa, and IFNg. IL- 10 was shown to decrease slightly upon contact. This phenomenon held true for T cells from all patients tested (n=8). Using single cell data, the theoretical protein secretion frequency was calculated for two cells and then compared to the observed rate of secretion for both two cells not in contact, and two cells in contact. In over 90% of cases, the theoretical protein secretion rate matched that of two cells not in contact.

A hybrid-parallel framework for the nonlinear seismic analysis of very tall buildings

FRAME3D, a program for the nonlinear seismic analysis of steel structures, has previously been used to study the collapse mechanisms of steel buildings up to 20 stories tall. The present thesis is inspired by the need to conduct similar analysis for much taller structures. It improves FRAME3D in two primary ways.

First, FRAME3D is revised to address specific nonlinear situations involving large displacement/rotation increments, the backup-subdivide algorithm, element failure, and extremely narrow joint hysteresis. The revisions result in superior convergence capabilities when modeling earthquake-induced collapse. The material model of a steel fiber is also modified to allow for post-rupture compressive strength.

Second, a parallel FRAME3D (PFRAME3D) is developed. The serial code is optimized and then parallelized. A distributed-memory divide-and-conquer approach is used for both the global direct solver and element-state updates. The result is an implicit finite-element hybrid-parallel program that takes advantage of the narrow-band nature of very tall buildings and uses nearest-neighbor-only communication patterns.

Using three structures of varied sized, PFRAME3D is shown to compute reproducible results that agree with that of the optimized 1-core version (displacement time-history response root-mean-squared errors are ~〖10〗^(-5) m) with much less wall time (e.g., a dynamic time-history collapse simulation of a 60-story building is computed in 5.69 hrs with 128 cores—a speedup of 14.7 vs. the optimized 1-core version). The maximum speedups attained are shown to increase with building height (as the total number of cores used also increases), and the parallel framework can be expected to be suitable for buildings taller than the ones presented here.

PFRAME3D is used to analyze a hypothetical 60-story steel moment-frame tube building (fundamental period of 6.16 sec) designed according to the 1994 Uniform Building Code. Dynamic pushover and time-history analyses are conducted. Multi-story shear-band collapse mechanisms are observed around mid-height of the building. The use of closely-spaced columns and deep beams is found to contribute to the building's “somewhat brittle” behavior (ductility ratio ~2.0). Overall building strength is observed to be sensitive to whether a model is fracture-capable.