Nagabhushana Prabhu

Dynamic resource allocation tor multimedia services in mobile communication environments

As demand for networked multimedia applications is increasing rapidly, it is important to provide these services in mobile communication environments. In this paper, we identify system requirements for base stations in order to support multimedia services. These requirements include supporting concurrent connections for multiple users, allocation of resources dynamically to satisfy diverse resource requirements for multimedia applications, and reallocation of resources during handoff incurred by user movement or newly generated calls. These requirements can be used to design an interface between land-based and mobile environments to handle one of the most challenging issues in multimedia communication: enforcing interstream and intrastream synchronizations. We propose two quality of presentation (QOP) parameters for evaluating the quality of mobile multimedia connections, and analyze the validity of these requirements. >

Accuracy-Constrained Privacy-Preserving Access Control Mechanismfor Relational Data

Access control mechanisms protect sensitive information from unauthorized users. However, when sensitive information is shared and a Privacy Protection Mechanism (PPM) is not in place, an authorized user can still compromise the privacy of a person leading to identity disclosure. A PPM can use suppression and generalization of relational data to anonymize and satisfy privacy requirements, e.g., k-anonymity and l-diversity, against identity and attribute disclosure. However, privacy is achieved at the cost of precision of authorized information. In this paper, we propose an accuracy-constrained privacy-preserving access control framework. The access control policies define selection predicates available to roles while the privacy requirement is to satisfy the k-anonymity or l-diversity. An additional constraint that needs to be satisfied by the PPM is the imprecision bound for each selection predicate. The techniques for workload-aware anonymization for selection predicates have been discussed in the literature. However, to the best of our knowledge, the problem of satisfying the accuracy constraints for multiple roles has not been studied before. In our formulation of the aforementioned problem, we propose heuristics for anonymization algorithms and show empirically that the proposed approach satisfies imprecision bounds for more permissions and has lower total imprecision than the current state of the art.

Optimization on Lie manifolds and pattern recognition

Several pattern recognition problems can be reduced in a natural way to the problem of optimizing a nonlinear function over a Lie manifold. However, optimization on Lie manifolds involves, in general, a large number of nonlinear equality constraints and is hence one of the hardest optimization problems. We show that exploiting the special structure of Lie manifolds allows one to devise a method for optimizing on Lie manifolds in a computationally efficient manner. The new method relies on the differential geometry of Lie manifolds and the underlying connections between Lie groups and their associated Lie algebras. We describe an application of the new Lie group method to the problem of diagnosing malignancy in the cytological extracts of breast tumors. The diagnosis method that we present has a mean sensitivity of 98.086% and a predictive index of 0.0602, making it the most accurate and reliable diagnostic method reported thus far.

Hamiltonian simple polytopes

AbstractWe show that for everyn> no(d) (n even ifd is odd) there exists a simpled-polytope withn vertices, whose graph admits a Hamiltonian circuit. The result sharpens and earlier lower bound due to Victor Klee.

Counting d -Step Paths in Extremal Dantzig Figures

Abstract. The d -step conjecture asserts that every d -polytope P with 2d facets has an edge-path of at most d steps between any two of its vertices. Klee and Walkup showed that to prove the d -step conjecture, it suffices to verify it for all Dantzig figures (P, w1,w2) , which are simple d -polytopes with 2d facets together with distinguished vertices w1 and w2 which have no common facet, and to consider only paths between w1 and w2 . This paper counts the number of d -step paths between w1 and w2 for certain Dantzig figures (P, w1, w2 ) which are extremal in the sense that P has the minimal and maximal vertices possible among such d -polytopes with 2d facets, which are d2 - d + 2 vertices (lower bound theorem) and

Canonical coordinates method for equality-constrained nonlinear optimization

2 { \lfloor \frac{3}{2} d - \frac{1}{2} \rfloor \choose \lfloor \frac{d}{2} \rfloor}

Gauge groups and data classification

vertices (upper bound theorem), respectively. These Dantzig figures have exactly 2d-1d -step paths.

A globally convergent method for finding zeros of smooth functions

Feasible-points methods have several appealing advantages over the infeasible-points methods for solving equality-constrained nonlinear optimization problems. The known feasible-points methods however solve, often large, systems of nonlinear constraint equations in each step in order to maintain feasibility. Solving nonlinear equations in each step not only slows down the algorithms considerably, but also the large amount of floating-point computation involved introduces considerable numerical inaccuracy into the overall computation. As a result, the commercial software packages for equality-constrained optimization are slow and not numerically robust. We present a radically new approach to maintaining feasibility--called the canonical coordinates method (CCM). The CCM, unlike previous methods, does not adhere to the coordinate system used in the problem specification. Rather, as the algorithm progresses CCM dynamically chooses, in each step, a coordinate system that is most appropriate for describing the local geometry around the current iterate. By dynamically changing the coordinate system to suit the local geometry, the CCM is able to maintain feasibility in equality-constrained nonlinear optimization without having to solve systems of nonlinear equations. We describe the CCM and present a proof of its convergence. We also present a few numerical examples which show that CCM can solve, in very few iterations, problems that cannot be solved using the commercial NLP solver in MATLAB 6.1.

A QUASILINEAR CLASSIFIER FOR COMPLETE SEPARATION OF A DICHOTOMY

We present a new method for constructing nonlinear classifiers. Given any two distinct sets of points in R^n the new method can construct, using gauge group techniques, a closed form expression of a surface, @F(x)=0, which separates the two sets. We also show that any two distinct sets of points in R^n can be separated by a polynomial surface and present an algorithm for constructing such polynomial surfaces. Finally we present two numerical examples to illustrate the new method.

Complexity of the Gravitational Method for Linear Programming

Computing a zero of a smooth function is an old and extensively researched problem in numerical computation. While a large body of results and algorithms has been reported on this problem in the literature, to the extent we are aware, the published literature does not contain a globally convergent algorithm for finding a zero of an arbitrary smooth function. In this paper we present the first globally convergent algorithm for computing a zero (if one exists) of a general smooth function. After presenting the algorithm and a proof of global convergence, we also clarify the connection between our algorithm and some known results in topological degree theory.