High-resolution and low-cost fabrication techniques are essential for nanotechnology to overcome the commercialization barrier to benefit our society. Since its inception nanoimprint has become the ideal technology to fabricate dense sub-micron structures over large areas with low cost, which are important to many applications such as high-density storage disks and diffractive optical devices. The decade-long development in nanoimprint equipment has reached a point where large-scale manufacturing of high-density nanostructures are possible. However, there are a few remaining issues that need to be studied before the advent of commercial application of nanoimprint. In this work we look at a pressing issue, long-term stability of the mold surfactant coating. It is important to understand the details of the surfactant wear during nanoimprint in order to limit defect density to a tolerable threshold in a high-volume manufacturing process. To study this we went through a nanoimprinting procedure and measured chemical and physical alterations in the coating. The surfactant wear information also helps to optimize the time interval for surfactant recoating to keep the fabrication throughput as high as possible. In this paper we characterize the stability of two commonly used surfactants as well as prescribe a new technique for mold anti-adhesion. Through this work we see that FDTS and OTS undergo significant degradation in air and gradual degradation by chain scission is observed during the nanoimprint procedure. It is also noted that an embedded anti-adhesion layer is effective for mold releasing.

This dissertation is devoted to several questions that arise in operator algebra theory. In the first part of the work we study the dilations of homomorphisms of subalgebras to the algebras that contain them. We consider the question whether a contractive homomorphism of a logmodular algebra into B(H) is completely contractive, where B(H) denotes the algebra of all bounded operators on a Hilbert space H. We show that every logmodular subalgebra of Mn(C) is unitary equivalent to an algebra of block upper triangular matrices, which was conjectured by V. Paulsen and M. Raghupathi. In particular, this shows that every unital contractive representation of a logmodular subalgebra of Mn(C) is automatically completely contractive. In the second part of the dissertation we investigate certain matrices composed of mixed, second?order moments of unitaries. The unitaries are taken from C??algebras with moments taken with respect to traces, or, alternatively, from matrix algebras with the usual trace. These sets are of interest in light of a theorem of E. Kirchberg about Connes' embedding problem and provide a new approach to it. Finally, we give a modification of I. Klep and M. Schweighofer?s algebraic reformulation of Connes' embedding problem by considering the ?-algebra of the countably generated free group. This allows us to consider only quadratic polynomials in unitary generators instead of arbitrary polynomials in self-adjoint generators.

In this thesis, we study two optimization problems which have a lot of important applications in diverse domains: Line Cover Problem (LCP) in Computational Geometry and Maximum Genus Embedding (MGE) in Topological Graph Theory. We study LCP whose decision version is known NP-Complete from the perspective of Parameterized Complexity, as well as classical techniques in Algorithm Design. In particular, we provide an exact algorithm in time O(n^3 2n) based on Dynamic Programming and initiate a dual problem of LCP in terms of Linear Programming Duality. We study the dual problem by applying approximation and kernelization, obtaining an approximation algorithm with ratio k - 1 and a kernel of size O(k^4). Then we survey related geometric properties on LCP. Finally we propose a Parameterized Algorithm to solve LCP with running time O*(k^k/1:35^k). We explore connections between the maximum genus of a graph and its cycle space consisting of fundamental cycles only. We revisit a known incorrect approach of finding a maximum genus embedding via computing a maximum pairing of intersected fundamental cycles with respect to an arbitrary spanning tree. We investigate the reason it failed and conclude it confused the concept of deficiency. Also, we characterize the upper-embeddablity of a graph in terms of maximum pairings of intersected fundamental cycles, i.e. a graph is upper-embeddable if and only if the number of maximum pairings of intersected fundamental cycles for any spanning tree is the same. Finally, we present a lower and an upper bound of the maximum number of vertex-disjoint cycles in a general graph, beta(G) - 2gammaM(G) and beta(G) - gammaM(G), only depending on maximum genus and cycle rank.

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Meshes and hypercubes are two most important communication and computation structures used in parallel computing. Network embedding problems for meshes and hypercubes on traditional network architectures have been intensively studied during the past years. With the emergence of new network architectures, the traditional network embedding results are not enough to solve the new requirements. The main objective of this thesis is to design efficient network embedding schemes for realizing meshes and hypercubes on a group of future network architectures. This thesis is organized into two parts. The first part focuses on embedding meshes/tori on a group of double-loop networks by evaluating the traditional embedding metrics, since double-loop networks have been intensively studied and proven to have many desirable properties for future network architecture. We propose a novel tessellation approach to partition the geometric plane of double-loop networks into a set of parallelogram tiles, called P-shape. Based on the characteristics of P-shape, we design a simple embedding scheme, namely P-shape embedding, that embeds arbitrary-shape meshes and tori on double-loop networks in a systematic way. A main merit of P-shape embedding is that a large fraction of embedded mesh/torus edges have edge dilation 1, resulting in a low average dilation. These are the first results, to our knowledge, on embedding meshes and tori on general doubleloop networks which is of great significance due to the popularity of these architectures. Our P-shape construction bridges between regular graphs and double-loop networks, and provides a powerful tool for studying the topological properties of double-loop networks. In the second part, we study efficient embedding schemes for realizing hypercubes on a group of array-basedWDMoptical networks by analyzing the new embedding metric of wavelength requirement, as WDM optical networking is becoming a promising technology for deployment in many applications in advanced telecommunication and parallel computing. We first design routing and wavelength assignments of both bidirectional and unidirectional hypercubes on WDM optical linear arrays, rings, meshes and tori with the consideration of communication directions. For each case, we identify a lower bound on the number of wavelengths required, and design the embedding scheme and wavelength assignment algorithm that uses a provably near-optimal number of wavelengths. To further reduce the wavelength requirement, we extend the results to WDM ring networks with additional links, namely WDM chordal rings. Based on our proposed embedding schemes, we provide the analysis of chord length with optimal number of wavelengths to realize hypercubes on 3-degree and 4-degree WDM chordal rings. Furthermore, we propose an embedding scheme for realizing dimensional hypercubes on WDM optical arrays by considering the hypercubes dimension by dimension, called lattice embedding, instead of embedding hypercubes with all dimensions. Based on lattice embedding, the number of wavelengths required to realize dimensional hypercube on WDM arrays can been significantly reduced compared to the previous results. By our embedding schemes, many communications and computations, originally designed based on hypercubes, can be directly implemented in WDM optical networks, and the wavelength requirements can be easily derived using our obtained results. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1345349 / Thesis (Ph.D.) - University of Adelaide, School of Computer Science, 2008

Indiana University-Purdue University Indianapolis (IUPUI) / Research on social networks and understanding the interactions of the users can be modeled as a task of graph mining, such as predicting nodes and edges in networks. Dealing with such unstructured data in large social networks has been a challenge for researchers in several years. Neural Networks have recently proven very successful in performing predictions on number of speech, image, and text data and have become the de facto method when dealing with such data in a large volume. Graph NeuralNetworks, however, have only recently become mature enough to be used in real large-scale graph prediction tasks, and require proper structure and data modeling to be viable and successful. In this research, we provide a new modeling of the social network which captures the attributes of the nodes from various dimensions. We also introduce the Neural Network architecture that is required for optimally utilizing the new data structure. Finally, in order to provide a hot-start for our model, we initialize the weights of the neural network using a pre-trained graph embedding method. We have also developed a new graph embedding algorithm. We will first explain how previous graph embedding methods are not optimal for all types of graphs, and then provide a solution on how to combat those limitations and come up with a new graph embedding method.

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There are many machine learning techniques that cannot be performed on graph-data. Techniques such as graph embedding, i.e mapping a graph to a vector, can open up a variety of machine learning solutions. This thesis addresses to what extent static graph embedding techniques can capture important characteristics of an IT-architecture graph, with the purpose of embedding the graphs in a common euclidean vector space that can serve as the state space in a reinforcement learning setup. The metric used for evaluating the performance of the embedding is the security of the graph, i.e the time it would take for an unauthorized attacker to penetrate the IT-architecture graph. The algorithms evaluated in this work are the node embedding methods node2vec and gat2vec and the graph embedding method graph2vec. The predictive results of the embeddings are compared with two baseline methods. The results of each of the algorithms mostly display a significant predictive performance improvement compared to the baseline, where the F1 score in some cases is doubled. Indeed, the results indicate that static graph embedding methods can in fact capture some information about the security of an IT-architecture. However, no conclusion can be made whether a static graph embedding is actually the best contender for posing as the state space in a reinforcement learning framework. To make a certain conclusion other options has to be researched, such as dynamic graph embedding methods. / Det är många maskininlärningstekniker som inte kan appliceras på data i form av en graf. Tekniker som graph embedding, med andra ord att mappa en graf till ett vektorrum, can öppna upp för en större variation av maskininlärningslösningar. Det här examensarbetet evaluerar hur väl statiska graph embeddings kan fånga viktiga säkerhetsegenskaper hos en IT-arkitektur som är modellerad som en graf, med syftet att användas i en reinforcement learning algoritm. Dom egenskaper i grafen som används för att validera embedding metoderna är hur lång tid det skulle ta för en obehörig attackerare att penetrera IT-arkitekturen. Algorithmerna som implementeras är node embedding metoderna node2vec och gat2vec, samt graph embedding metoden graph2vec. Dom prediktiva resultaten är jämförda med två basmetoder. Resultaten av alla tre metoderna visar tydliga förbättringar relativt basmetoderna, där F1 värden i några fall uppvisar en fördubbling. Det går alltså att dra slutsatsen att att alla tre metoder kan fånga upp säkerhetsegenskaper i en IT-arkitektur. Dock går det inte att säga att statiska graph embeddings är den bästa lösningen till att representera en graf i en reinforcement learning algoritm, det finns andra komplikationer med statiska metoder, till exempel att embeddings från dessa metoder inte kan generaliseras till data som inte var använd till träning. För att kunna dra en absolut slutsats krävs mer undersökning, till exempel av dynamiska graph embedding metoder.

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In medical images, intensity changes caused by certain pathology can change the topology of image level-sets and are thus commonly referred to as topological changes. Topological changes cause false deformation in existing deformable registration algorithms, which in turn leads to unreliable observations in the clinical study that relies on the deformation fields, such as deformation based morphometry (DBM). In this work, we develop a new deformable registration algorithm for images with topological changes. In our proposed algorithm, 3D images are embedded as 4D surfaces in a Riemannian space. The registration is therefore conducted as a surface evolution, which is modeled by a diffusion process. Our algorithm differs from existing methods in the sense that it takes an a-priori estimation of areas with topological change as an additional input and generates dense deformation vector fields which are free of false deformation. In particular, the output of our algorithm is composed of a diffeomorphic deformation field and an intensity displacement which corrects intensity difference caused by topological changes. By conducting multiple sets of experiments, we demonstrate that our proposed algorithm is capable of accurately registering images with considerable topological changes. More importantly, the resulting deformation field is not impacted by topological changes, i.e., there is no false deformation. / Ph. D.