U(2) invariant squeezing properties of pair coherent states

The U(2) invariant approach is delineated for the pair coherent states to explore their squeezing properties. This approach is useful for a complete analysis of the squeezing properties of these two-mode states. We use the maximally compact subgroup U(2) of Sp(4,R) to mix the modes, thus allowing us to search over all possible quadratures for squeezing. The variance matrix for the pair coherent states turns out to be analytically diagonalisable, giving us a handle over its least eigenvalue, through which we are able to pin down the squeezing properties of these states. In order to explicitly demonstrate the role played by U(2) transformations, we connect our results to the previous analysis of squeezing for the pair coherent states.Comment: 6 pages revtex, one ps figure included using psfi

Exponential Family Hybrid Semi-Supervised Learning

We present an approach to semi-supervised learning based on an exponential family characterization. Our approach generalizes previous work on coupled priors for hybrid generative/discriminative models. Our model is more flexible and natural than previous approaches. Experimental results on several data sets show that our approach also performs better in practice.Comment: 6 pages, 3 figure

Laser Surface Engineering of composite titanium diboride coating on steel : synthesis and characterization

The aim of the present study was to identify and develop an unique combination of coating technique and material, which could target its properties similar to that of an ideal coating . In the present study, Nd:YAG laser was used as a tool to deposit ultrahard TiB2 ceramic on AISI 1010 steel within a fixed envelope of processing parameters such as laser power and traverse speed. The thrust of the present study is on the material properties and behavior of the TiB2 coating within the fixed envelope of these processing parameters. A uniform, continuous and crack free coating with metallurgically sound interface is obtained. Coating is “composite” in nature, comprising TiB2 particles and the Fe from steel trapped in the laser melt zone. Such coating has been evaluated for various properties such as mechanical (hardness, elastic modulus,interfacial energy, fracture toughness and fracture morphology), chemical and structural(x-ray diffraction, SEM, TEM and HRTEM) and high temperature oxidation and corrosion properties. Coating is hard and tough in nature. A semi-quantitative model has been developed to estimate the elastic modulus of TiB2 coating using nanoindentation technique. It also has been concluded that TiB2 coating has a high interfacial energy suggesting a stronger and adherent interface. Composite TiB2 coating has a significant oxidation resistance up to 800°C. Also, it has shown improved high temperature corrosion resistance against liquid aluminum. Such features contribute significantly towards the goal of achieving an ideal coating

Geometric Methods in Machine Learning and Data Mining

In machine learning, the standard goal of is to find an appropriate statistical model from a model space based on the training data from a data space; while in data mining, the goal is to find interesting patterns in the data from a data space. In both fields, these spaces carry geometric structures that can be exploited using methods that make use of these geometric structures (we shall call them geometric methods), or the problems themselves can be formulated in a way that naturally appeal to these methods. In such cases, studying these geometric structures and then using appropriate geometric methods not only gives insight into existing algorithms, but also helps build new and better algorithms. In my research, I develop methods that exploit geometric structure of problems for a variety of machine learning and data mining problems, and provide strong theoretical and empirical evidence in favor of using them. My dissertation is divided into two parts. In the first part, I develop algorithms to solve a well known problem in data mining i.e. distance embedding problem. In particular, I use tools from computational geometry to build a unified framework for solving a distance embedding problem known as multidimensional scaling (MDS). This geometry-inspired framework results in algorithms that can solve different variants of MDS better than previous state-of-the-art methods. In addition, these algorithms come with many other attractive properties: they are simple, intuitive, easily parallelizable, scalable, and can handle missing data. Furthermore, I extend my unified MDS framework to build scalable algorithms for dimensionality reduction, and also to solve a sensor network localization problem for mobile sensors. Experimental results show the effectiveness of this framework across all problems. In the second part of my dissertation, I turn to problems in machine learning, in particular, use geometry to reason about conjugate priors, develop a model that hybridizes between discriminative and generative frameworks, and build a new set of generative-process-driven kernels. More specifically, this part of my dissertation is devoted to the study of the geometry of the space of probabilistic models associated with statistical generative processes. This study --- based on the theory well grounded in information geometry --- allows me to reason about the appropriateness of conjugate priors from a geometric perspective, and hence gain insight into the large number of existing models that rely on these priors. Furthermore, I use this study to build hybrid models more naturally i.e., by combining discriminative and generative methods using the geometry underlying them, and also to build a family of kernels called generative kernels that can be used as off-the-shelf tool in any kernel learning method such as support vector machines. My experiments of generative kernels demonstrate their effectiveness providing further evidence in favor of using geometric methods