ON APPROXIMATION METHODS FOR UNBOUNDED OPERATORS

Department of Mathematics, Cochin University of Science and Technology

On Implementing Joins, Aggregates and Universal Quantifier in Temporal Databases using SQL Standards

A feasible way of implementing a temporal database is by mapping temporal data model onto a conventional data model followed by a commercial database management system. Even though extensions were proposed to standard SQL for supporting temporal databases, such proposals have not yet come across standardization processes. This paper attempts to implement database operators such as aggregates and universal quantifier for temporal databases, implemented on top of relational database systems, using currently available SQL standards.

A Study of Elementary Operators

Department of Mathematics, Cochin University of Science and Technology

Spectral Analysis of Bounded Self-adjoint operators - A Linear Algebraic Approach

This thesis Entitled Spectral theory of bounded self-adjoint operators -A linear algebraic approach.The main results of the thesis can be classified as three different approaches to the spectral approximation problems. The truncation method and its perturbed versions are part of the classical linear algebraic approach to the subject. The usage of block Toeplitz-Laurent operators and the matrix valued symbols is considered as a particular example where the linear algebraic techniques are effective in simplifying problems in inverse spectral theory. The abstract approach to the spectral approximation problems via pre-conditioners and Korovkin-type theorems is an attempt to make the computations involved, well conditioned. However, in all these approaches, linear algebra comes as the central object. The objective of this study is to discuss the linear algebraic techniques in the spectral theory of bounded self-adjoint operators on a separable Hilbert space. The usage of truncation method in approximating the bounds of essential spectrum and the discrete spectral values outside these bounds is well known. The spectral gap prediction and related results was proved in the second chapter. The discrete versions of Borg-type theorems, proved in the third chapter, partly overlap with some known results in operator theory. The pure linear algebraic approach is the main novelty of the results proved here.

A Study of Morphological Operators with Applications

The present work deals with the A study of morphological opertors with applications. Morphology is now a.necessary tool for engineers involved with imaging applications. Morphological operations have been viewed as filters the properties of which have been well studied (Heijmans, 1994). Another well-known class of non-linear filters is the class of rank order filters (Pitas and Venetsanopoulos, 1990). Soft morphological filters are a combination of morphological and weighted rank order filters (Koskinen, et al., 1991, Kuosmanen and Astola, 1995). They have been introduced to improve the behaviour of traditional morphological filters in noisy environments. The idea was to slightly relax the typical morphological definitions in such a way that a degree of robustness is achieved, while most of the desirable properties of typical morphological operations are maintained. Soft morphological filters are less sensitive to additive noise and to small variations in object shape than typical morphological filters. They can remove positive and negative impulse noise, preserving at the same time small details in images. Currently, Mathematical Morphology allows processing images to enhance fuzzy areas, segment objects, detect edges and analyze structures. The techniques developed for binary images are a major step forward in the application of this theory to gray level images. One of these techniques is based on fuzzy logic and on the theory of fuzzy sets.Fuzzy sets have proved to be strongly advantageous when representing in accuracies, not only regarding the spatial localization of objects in an image but also the membership of a certain pixel to a given class. Such inaccuracies are inherent to real images either because of the presence of indefinite limits between the structures or objects to be segmented within the image due to noisy acquisitions or directly because they are inherent to the image formation methods.

On infinite graphs and related matrices

This thesis Entitled On Infinite graphs and related matrices.ln the last two decades (iraph theory has captured wide attraction as a Mathematical model for any system involving a binary relation. The theory is intimately related to many other branches of Mathematics including Matrix Theory Group theory. Probability. Topology and Combinatorics . and has applications in many other disciplines..Any sort of study on infinite graphs naturally involves an attempt to extend the well known results on the much familiar finite graphs. A graph is completely determined by either its adjacencies or its incidences. A matrix can convey this information completely. This makes a proper labelling of the vertices. edges and any other elements considered, an inevitable process. Many types of labelling of finite graphs as Cordial labelling, Egyptian labelling, Arithmetic labeling and Magical labelling are available in the literature. The number of matrices associated with a finite graph are too many For a study ofthis type to be exhaustive. A large number of theorems have been established by various authors for finite matrices. The extension of these results to infinite matrices associated with infinite graphs is neither obvious nor always possible due to convergence problems. In this thesis our attempt is to obtain theorems of a similar nature on infinite graphs and infinite matrices. We consider the three most commonly used matrices or operators, namely, the adjacency matrix

Message Integrity in the World Wide Web: Use of Nested Hash Function and a Fast Stream Cipher

The focus of this work is to provide authentication and confidentiality of messages in a swift and cost effective manner to suit the fast growing Internet applications. A nested hash function with lower computational and storage demands is designed with a view to providing authentication as also to encrypt the message as well as the hash code using a fast stream cipher MAJE4 with a variable key size of 128-bit or 256-bit for achieving confidentiality. Both nested Hash function and MAJE4 stream cipher algorithm use primitive computational operators commonly found in microprocessors; this makes the method simple and fast to implement both in hardware and software. Since the memory requirement is less, it can be used for handheld devices for security purposes.

`A Study on Ultra L-topologies and Lattices of L-topologies'

The thesis is divided into nine chapters including introduction. Mainly we determine ultra L-topologies in the lattice of L- topologies and study their properties. We nd some sublattices in the lattice of L-topologies and study their properties. Also we study the lattice structure of the set of all L-closure operators on a set X.

Effectiveness Of Feature Detection Operators On The Performance Of Iris Biometric Recognition System

Iris Recognition is a highly efficient biometric identification system with great possibilities for future in the security systems area.Its robustness and unobtrusiveness, as opposed tomost of the currently deployed systems, make it a good candidate to replace most of thesecurity systems around. By making use of the distinctiveness of iris patterns, iris recognition systems obtain a unique mapping for each person. Identification of this person is possible by applying appropriate matching algorithm.In this paper, Daugman’s Rubber Sheet model is employed for irisnormalization and unwrapping, descriptive statistical analysis of different feature detection operators is performed, features extracted is encoded using Haar wavelets and for classification hammingdistance as a matching algorithm is used. The system was tested on the UBIRIS database. The edge detection algorithm, Canny, is found to be the best one to extract most of the iris texture. The success rate of feature detection using canny is 81%, False Accept Rate is 9% and False Reject Rate is 10%.

Artificial boundary conditions for the Stokes and Navier-Stokes equations in domains that are layer-like at infinity

Artificial boundary conditions are presented to approximate solutions to Stokes- and Navier-Stokes problems in domains that are layer-like at infinity. Based on results about existence and asymptotics of the solutions v^infinity, p^infinity to the problems in the unbounded domain Omega the error v^infinity - v^R, p^infinity - p^R is estimated in H^1(Omega_R) and L^2(Omega_R), respectively. Here v^R, p^R are the approximating solutions on the truncated domain Omega_R, the parameter R controls the exhausting of Omega. The artificial boundary conditions involve the Steklov-Poincare operator on a circle together with its inverse and thus turn out to be a combination of local and nonlocal boundary operators. Depending on the asymptotic decay of the data of the problems, in the linear case the error vanishes of order O(R^{-N}), where N can be arbitrarily large.

User Profile Management and Selection in Context-Aware Service Platforms for Networks Beyond 3G

In recent years, progress in the area of mobile telecommunications has changed our way of life, in the private as well as the business domain. Mobile and wireless networks have ever increasing bit rates, mobile network operators provide more and more services, and at the same time costs for the usage of mobile services and bit rates are decreasing. However, mobile services today still lack functions that seamlessly integrate into users’ everyday life. That is, service attributes such as context-awareness and personalisation are often either proprietary, limited or not available at all. In order to overcome this deficiency, telecommunications companies are heavily engaged in the research and development of service platforms for networks beyond 3G for the provisioning of innovative mobile services. These service platforms are to support such service attributes. Service platforms are to provide basic service-independent functions such as billing, identity management, context management, user profile management, etc. Instead of developing own solutions, developers of end-user services such as innovative messaging services or location-based services can utilise the platform-side functions for their own purposes. In doing so, the platform-side support for such functions takes away complexity, development time and development costs from service developers. Context-awareness and personalisation are two of the most important aspects of service platforms in telecommunications environments. The combination of context-awareness and personalisation features can also be described as situation-dependent personalisation of services. The support for this feature requires several processing steps. The focus of this doctoral thesis is on the processing step, in which the user’s current context is matched against situation-dependent user preferences to find the matching user preferences for the current user’s situation. However, to achieve this, a user profile management system and corresponding functionality is required. These parts are also covered by this thesis. Altogether, this thesis provides the following contributions: The first part of the contribution is mainly architecture-oriented. First and foremost, we provide a user profile management system that addresses the specific requirements of service platforms in telecommunications environments. In particular, the user profile management system has to deal with situation-specific user preferences and with user information for various services. In order to structure the user information, we also propose a user profile structure and the corresponding user profile ontology as part of an ontology infrastructure in a service platform. The second part of the contribution is the selection mechanism for finding matching situation-dependent user preferences for the personalisation of services. This functionality is provided as a sub-module of the user profile management system. Contrary to existing solutions, our selection mechanism is based on ontology reasoning. This mechanism is evaluated in terms of runtime performance and in terms of supported functionality compared to other approaches. The results of the evaluation show the benefits and the drawbacks of ontology modelling and ontology reasoning in practical applications.

Development and applications of density matrix functional theory of generalized Hubbard Models

In dieser Doktorarbeit wird eine akkurate Methode zur Bestimmung von Grundzustandseigenschaften stark korrelierter Elektronen im Rahmen von Gittermodellen entwickelt und angewandt. In der Dichtematrix-Funktional-Theorie (LDFT, vom englischen lattice density functional theory) ist die Ein-Teilchen-Dichtematrix γ die fundamentale Variable. Auf der Basis eines verallgemeinerten Hohenberg-Kohn-Theorems ergibt sich die Grundzustandsenergie Egs[γgs] = min° E[γ] durch die Minimierung des Energiefunktionals E[γ] bezüglich aller physikalischer bzw. repräsentativer γ. Das Energiefunktional kann in zwei Beiträge aufgeteilt werden: Das Funktional der kinetischen Energie T[γ], dessen lineare Abhängigkeit von γ genau bekannt ist, und das Funktional der Korrelationsenergie W[γ], dessen Abhängigkeit von γ nicht explizit bekannt ist. Das Auffinden präziser Näherungen für W[γ] stellt die tatsächliche Herausforderung dieser These dar. Einem Teil dieser Arbeit liegen vorausgegangene Studien zu Grunde, in denen eine Näherung des Funktionals W[γ] für das Hubbardmodell, basierend auf Skalierungshypothesen und exakten analytischen Ergebnissen für das Dimer, hergeleitet wird. Jedoch ist dieser Ansatz begrenzt auf spin-unabhängige und homogene Systeme. Um den Anwendungsbereich von LDFT zu erweitern, entwickeln wir drei verschiedene Ansätze zur Herleitung von W[γ], die das Studium von Systemen mit gebrochener Symmetrie ermöglichen. Zuerst wird das bisherige Skalierungsfunktional erweitert auf Systeme mit Ladungstransfer. Eine systematische Untersuchung der Abhängigkeit des Funktionals W[γ] von der Ladungsverteilung ergibt ähnliche Skalierungseigenschaften wie für den homogenen Fall. Daraufhin wird eine Erweiterung auf das Hubbardmodell auf bipartiten Gittern hergeleitet und an sowohl endlichen als auch unendlichen Systemen mit repulsiver und attraktiver Wechselwirkung angewandt. Die hohe Genauigkeit dieses Funktionals wird aufgezeigt. Es erweist sich jedoch als schwierig, diesen Ansatz auf komplexere Systeme zu übertragen, da bei der Berechnung von W[γ] das System als ganzes betrachtet wird. Um dieses Problem zu bewältigen, leiten wir eine weitere Näherung basierend auf lokalen Skalierungseigenschaften her. Dieses Funktional ist lokal bezüglich der Gitterplätze formuliert und ist daher anwendbar auf jede Art von geordneten oder ungeordneten Hamiltonoperatoren mit lokalen Wechselwirkungen. Als Anwendungen untersuchen wir den Metall-Isolator-Übergang sowohl im ionischen Hubbardmodell in einer und zwei Dimensionen als auch in eindimensionalen Hubbardketten mit nächsten und übernächsten Nachbarn. Schließlich entwickeln wir ein numerisches Verfahren zur Berechnung von W[γ], basierend auf exakten Diagonalisierungen eines effektiven Vielteilchen-Hamilton-Operators, welcher einen von einem effektiven Medium umgebenen Cluster beschreibt. Dieser effektive Hamiltonoperator hängt von der Dichtematrix γ ab und erlaubt die Herleitung von Näherungen an W[γ], dessen Qualität sich systematisch mit steigender Clustergröße verbessert. Die Formulierung ist spinabhängig und ermöglicht eine direkte Verallgemeinerung auf korrelierte Systeme mit mehreren Orbitalen, wie zum Beispiel auf den spd-Hamilton-Operator. Darüber hinaus berücksichtigt sie die Effekte kurzreichweitiger Ladungs- und Spinfluktuationen in dem Funktional. Für das Hubbardmodell wird die Genauigkeit der Methode durch Vergleich mit Bethe-Ansatz-Resultaten (1D) und Quanten-Monte-Carlo-Simulationen (2D) veranschaulicht. Zum Abschluss wird ein Ausblick auf relevante zukünftige Entwicklungen dieser Theorie gegeben.

Optimization-Based Robotic Manipulation for Safe Interaction with Human Operators

This thesis investigates a method for human-robot interaction (HRI) in order to uphold productivity of industrial robots like minimization of the shortest operation time, while ensuring human safety like collision avoidance. For solving such problems an online motion planning approach for robotic manipulators with HRI has been proposed. The approach is based on model predictive control (MPC) with embedded mixed integer programming. The planning strategies of the robotic manipulators mainly considered in the thesis are directly performed in the workspace for easy obstacle representation. The non-convex optimization problem is approximated by a mixed-integer program (MIP). It is further effectively reformulated such that the number of binary variables and the number of feasible integer solutions are drastically decreased. Safety-relevant regions, which are potentially occupied by the human operators, can be generated online by a proposed method based on hidden Markov models. In contrast to previous approaches, which derive predictions based on probability density functions in the form of single points, such as most likely or expected human positions, the proposed method computes safety-relevant subsets of the workspace as a region which is possibly occupied by the human at future instances of time. The method is further enhanced by combining reachability analysis to increase the prediction accuracy. These safety-relevant regions can subsequently serve as safety constraints when the motion is planned by optimization. This way one arrives at motion plans that are safe, i.e. plans that avoid collision with a probability not less than a predefined threshold. The developed methods have been successfully applied to a developed demonstrator, where an industrial robot works in the same space as a human operator. The task of the industrial robot is to drive its end-effector according to a nominal sequence of grippingmotion-releasing operations while no collision with a human arm occurs.

Farmers’ knowledge and perceptions of potato pests and their management in Uganda

As we initiate entomological research on potato (Solanum tuberosum L.) in Uganda, there is need to understand farmers’ knowledge of existing insect pest problems and their management practices. Such information is important for designing a suitable intervention and successful integrated pest management (IPM) strategy. A farm household survey using a structured questionnaire was conducted among 204 potato farmers in six districts of Uganda (i.e., Kabale, Kisoro, Mbale, Kapchorwa, Mubende, and Kyegegwa) during August and September 2013. Diseases, insect pests, price fluctuations, and low market prices were the four highest ranked constraints in potato production, in order of decreasing importance. Cutworms (Agrotis spp.), aphids (Myzus persicae (Sulzer)), and potato tuber moth (Phthorimaea operculella (Zeller)) were the three most severe insect pests. Ants (Dorylis orantalis Westwood), whiteflies (Bemisia tabaci (Gennadius)), and leafminer flies (Liriomyza huidobrensis (Blanchard)) were pests of moderate importance. Major yield losses are predominantly due to late blight (Phytophthora infestans (Mont.) de Bary) and reached 100% without chemical control in the districts of Kabale, Kisoro, Mbale, and Kapchorwa. On average, farmers had little to moderate knowledge about pest characteristics. The predominant control methods were use of fungicides (72% of respondents) and insecticides (62% of respondents). On average, only 5% of the 204 farmers knew about insect pests and their natural enemies. This lack of knowledge calls for training of both farmers and extension workers in insect pest identification, their biology, and control. Empowering farmers with knowledge about insect pests is essential for the reduction of pesticide misuse and uptake of more environmentally friendly approaches like IPM. Field surveys would need follow-up in order to assess the actual field infestation rates and intensities of each insect pest and compare the results with the responses received from farmers.

New Architectural Models for Visibly Controllable Computing: The Relevance of Dynamic Object Oriented Architectures and Plan Based Computing Models

Traditionally, we've focussed on the question of how to make a system easy to code the first time, or perhaps on how to ease the system's continued evolution. But if we look at life cycle costs, then we must conclude that the important question is how to make a system easy to operate. To do this we need to make it easy for the operators to see what's going on and to then manipulate the system so that it does what it is supposed to. This is a radically different criterion for success. What makes a computer system visible and controllable? This is a difficult question, but it's clear that today's modern operating systems with nearly 50 million source lines of code are neither. Strikingly, the MIT Lisp Machine and its commercial successors provided almost the same functionality as today's mainstream sytsems, but with only 1 Million lines of code. This paper is a retrospective examination of the features of the Lisp Machine hardware and software system. Our key claim is that by building the Object Abstraction into the lowest tiers of the system, great synergy and clarity were obtained. It is our hope that this is a lesson that can impact tomorrow's designs. We also speculate on how the spirit of the Lisp Machine could be extended to include a comprehensive access control model and how new layers of abstraction could further enrich this model.