One problem, considered important in Banach space theory since at least the 1970’s, asks for intrinsic characterizations of subspaces of a Banach space with an unconditional basis. A more general question is to give necessary and sufficient conditions for operators from Lp (2 < p < 1) to factor through `p. In this dissertaion, solutions for the above problems are provided. More precisely, I prove that for a reflexive Banach space, being a subspace of a reflexive space with an unconditional basis or being a quotient of such a space, is equivalent to having the unconditional tree property. I also show that a bounded linear operator from Lp (2 < p < 1) factors through `p if and only it satisfies an upper-(C, p)-tree estimate. Results are then extended to operators from asymptotic lp spaces.

Thesis (Ph. D.)--Oregon State University, 1990. / Typescript (photocopy). Includes bibliography (leaf 42). Also available on the World Wide Web.

Thesis--Wisconsin. / Vita. Includes bibliographical references (leaves 276-279).

published_or_final_version / abstract / toc / Mathematics / Master / Master of Philosophy

Algebraic geometry is the study of solutions in polynomial equations using objects and shapes. Differential geometry is based on surfaces, curves, and dimensions of shapes and applying calculus and algebra. Desingularizing the singularities of a variety plays an important role in research in algebraic and differential geometry. Toroidal Embedding is one of the tools used in desingularization. Therefore, Toroidal Embedding and desingularization will be the main focus of my project. In this paper, we first provide a brief introduction on Toroidal Embedding, then show an explicit construction on how to smooth a variety with singularity through Toroidal Embeddings.

Thesis (M. Phil.)--University of Hong Kong, 2005. / Title proper from title frame. Also available in printed format.

Thesis--Wisconsin. / Vita. Includes bibliographical references (leaves 46-47).

As computer networks grow and demonstrate more complicated and intricate behaviors, traditional intrusion detections systems have fallen behind in their ability to protect network resources. Machine learning has stepped to the forefront of intrusion detection research due to its potential to predict future behaviors. However, training these systems requires network data such as NetFlow that contains information regarding relationships between hosts, but requires human understanding to extract. Additionally, standard methods of encoding this categorical data struggles to capture similarities between points. To counteract this, we evaluate a method of embedding IP addresses and transport-layer ports into a continuous space, called IP2Vec. We demonstrate this embedding on two separate datasets, CTU'13 and UGR'16, and combine the UGR'16 embedding with several machine learning methods. We compare the models with and without the embedding to evaluate the benefits of including network behavior into an intrusion detection system. We show that the addition of embeddings improve the F1-scores for all models in the multiclassification problem given in the UGR'16 data. / MS / As computer networks grow and demonstrate more complicated and intricate behaviors, traditional network protection tools like firewalls struggle to protect personal computers and servers. Machine learning has stepped to the forefront to counteract this by learning and predicting behavior on a network. However, this learned behavior fails to capture much of the information regarding relationships between computers on a network. Additionally, standard techniques to convert network information into numbers struggles to capture many of the similarities between machines. To counteract this, we evaluate a method to capture relationships between IP addresses and ports, called an embedding. We demonstrate this embedding on two different datasets of network traffic, and evaluate the embedding on one dataset with several machine learning methods. We compare the models with and without the embedding to evaluate the benefits of including network behavior into an intrusion detection system. We show that including network behavior into machine learning models improves the performance of classifying attacks found in the UGR’16 data.

Word embeddings is a useful method that has shown enormous success in various NLP tasks, not only in open domain but also in biomedical domain. The biomedical domain provides various domain specific resources and tools that can be exploited to improve performance of these word embeddings. However, most of the research related to word embeddings in biomedical domain focuses on analysis of model architecture, hyper-parameters and input text. In this paper, we use SemMedDB to design new sentences called `Semantic Sentences'. Then we use these sentences in addition to biomedical text as inputs to the word embedding model. This approach aims at introducing biomedical semantic types defined by UMLS, into the vector space of word embeddings. The semantically rich word embeddings presented here rivals state of the art biomedical word embedding in both semantic similarity and relatedness metrics up to 11%. We also demonstrate how these semantic types in word embeddings can be utilized.

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