On Some Infinite Convex Invariants

The present study on some infinite convex invariants. The origin of convexity can be traced back to the period of Archimedes and Euclid. At the turn of the nineteenth centaury , convexicity became an independent branch of mathematics with its own problems, methods and theories. The convexity can be sorted out into two kinds, the first type deals with generalization of particular problems such as separation of convex sets[EL], extremality[FA], [DAV] or continuous selection Michael[M1] and the second type involved with a multi- purpose system of axioms. The theory of convex invariants has grown out of the classical results of Helly, Radon and Caratheodory in Euclidean spaces. Levi gave the first general definition of the invariants Helly number and Radon number. The notation of a convex structure was introduced by Jamison[JA4] and that of generating degree was introduced by Van de Vel[VAD8]. We also prove that for a non-coarse convex structure, rank is less than or equal to the generating degree, and also generalize Tverberg’s theorem using infinite partition numbers. Compare the transfinite topological and transfinite convex dimensions

Study on Fuzzy Ordered FuzzyTopological Spaces

In this study we combine the notions of fuzzy order and fuzzy topology of Chang and define fuzzy ordered fuzzy topological space. Its various properties are analysed. Product, quotient, union and intersection of fuzzy orders are introduced. Besides, fuzzy order preserving maps and various fuzzy completeness are investigated. Finally an attempt is made to study the notion of generalized fuzzy ordered fuzzy topological space by considering fuzzy order defined on a fuzzy subset.

Secret Sharing Schemes Using Visual Cryptography

Secret sharing schemes allow a secret to be shared among a group of participants so that only qualified subsets of participants can recover the secret. A visual cryptography scheme (VCS) is a special kind of secret sharing scheme in which the secret to share consists of an image and the shares consist of xeroxed transparencies which are stacked to recover the shared image. In this thesis we have given the theoretical background of Secret Sharing Schemes and the historical development of the subject. We have included a few examples to improve the readability of the thesis. We have tried to maintain the rigor of the treatment of the subject. The limitations and disadvantages of the various forms secret sharing schemes are brought out. Several new schemes for both dealing and combining are included in the thesis. We have introduced a new number system, called, POB number system. Representation using POB number system has been presented. Algorithms for finding the POB number and POB value are given.We have also proved that the representation using POB number system is unique and is more efficient. Being a new system, there is much scope for further development in this area.

Dynamical aspects of coupled Rossler systems: effects of noise

Nonlinear time series analysis is employed to study the complex behaviour exhibited by a coupled pair of Rossler systems. Dimensional analysis with emphasis on the topological correlation dimension and the Kolmogorov entropy of the system is carried out in the coupling parameter space. The regime of phase synchronization is identified and the extent of synchronization between the systems constituting the coupled system is quantified by the phase synchronization index. The effect of noise on the coupling between the systems is also investigated. An exhaustive study of the topological, dynamical and synchronization properties of the nonlinear system under consideration in its characteristic parameter space is attempted.

Development of a Novel Wideband Cylindrical Dielectric Resonator Antenna

The author presents the development of a new dielectric resonator antenna(DRA) suitable for wideband wireless communication applications.The design comprises of a simple cylindrical dielectric resonator (DR) and a microstrip feed, in a low radiation-Q structure,enabling wide impedance bandwidth.The radiation pattern is conical shaped,resulted from thew low-Q structure.Dielectric constant of the DR,its dimensions and topological parameters of the feed line are the major design parameters of the antenna.By proper selection of these parameters,the DRA can be operated over a wideband width covering multiple wireless applications.The antenna is simulated using Ansoft HFSS TM and measured using HP 8510C vector network analyser.Some of the measured results are confirmed by using the Finite Difference Time Domain(FDTD) technique implemented in MATLAB.

Some problems in set topology relating group of homeomorphisms and order

In this thesis we investigate some problems in set theoretical topology related to the concepts of the group of homeomorphisms and order. Many problems considered are directly or indirectly related to the concept of the group of homeomorphisms of a topological space onto itself. Order theoretic methods are used extensively. Chapter-l deals with the group of homeomorphisms. This concept has been investigated by several authors for many years from different angles. It was observed that nonhomeomorphic topological spaces can have isomorphic groups of homeomorphisms. Many problems relating the topological properties of a space and the algebraic properties of its group of homeomorphisms were investigated. The group of isomorphisms of several algebraic, geometric, order theoretic and topological structures had also been investigated. A related concept of the semigroup of continuous functions of a topological space also received attention

Depinning transition of dislocation assemblies: Pileups and low-angle grain boundaries

We investigate the depinning transition occurring in dislocation assemblies. In particular, we consider the cases of regularly spaced pileups and low-angle grain boundaries interacting with a disordered stress landscape provided by solute atoms, or by other immobile dislocations present in nonactive slip systems. Using linear elasticity, we compute the stress originated by small deformations of these assemblies and the corresponding energy cost in two and three dimensions. Contrary to the case of isolated dislocation lines, which are usually approximated as elastic strings with an effective line tension, the deformations of a dislocation assembly cannot be described by local elastic interactions with a constant tension or stiffness. A nonlocal elastic kernel results as a consequence of long-range interactions between dislocations. In light of this result, we revise statistical depinning theories of dislocation assemblies and compare the theoretical results with numerical simulations and experimental data.

Rigorous characterization of oxygen vacancies in ionic oxides

Charged and neutral oxygen vacancies in the bulk and on perfect and defective surfaces of MgO are characterized as quantum-mechanical subsystems chemically bonded to the host lattice and containing most of the charge left by the removed oxygens. Attractors of the electron density appear inside the vacancy, a necessary condition for the existence of a subsystem according to the atoms in molecules theory. The analysis of the electron localization function also shows attractors at the vacancy sites, which are associated to a localization basin shared with the valence domain of the nearest oxygens. This polyatomic superanion exhibits chemical trends guided by the formal charge and the coordination of the vacancy. The topological approach is shown to be essential to understand and predict the nature and chemical reactivity of these objects. There is not a vacancy but a coreless pseudoanion that behaves as an activated host oxygen.

SPATIAL CLUSTERING ALGORITHMS-AN OVERVIEW.

An Overview of known spatial clustering algorithms The space of interest can be the two-dimensional abstraction of the surface of the earth or a man-made space like the layout of a VLSI design, a volume containing a model of the human brain, or another 3d-space representing the arrangement of chains of protein molecules. The data consists of geometric information and can be either discrete or continuous. The explicit location and extension of spatial objects define implicit relations of spatial neighborhood (such as topological, distance and direction relations) which are used by spatial data mining algorithms. Therefore, spatial data mining algorithms are required for spatial characterization and spatial trend analysis. Spatial data mining or knowledge discovery in spatial databases differs from regular data mining in analogous with the differences between non-spatial data and spatial data. The attributes of a spatial object stored in a database may be affected by the attributes of the spatial neighbors of that object. In addition, spatial location, and implicit information about the location of an object, may be exactly the information that can be extracted through spatial data mining

Using Neural Network Classifier Support Vector Machine Regression for the prediction of Melting Point of Drug – like compounds

In our study we use a kernel based classification technique, Support Vector Machine Regression for predicting the Melting Point of Drug – like compounds in terms of Topological Descriptors, Topological Charge Indices, Connectivity Indices and 2D Auto Correlations. The Machine Learning model was designed, trained and tested using a dataset of 100 compounds and it was found that an SVMReg model with RBF Kernel could predict the Melting Point with a mean absolute error 15.5854 and Root Mean Squared Error 19.7576

Agri-environmental evaluation of traditional and alternative corn production systems in Chiapas, Mexico

This study evaluates the effects of environmental variables on traditional and alternative agroecosystems in three Ejidos (communal lands) in the Chiapas rainforest in Mexico. The tests occurred within two seasonal agricultural cycles. In spring-summer, experiments were performed with the traditional slash, fell and burn (S-F-B) system, no-burn systems and rotating systems with Mucuna deeringiana Bort., and in the autumn-winter agricultural cycle, three no-burn systems were compared to evaluate the effect of alternative sowing with corn (no-burn and topological modification of sowing). The results show a high floristic diversity in the study area (S_S = 4 - 23%), with no significant differences among the systems evaluated. In the first cycle, the analysis of the agronomical variables of the corn indicated better properties in the fallowing systems, with an average yield of 1950 kg ha^‑1, but there was variation related to the number of years left fallow. In the second cycle, the yields were positive for the alternative technology (average yield 3100 kg ha^‑1). The traditional S-F-B systems had reduced pests and increased organic matter and soil phosphorous content. These results are the consequence of fallow periods and adaptation to the environment; thus, this practice in the Chiapas rainforest constitutes an ethnocultural reality, which is unlikely to change in the near future if the agrosystems are managed based on historical principles.

Schauder – Zur Dekonstruktion eines Spürens

Zusammenfassung: Ziel der Arbeit ist den Sinn von Schauder philosophisch zu erhellen. An einem Einzelphänomen, wie es so bisher nicht behandelt wurde, wird zugleich das Geflecht von Affekt/Emotion/Gefühl, gestützt auf Hegel, Heidegger, Husserl, Freud und Lacan, in immer neuen Ansätzen kritisch reflektiert und Zug um Zug mit Derrida dekonstruiert. In einem Textverfahren, das sich auch grafisch durch gegenübergestellte Kolumnen auszeichnet, werden heterogene Ansätze zum Sinn von Schauder mit dekonstruktivistischen Einsichten konfrontiert. Die Ansätze, Schauder über Datum, Begriff, Phänomen oder Strukturelement bestimmen zu wollen, durchdringen sich dabei mit denjenigen, die sich einer solchen Bestimmung entziehen (Hegels Negativität, Heideggers Seinsentzug oder Lacans Signifikantenmangel). Am Fokus Schauder, an dem sich das Fiktive einer mit sich selbst identischen Präsenz besonders eindringlich darstellt, werden so spezifische Aporien der Metaphysik der Präsenz entfaltet und die Geschlossenheit logozentristischer Systeme in die Bewegung einer anderen Öffnung und Schließung im Sinn der Schrift bzw. des allgemeinen Textes transformiert. Neben der différance, dem Entzug der Metapher, dem Supplement und dem Gespenstischen stützt sich die Arbeit auf die Iterabilität, bei der im selben Zug die Identität des Sinns gestiftet und zerstreut wird (Dissemination). Im Kapitel Piloerection werden Ambivalenzen und Paradoxien des Schauders am Beispiel von computergestützten empirisch-psychologischen Studien aufgezeigt. Im Kapitel Atopologie des Schauders prädikative, propositionale und topologische Bedingungen zum Sinn von Schauder analysiert und dekonstruiert. Ebenso, im Folgekapitel Etymon, etymologische und technisch-mediale Bedingungen. Im Schlußkapitel Maß, Anmaß, Unmaß der Empfindung des Schauders wird am Beispiel der konkreten Beiträge zum Schauder von Aristoteles, Kant, Fechner, Otto, Klages, Lorenz und Adorno aufgezeigt, dass (1) ein Schauder nicht von einem Außen aus an-gemessen werden kann, (2) sich im Schauder die metaphysische Opposition von Fiktion und Realität in einer Unentscheidbarkeit zerstreut, (3) dass trotz der Heterogenität der Ansätze in diesen Beiträgen eine Komplizenschaft zum Ausdruck kommt: ein Begehren nach Präsenz, das durch den Ausschluß des Anderen zugleich die Gewalt des Einen produziert, (4) dass der Signifikant Schauder, der selbst in Abwesenheit eines Referenten, eines bestimmten Signifikats, einer aktuellen Bedeutungs­intention, eines Sen­ders oder Empfängers funktioniert, als verändertes Zu­rückbleiben eines differenzieller Zeichens betrachtet werden muss, als Effekt von Spuren, die sich nur in ihrem eige­nen Auslöschen ereignen. Die Arbeit schließt mit dem Vorschlag, Spüren jenseits von Arché, Telos oder Eschaton, jenseits eines Phallogozentrismus in der derridaschen Spur zu denken. Nicht zuletzt über diese Pfropfung, wie sie im Französischen [trace] so nicht möglich ist, schließt sie als deutschsprachiger Beitrag an sein Werk an.

A Distributed Model for Mobile Robot Environment-Learning and Navigation

A distributed method for mobile robot navigation, spatial learning, and path planning is presented. It is implemented on a sonar-based physical robot, Toto, consisting of three competence layers: 1) Low-level navigation: a collection of reflex-like rules resulting in emergent boundary-tracing. 2) Landmark detection: dynamically extracts landmarks from the robot's motion. 3) Map learning: constructs a distributed map of landmarks. The parallel implementation allows for localization in constant time. Spreading of activation computes both topological and physical shortest paths in linear time. The main issues addressed are: distributed, procedural, and qualitative representation and computation, emergent behaviors, dynamic landmarks, minimized communication.

Understanding Subsystems in Biology through Dimensionality Reduction, Graph Partitioning and Analytical Modeling

Biological systems exhibit rich and complex behavior through the orchestrated interplay of a large array of components. It is hypothesized that separable subsystems with some degree of functional autonomy exist; deciphering their independent behavior and functionality would greatly facilitate understanding the system as a whole. Discovering and analyzing such subsystems are hence pivotal problems in the quest to gain a quantitative understanding of complex biological systems. In this work, using approaches from machine learning, physics and graph theory, methods for the identification and analysis of such subsystems were developed. A novel methodology, based on a recent machine learning algorithm known as non-negative matrix factorization (NMF), was developed to discover such subsystems in a set of large-scale gene expression data. This set of subsystems was then used to predict functional relationships between genes, and this approach was shown to score significantly higher than conventional methods when benchmarking them against existing databases. Moreover, a mathematical treatment was developed to treat simple network subsystems based only on their topology (independent of particular parameter values). Application to a problem of experimental interest demonstrated the need for extentions to the conventional model to fully explain the experimental data. Finally, the notion of a subsystem was evaluated from a topological perspective. A number of different protein networks were examined to analyze their topological properties with respect to separability, seeking to find separable subsystems. These networks were shown to exhibit separability in a nonintuitive fashion, while the separable subsystems were of strong biological significance. It was demonstrated that the separability property found was not due to incomplete or biased data, but is likely to reflect biological structure.

Lecture notes

Lecture notes in LaTex