A regular texture is formed from a regular congruent tiling of perceptually meaningful texture elements, also known as textons. If the tiling statistically deviates from regularity, either by texton structure, colour, or size, the texture is called near-regular. If we continue to perturb the tiling, the texture becomes stochastic. The set of possible textures that lie between regular and stochastic make up the texture spectrum: regular, near-regular, regular, near-stochastic, and stochastic. <p>In this thesis we provide a solution to the problem of creating, from a near-regular texture, a lattice which defines the placement of textons. We divide the problem into two distinct sub-areas: finding textons within an image, and lattice creation using both an ad-hoc method and a graph-theoretic method. <p>The problem of finding textons within an image is addressed using correlation. A texton selected by the user is correlated with the image and points of high correlation are extracted using non-maximal suppression. To extend this framework to irregular textures, we present early results on the use of feature space during correlation. We also present a method of correcting for a specific type of error in the texton finding result using frequency-space analysis. <p>Given texton locations, we provide two methods of creating a lattice. The ad-hoc method is able to create a lattice in spite of inconsistencies in the texton locating data. However, as texture becomes irregular the ad-hoc lattice construction method fails to correctly connect textons. To overcome this failure we adapt methods of creating proximity graphs, which join two textons whose neighbourhoods satisfy certain criteria, to our problem. The proximity graphs are parameterized for selection of the most appropriate graph choice for a given texture, solving the general lattice construction problem given correct texton locations. <p>In the output of the algorithm, centres of textons will be connected by edges in the lattice following the structure of texton placement within the input image. More precisely, for a texture T, we create a graph G = (V,E) dependent on T, where V is a set of texton centres, and E ={(v_i, v_j)} is a set of edges, where v_i, v_j are in V. Each edge e in E connects texton centre v in V to its most perceptually sensible neighbours.

Within the last decade, the importance of flexibility and efficiency has increased in the manufacturing sector. The rising level of uncertainty in consumer preferences has caused many organizations to aggressively search for cost reductions and other sources of competitive advantage. This fact has resulted in an increased implementation of advanced manufacturing technologies (AMT). A number of studies propose that the implementation of AMT must be accompanied by a shift in supporting organizational practices to realize the greatest performance enhancement. As yet, the complementarities between organizational policies and AMT have not been determined. Using assumptions about complementarities in manufacturing made by Milgrom and Roberts (1995) in conjunction with a comprehensive AMT survey (Survey of Advanced Technology in Canadian Manufacturing-1998) a model of manufacturing plant productivity was developed. Constrained regression analysis reveals that the use of AMT, as well as various organizational policies, depends both on the size of the plant as well as the industry in which it operates. Factor analysis of the over 70 variables found that regardless of the nature of the variable (business strategy, source of implementation support, AMT, etc. ), all design elements factored together. The factor analysis also shows that large firms who use AMT also have many design technologies. This result differs for smaller firms where the use of AMT is highly correlated with perceived benefits of the technology and a large number of sources of implementation support. The analysis also supports the distinction of high technology (highly innovative) industries and low technology (low levels of innovation) industries since electronics, chemicals and automotive have a large percentage of plants with all of the model factors whereas the textile, non-metal and lumber industries have very few plants with all of the model factors. The results show that there are important differences that should be considered when creating policies to encourage innovation and the use of AMT for the various manufacturing industries and plant sizes.

In the last decade, there has been an explosive growth in different applications of wireless technology, due to users' increasing expectations for multi-media services. With the current trend, the present systems will not be able to handle the required data traffic. Lattice codes have attracted considerable attention in recent years, because they provide high data rate constellations. In this thesis, the applications of implementing lattice codes in different communication systems are investigated. The thesis is divided into two major parts. Focus of the first part is on constellation shaping and the problem of lattice labeling. The second part is devoted to the lattice decoding problem. In constellation shaping technique, conventional constellations are replaced by lattice codes that satisfy some geometrical properties. However, a simple algorithm, called lattice labeling, is required to map the input data to the lattice code points. In the first part of this thesis, the application of lattice codes for constellation shaping in Orthogonal Frequency Division Multiplexing (OFDM) and Multi-Input Multi-Output (MIMO) broadcast systems are considered. In an OFDM system a lattice code with low Peak to Average Power Ratio (PAPR) is desired. Here, a new lattice code with considerable PAPR reduction for OFDM systems is proposed. Due to the recursive structure of this lattice code, a simple lattice labeling method based on Smith normal decomposition of an integer matrix is obtained. A selective mapping method in conjunction with the proposed lattice code is also presented to further reduce the PAPR. MIMO broadcast systems are also considered in the thesis. In a multiple antenna broadcast system, the lattice labeling algorithm should be such that different users can decode their data independently. Moreover, the implemented lattice code should result in a low average transmit energy. Here, a selective mapping technique provides such a lattice code. Lattice decoding is the focus of the second part of the thesis, which concerns the operation of finding the closest point of the lattice code to any point in N-dimensional real space. In digital communication applications, this problem is known as the integer least-square problem, which can be seen in many areas, e.g. the detection of symbols transmitted over the multiple antenna wireless channel, the multiuser detection problem in Code Division Multiple Access (CDMA) systems, and the simultaneous detection of multiple users in a Digital Subscriber Line (DSL) system affected by crosstalk. Here, an efficient lattice decoding algorithm based on using Semi-Definite Programming (SDP) is introduced. The proposed algorithm is capable of handling any form of lattice constellation for an arbitrary labeling of points. In the proposed methods, the distance minimization problem is expressed in terms of a binary quadratic minimization problem, which is solved by introducing several matrix and vector lifting SDP relaxation models. The new SDP models provide a wealth of trade-off between the complexity and the performance of the decoding problem.

In multiple-input multiple-output (MIMO) systems, the use of lattice reduction methods such as the one proposed by Lenstra-Lenstra-Lovasz (LLL) significantly improves the performance of the suboptimal solutions like zero-forcing (ZF) and zero-forcing deceision-feedback-equalizer (ZF-DFE). Today's high rate data communication demands faster lattice reduction methods. Taking advantage of the temporal correlation of a Rayleigh fading channel, a new method is proposed to reduce the complexity of the lattice reduction methods. The proposed method achieves the same error performance as the original lattice reduction methods, but significantly reduces the complexity of lattice reduction algorithm. The proposed method can be used in any MIMO scenario, such as the MIMO detection, and broadcast cases, which are studied in this work.

Within the last decade, the importance of flexibility and efficiency has increased in the manufacturing sector. The rising level of uncertainty in consumer preferences has caused many organizations to aggressively search for cost reductions and other sources of competitive advantage. This fact has resulted in an increased implementation of advanced manufacturing technologies (AMT). A number of studies propose that the implementation of AMT must be accompanied by a shift in supporting organizational practices to realize the greatest performance enhancement. As yet, the complementarities between organizational policies and AMT have not been determined. Using assumptions about complementarities in manufacturing made by Milgrom and Roberts (1995) in conjunction with a comprehensive AMT survey (Survey of Advanced Technology in Canadian Manufacturing-1998) a model of manufacturing plant productivity was developed. Constrained regression analysis reveals that the use of AMT, as well as various organizational policies, depends both on the size of the plant as well as the industry in which it operates. Factor analysis of the over 70 variables found that regardless of the nature of the variable (business strategy, source of implementation support, AMT, etc. ), all design elements factored together. The factor analysis also shows that large firms who use AMT also have many design technologies. This result differs for smaller firms where the use of AMT is highly correlated with perceived benefits of the technology and a large number of sources of implementation support. The analysis also supports the distinction of high technology (highly innovative) industries and low technology (low levels of innovation) industries since electronics, chemicals and automotive have a large percentage of plants with all of the model factors whereas the textile, non-metal and lumber industries have very few plants with all of the model factors. The results show that there are important differences that should be considered when creating policies to encourage innovation and the use of AMT for the various manufacturing industries and plant sizes.

This thesis investigates lattice compression of polynomial matrices over finite fields. For an m x n matrix, the goal of lattice compression is to find an m x (m+k) matrix, for some relatively small k, such that the lattice span of two matrices are equivalent. For any m x n polynomial matrix with degree bound d, it can be compressed by multiplying by a random n x (m+k) matrix B with degree bound s. In this thesis, we prove that there is a positive probability that L(A)=L(AB) with k(s+1)=\Theta(\log(md)). This is shown to hold even when s=0 (i.e., where B is a matrix of constants). We also design a competitive probabilistic lattice compression algorithm of the Las Vegas type that has a positive probability of success on any input and requires O~(nm^{\theta-1}B(d)) field operations.

In the last decade, there has been an explosive growth in different applications of wireless technology, due to users' increasing expectations for multi-media services. With the current trend, the present systems will not be able to handle the required data traffic. Lattice codes have attracted considerable attention in recent years, because they provide high data rate constellations. In this thesis, the applications of implementing lattice codes in different communication systems are investigated. The thesis is divided into two major parts. Focus of the first part is on constellation shaping and the problem of lattice labeling. The second part is devoted to the lattice decoding problem. In constellation shaping technique, conventional constellations are replaced by lattice codes that satisfy some geometrical properties. However, a simple algorithm, called lattice labeling, is required to map the input data to the lattice code points. In the first part of this thesis, the application of lattice codes for constellation shaping in Orthogonal Frequency Division Multiplexing (OFDM) and Multi-Input Multi-Output (MIMO) broadcast systems are considered. In an OFDM system a lattice code with low Peak to Average Power Ratio (PAPR) is desired. Here, a new lattice code with considerable PAPR reduction for OFDM systems is proposed. Due to the recursive structure of this lattice code, a simple lattice labeling method based on Smith normal decomposition of an integer matrix is obtained. A selective mapping method in conjunction with the proposed lattice code is also presented to further reduce the PAPR. MIMO broadcast systems are also considered in the thesis. In a multiple antenna broadcast system, the lattice labeling algorithm should be such that different users can decode their data independently. Moreover, the implemented lattice code should result in a low average transmit energy. Here, a selective mapping technique provides such a lattice code. Lattice decoding is the focus of the second part of the thesis, which concerns the operation of finding the closest point of the lattice code to any point in N-dimensional real space. In digital communication applications, this problem is known as the integer least-square problem, which can be seen in many areas, e.g. the detection of symbols transmitted over the multiple antenna wireless channel, the multiuser detection problem in Code Division Multiple Access (CDMA) systems, and the simultaneous detection of multiple users in a Digital Subscriber Line (DSL) system affected by crosstalk. Here, an efficient lattice decoding algorithm based on using Semi-Definite Programming (SDP) is introduced. The proposed algorithm is capable of handling any form of lattice constellation for an arbitrary labeling of points. In the proposed methods, the distance minimization problem is expressed in terms of a binary quadratic minimization problem, which is solved by introducing several matrix and vector lifting SDP relaxation models. The new SDP models provide a wealth of trade-off between the complexity and the performance of the decoding problem.

In multiple-input multiple-output (MIMO) systems, the use of lattice reduction methods such as the one proposed by Lenstra-Lenstra-Lovasz (LLL) significantly improves the performance of the suboptimal solutions like zero-forcing (ZF) and zero-forcing deceision-feedback-equalizer (ZF-DFE). Today's high rate data communication demands faster lattice reduction methods. Taking advantage of the temporal correlation of a Rayleigh fading channel, a new method is proposed to reduce the complexity of the lattice reduction methods. The proposed method achieves the same error performance as the original lattice reduction methods, but significantly reduces the complexity of lattice reduction algorithm. The proposed method can be used in any MIMO scenario, such as the MIMO detection, and broadcast cases, which are studied in this work.

A regular texture is formed from a regular congruent tiling of perceptually meaningful texture elements, also known as textons. If the tiling statistically deviates from regularity, either by texton structure, colour, or size, the texture is called near-regular. If we continue to perturb the tiling, the texture becomes stochastic. The set of possible textures that lie between regular and stochastic make up the texture spectrum: regular, near-regular, regular, near-stochastic, and stochastic. <p>In this thesis we provide a solution to the problem of creating, from a near-regular texture, a lattice which defines the placement of textons. We divide the problem into two distinct sub-areas: finding textons within an image, and lattice creation using both an ad-hoc method and a graph-theoretic method. <p>The problem of finding textons within an image is addressed using correlation. A texton selected by the user is correlated with the image and points of high correlation are extracted using non-maximal suppression. To extend this framework to irregular textures, we present early results on the use of feature space during correlation. We also present a method of correcting for a specific type of error in the texton finding result using frequency-space analysis. <p>Given texton locations, we provide two methods of creating a lattice. The ad-hoc method is able to create a lattice in spite of inconsistencies in the texton locating data. However, as texture becomes irregular the ad-hoc lattice construction method fails to correctly connect textons. To overcome this failure we adapt methods of creating proximity graphs, which join two textons whose neighbourhoods satisfy certain criteria, to our problem. The proximity graphs are parameterized for selection of the most appropriate graph choice for a given texture, solving the general lattice construction problem given correct texton locations. <p>In the output of the algorithm, centres of textons will be connected by edges in the lattice following the structure of texton placement within the input image. More precisely, for a texture T, we create a graph G = (V,E) dependent on T, where V is a set of texton centres, and E ={(v_i, v_j)} is a set of edges, where v_i, v_j are in V. Each edge e in E connects texton centre v in V to its most perceptually sensible neighbours.

This research focuses on the characterization of the structure and mechanical behavior of metal nanowires. Molecular dynamics simulations with embedded-atom method (EAM) potentials are used. A novel shape memory effect and pseudoelastic behavior of single-crystalline FCC metal (Cu, Ni, and Au) nanowires are discovered. Specifically, upon tensile loading and unloading, these wires can recover elongations of up to 50%, well beyond the recoverable strains of 5-8% typical for most bulk shape memory alloys. This novel behavior arises from a reversible lattice reorientation driven by the high surface-stress-induced internal stresses at the nanoscale. It exists over a wide range of temperature and is associated with response times on the order of nanoseconds, making the nanowires attractive functional components for a new generation of biosensors, transducers, and interconnects in nano-electromechanical systems. It is found that this novel shape memory behavior only exists at the nanometer scale but not in bulk metals. The reason is that only at the nanoscale is the surface-stress-induced driving force large enough to initiate the transformation. The lattice reorientation process is also temperature-dependent because thermal energy facilitates the overcoming of the energy barrier for the transformation. Therefore, nanowires show either pseudoelasticity or shape memory effect depending on whether the transformation is induced by unloading or heating. It is also found that not all FCC nanowires show shape memory behavior. Only FCC metals with higher tendency for twinning (such as Cu, Au, Ni) show the shape memory because twinning leads to the reversible lattice reorientation. On the other hand, FCC metals with low likelihood of twinning (such as Al) do not show shape memory because these wires deforms via crystal slip, which leads to irreversible deformation. A micromechanical continuum model is developed to characterize the shape memory behavior observed. This model treats the lattice reorientation process as a smooth transition between a series of phase-equilibrium states superimposed with a dissipative twin boundary propagation process. This model captures the major characteristics of the unique behavior due to lattice reorientation and accounts for the size and temperature effects, yielding results in excellent agreement with the results of molecular dynamics simulations.