My primary and current research work is in the general spirit of algebras of logic, lattice theory, hyper structures and applications. A partially ordered set, or poset for short is a pair (P, ≤) where P is a set and ≤ a partial order on P. A poset (P, ≤) is called a lattice if every pair x, y ∈ P has a least upper bound x ∨ y and a greatest lowest bound x ∧ y in P. A lattice is bounded if it h...

The information age has witnessed a proliferation of personal data available in digital form that can be stored and analyzed. On the one hand, this has led to the development of data mining tools that aim to infer useful trends from this data. But, on the other hand, easy access to personal data poses a threat to individual privacy. My main research interest lies in the area of designing algori...

My recent and ongoing research is focused on the interpretation of referring expressions (e.g. she, Rosa, that woman, the woman we talked about yesterday) as a window on the semantics-pragmatics interface. Referring expressions have attracted a great deal of interest in fields concerned with linguistic meaning, including semantics, psycholinguistics, and the philosophy of language, because they...

• Symmetry analysis of differential equations: classical and nonclassical symmetries, potential symmetries, group–invariant solutions, variational symmetries and conservation laws • Applications of symmetry analysis theory to mathematical models arising in mathematical physics, mathematical biology, image processing, engineering, financial mathematics and other research fields • Geometric appro...

My primary area of research has been algebraic geometry and its interaction with the theory of linear systems of partial differential equations (PDEs). This interaction is provided through the study of D-modules; i.e., modules over the ring of algebraic differential operators. The computational aspects of the subject interest me most. The use of Gröbner bases yields relatively effective algorit...

My principal research interests lie in planning the motions of movable objects such as proteins and robots. This work [5], unified under the theme of intelligent motion planning, addresses important questions of analysis and feasibility in both robotic [1,2,9] and biological domains [3,4,6–8,10,12]. While these sound like divergent domains, we have shown that the same underlying algorithmic fra...

My goal is to improve the manageability of computing systems. Coping with increasing complexity is one of the major challenges facing the computing industry today, and for the foreseeable future. Complexity impacts many of the activities associated with realizing computing systems including, but not limited to, aspects of system-construction, system-testing, system-deployment, systemconfigurati...

Generic absoluteness. Paul Cohen’s work in the 1960s struck a blow against the idea of mathematics as absolute truth. Cohen showed that there is a natural mathematical statement, namely the Continuum Hypothesis, whose truth cannot be proved or disproved in ZFC. (Gödel sentences were discovered earlier but are arguably not natural mathematical statements.) Cohen’s method, called forcing, enlarge...

I. Overview of Research Plan: Computational Nanotechnology Research in nanotechnology is undergoing a paradigm shift. A bottom-up or self-assembly approach is being investigated as an alternative to the current top-down approach. Most significantly, the shift from the exclusive use of lithography for device fabrication opens the field to not only novel fabrication schemes but the incorporation ...

I intend to pursue research on the principles of database systems. I have worked on the problems in information integration and interoperation especially from autonomous, heterogenous data sources over the Internet. In the future, I plan to extend my research in the areas of information processing, databases and the Internet where problems of interoperation occur. I expect that my research will...