Star Decompositions of Bipartite Graphs

In Chapter 1, we will introduce the definitions and the notations used throughout this thesis. We will also survey some prior research pertaining to graph decompositions, with special emphasis on star-decompositions and decompositions of bipartite graphs. Here we will also introduce some basic algorithms and lemmas that are used in this thesis. In Chapter 2, we will focus primarily on decomposition of complete bipartite graphs. We will also cover the necessary and sufficient conditions for the decomposition of complete bipartite graphs minus a 1-factor, also known as crown graphs and show that all complete bipartite graphs and crown graphs have a decomposition into stars when certain necessary conditions for the decomposition are met. This is an extension of the results given in "On claw-decomposition of complete graphs and complete bigraphs" by Yamamoto, et. al. We will propose a construction for the decomposition of the graphs. In Chapter 3, we focus on the decomposition of complete equipartite tripartite graphs. This result is similar to the results of "On Claw-decomposition of complete multipartite graphs" by Ushio and Yamamoto. Our proof is again by construction and we propose how it might extend to equipartite multipartite graphs. We will also discuss the 3-star decomposition of complete tripartite graphs. In Chapter 4 , we will discuss the star decomposition of 4-regular bipartite graphs, with particular emphasis on the decomposition of 4-regular bipartite graphs into 3-stars. We will propose methods to extend our strategies to model the problem as an optimization problem. We will also look into the probabilistic method discussed in "Tree decomposition of Graphs" by Yuster and how we might modify the results of this paper to star decompositions of bipartite graphs. In Chapter 5, we summarize the findings in this thesis, and discuss the future work and research in star decompositions of bipartite and multipartite graphs

Ensemble learning of high dimension datasets

Ensemble learning, an approach in Machine Learning, makes decisions based on the collective decision of a committee of learners to solve complex tasks with minimal human intervention. Advances in computing technology have enabled researchers build datasets with the number of features in the order of thousands and enabled building more accurate predictive models. Unfortunately, high dimensional datasets are especially challenging for machine learning due to the phenomenon dubbed as the "curse of dimensionality". One approach to overcoming this challenge is ensemble learning using Random Subspace (RS) method, which has been shown to perform very well empirically however with few theoretical explanations to said effectiveness for classification tasks. In this thesis, we aim to provide theoretical insights into RS ensemble classifiers to give a more in-depth understanding of the theoretical foundations of other ensemble classifiers. We investigate the conditions for norm-preservations in RS projections. Insights into this provide us with the theoretical basis for RS in algorithms that are based on the geometry of the data (i.e. clustering, nearest-neighbour). We then investigate the guarantees for the dot products of two random vectors after RS projection. This guarantee is useful to capture the geometric structure of a classification problem. We will then investigate the accuracy of a majority vote ensemble using a generalized Polya-Urn model, and how the parameters of the model are derived from diversity measures. We will discuss the practical implications of the model, explore the noise tolerance of ensembles, and give a plausible explanation for the effectiveness of ensembles. We will provide empirical corroboration for our main results with both synthetic and real-world high-dimensional data. We will also discuss the implications of our theory on other applications (i.e. compressive sensing). Based on our results, we will propose a method of building ensembles for Deep Neural Network image classifications using RS projections without needing to retrain the neural network, which showed improved accuracy and very good robustness to adversarial examples. Ultimately, we hope that the insights gained in this thesis would make in-roads towards the answer to a key open question for ensemble classifiers, "When will an ensemble of weak learners outperform a single carefully tuned learner?

Linear dimensionality reduction in linear time: Johnson-Lindenstrauss-type guarantees for random subspace

We consider the problem of efficient randomized dimensionality reduction with norm-preservation guarantees. Specifically we prove data-dependent Johnson-Lindenstrauss-type geometry preservation guarantees for Ho's random subspace method: When data satisfy a mild regularity condition -- the extent of which can be estimated by sampling from the data -- then random subspace approximately preserves the Euclidean geometry of the data with high probability. Our guarantees are of the same order as those for random projection, namely the required dimension for projection is logarithmic in the number of data points, but have a larger constant term in the bound which depends upon this regularity. A challenging situation is when the original data have a sparse representation, since this implies a very large projection dimension is required: We show how this situation can be improved for sparse binary data by applying an efficient `densifying' preprocessing, which neither changes the Euclidean geometry of the data nor requires an explicit matrix-matrix multiplication. We corroborate our theoretical findings with experiments on both dense and sparse high-dimensional datasets from several application domains

A diversity-aware model for majority vote ensemble accuracy

Ensemble classifiers are a successful and popular approach for classification, and are frequently found to have better generalization performance than single models in practice. Although it is widely recognized that ‘diversity’ between ensemble members is important in achieving these performance gains, for classification ensembles it is not widely understood which diversity measures are most predictive of ensemble performance, nor how large an ensemble should be for a particular application. In this paper, we explore the predictive power of several common diversity measures and show – with extensive experiments – that contrary to earlier work that finds no clear link between these diversity measures (in isolation) and ensemble accuracy instead by using the ρ diversity measure of Sneath and Sokal as an estimator for the dispersion parameter of a Polya-Eggenberger distribution we can predict, independently of the choice of base classifier family, the accuracy of a majority vote classifier ensemble ridiculously well. We discuss our model and some implications of our findings – such as diversity-aware (non-greedy) pruning of a majority-voting ensemble

Perceptual improvements for Super-Resolution of Satellite Imagery

Super-resolution of satellite imagery poses unique challenges. We propose a hybrid method comprising two existing deep network super-resolution approaches, namely a feedforward network called DeepSUM, and ESRGAN, a GAN-based approach, to super-resolve multiple low-resolution images by a factor of four to obtain a single high-resolution image. We also introduce a novel loss function, called variation loss, to better define edges and textures to create a sharper, perceptually better output. Using our hybrid, we inherit some of the advantages of both deep learning approaches, resulting in super-resolved images that better show boundaries, textures, and details

Cross-Regulation between Oncogenic BRAFV600E Kinase and the MST1 Pathway in Papillary Thyroid Carcinoma

BACKGROUND:The BRAF(V600E) mutation leading to constitutive signaling of MEK-ERK pathways causes papillary thyroid cancer (PTC). Ras association domain family 1A (RASSF1A), which is an important regulator of MST1 tumor suppressor pathways, is inactivated by hypermethylation of its promoter region in 20 to 32% of PTC. However, in PTC without RASSF1A methylation, the regulatory mechanisms of RASSF1A-MST1 pathways remain to be elucidated, and the functional cooperation or cross regulation between BRAF(V600E) and MST1,which activates Foxo3,has not been investigated. METHODOLOGY/PRINCIPAL FINDINGS:The negative regulators of the cell cycle, p21 and p27, are strongly induced by transcriptional activation of FoxO3 in BRAF(V600E) positive thyroid cancer cells. The FoxO3 transactivation is augmented by RASSF1A and the MST1 signaling pathway. Interestingly, introduction of BRAF(V600E)markedly abolished FoxO3 transactivation and resulted in the suppression of p21 and p27 expression. The suppression of FoxO3 transactivation by BRAF(V600E)is strongly increased by coexpression of MST1 but it is not observed in the cells in which MST1, but not MST2,is silenced. Mechanistically, BRAF(V600E)was able to bind to the C-terminal region of MST1 and resulted in the suppression of MST1 kinase activities. The induction of the G1-checkpoint CDK inhibitors, p21 and p27,by the RASSF1A-MST1-FoxO3 pathway facilitates cellular apoptosis, whereas addition of BRAF(V600E) inhibits the apoptotic processes through the inactivation of MST1. Transgenic induction of BRAF(V600E)in the thyroid gland results in cancers resembling human papillary thyroid cancers. The development of BRAF(V600E)transgenic mice with the MST1 knockout background showed that these mice had abundant foci of poorly differentiated carcinomas and large areas without follicular architecture or colloid formation. CONCLUSIONS/SIGNIFICANCE:The results of this study revealed that the oncogenic effect of BRAF(V600E) is associated with the inhibition of MST1 tumor suppressor pathways, and that the activity of RASSF1A-MST1-FoxO3 pathways determines the phenotypes of BRAF(V600E) tumors

Electromagnetic Wave Theory and Applications

Contains table of contents for Section 3 and reports on five research projects.U.S. Department of Transportation Contract DTRS-57-88-C-00078TTD13U.S. Department of Transportation Contract DTRS-57-88-C-00078TTD30Defense Advanced Research Projects Agency Contract MDA972-90-C-0021Digital Equipment CorporationIBM CorporationJoint Services Electronics Program Contract DAAL03-89-C-0001Joint Services Electronics Program Contract DAAL03-92-C-0001Schlumberger-Doll ResearchU.S. Navy - Office of Naval Research Grant N00014-90-J-1002U.S. Navy - Office of Naval Research Grant N00014-89-J-1019National Aeronautics and Space Administration Grant NAGW-1617National Aeronautics and Space Administration Grant 958461National Aeronautics and Space Administration Grant NAGW-1272U.S. Army Corp of Engineers Contract DACA39-87-K-0022U.S. Navy - Office of Naval Research Grant N00014-89-J-110

Targeting breast cancer stem cells

The cancer stem cell (CSC) hypothesis postulates that tumors are maintained by a self‐renewing CSC population that is also capable of differentiating into non‐self‐renewing cell populations that constitute the bulk of the tumor. Although, the CSC hypothesis does not directly address the cell of origin of cancer, it is postulated that tissue‐resident stem or progenitor cells are the most common targets of transformation. Clinically, CSCs are predicted to mediate tumor recurrence after chemo‐ and radiation‐therapy due to the relative inability of these modalities to effectively target CSCs. If this is the case, then CSC must be efficiently targeted to achieve a true cure. Similarities between normal and malignant stem cells, at the levels of cell‐surface proteins, molecular pathways, cell cycle quiescence, and microRNA signaling present challenges in developing CSC‐specific therapeutics. Approaches to targeting CSCs include the development of agents targeting known stem cell regulatory pathways as well as unbiased high‐throughput siRNA or small molecule screening. Based on studies of pathways present in normal stem cells, recent work has identified potential “Achilles heals” of CSC, whereas unbiased screening provides opportunities to identify new pathways utilized by CSC as well as develop potential therapeutic agents. Here, we review both approaches and their potential to effectively target breast CSC.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135704/1/mol2201045404.pd

Evaluation of individual and ensemble probabilistic forecasts of COVID-19 mortality in the United States

Short-term probabilistic forecasts of the trajectory of the COVID-19 pandemic in the United States have served as a visible and important communication channel between the scientific modeling community and both the general public and decision-makers. Forecasting models provide specific, quantitative, and evaluable predictions that inform short-term decisions such as healthcare staffing needs, school closures, and allocation of medical supplies. Starting in April 2020, the US COVID-19 Forecast Hub (https://covid19forecasthub.org/) collected, disseminated, and synthesized tens of millions of specific predictions from more than 90 different academic, industry, and independent research groups. A multimodel ensemble forecast that combined predictions from dozens of groups every week provided the most consistently accurate probabilistic forecasts of incident deaths due to COVID-19 at the state and national level from April 2020 through October 2021. The performance of 27 individual models that submitted complete forecasts of COVID-19 deaths consistently throughout this year showed high variability in forecast skill across time, geospatial units, and forecast horizons. Two-thirds of the models evaluated showed better accuracy than a naïve baseline model. Forecast accuracy degraded as models made predictions further into the future, with probabilistic error at a 20-wk horizon three to five times larger than when predicting at a 1-wk horizon. This project underscores the role that collaboration and active coordination between governmental public-health agencies, academic modeling teams, and industry partners can play in developing modern modeling capabilities to support local, state, and federal response to outbreaks