14665111
Oblivious Symmetric Alternation
We introduce a new class $\rm {O}^p_2$ as a subclass of the symmetric alternation class $\rm {S}^p_2$. An $\rm {O}^p_2$ proof system has the flavor of an $\rm {S}^p_2$ proof system, but it is more restrictive in nature. In an $\rm {S}^p_2$ proof system, we have two competing provers and a verifier such that for any input, the honest prover has an irrefutable certificate. In an $\rm {O}^p_2$ proof system, we require that the irrefutable certificates depend only on the length of the input, not on the input itself. In other words, the irrefutable proofs are oblivious of the input. For this reason, we call the new class oblivious symmetric alternation. While this might seem slightly contrived, it turns out that this class helps us improve some existing results. For instance, we show that if NP⊂P/poly then $\rm PH = {O}^p_2$, whereas the best known collapse under the same hypothesis was $\rm PH = {S}^p_2$. 
 
We also define classes $\rm Y{O}^p_2$ and $\rm N{O}^p_2$, bearing relations to $\rm {O}^p_2$ as NP and coNP are to P, and show that these along with $\rm {O}^p_2$ form a hierarchy, similar to the polynomial hierarchy. We investigate other inclusions involving these classes and strengthen some known results. For example, we show that $\rm MA \subseteq N{O}^p_2$ which sharpens the known result $\rm MA \subseteq {S}^p_2$ [16]. Another example is our result that $\rm AM \subseteq O_2 \cdot NP \subseteq {\prod}^p_2$, which is an improved upper bound on AM. Finally, we also prove better collapses for the 2-queries problem as discussed by [12,1,7]. We prove that $\rm P^{NP[1]} = P^{NP[2]} \Longrightarrow PH = {NO}^p_2 \cap Y{O}^p_2$.
411400
Parity Problems in Planar Graphs
We consider the problem of counting the number of spanning trees in planar graphs. We prove tight bounds on the complexity of the problem, both in general and especially in the modular setting. We exhibit the problem to be complete for Logspace when the modulus is 2k, for constant k. On the other hand, we show that for any other modulus and in the non-modular case, our problem is as hard in the planar case as for the case of arbitrary graphs. This completely settles the question regarding the complexity of modular computation of the number of spanning trees in planar graphs. The techniques used rely heavily on algebraic-topology. In the spirit of counting problems modulo 2k, we also exhibit a highly parallel oplusL algorithm for finding the value of a Permanent modulo 2k. Previously, the best known result in this direction was Valiant's result that this problem lies in P.
26846276
Hierarchical representation of digitized curves through dominant point detection
Hierarchical data structures play a key role in representation of spatial data. This paper proposes an algorithm for constructing hierarchical representations of digitized curves based on the dominant points of the curve. The comparison of the proposed scheme with the other hierarchical representation schemes viz. Arc Tree and Strip Tree reveals that the proposed algorithm is generally better than the Arc Tree and compares well with the Strip Tree scheme.
14932066
On line predictive appearance-based tracking
We present a novel predictive statistical framework to improve the performance of an eigentracker. In addition, we use fast and efficient eigenspace updates to learn new views of the object being tracked on the fly. We also incorporate a new importance sampling mechanism which increases the robustness of the eigentracker and enables it to track nonconvex objects better. Our eigentracker is flexible-it is possible to use it symbolically with other trackers. We show its successful application in hand gesture analysis; and face and person tracking.
14820946
A hierarchical monothetic document clustering algorithm for summarization and browsing search results
Organizing Web search results into a hierarchy of topics and sub-topics facilitates browsing the collection and locating results of interest. In this paper, we propose a new hierarchical monothetic clustering algorithm to build a topic hierarchy for a collection of search results retrieved in response to a query. At every level of the hierarchy, the new algorithm progressively identifies topics in a way that maximizes the coverage while maintaining distinctiveness of the topics. We refer the proposed algorithm to as DisCover. Evaluating the quality of a topic hierarchy is a non-trivial task, the ultimate test being user judgment. We use several objective measures such as coverage and reach time for an empirical comparison of the proposed algorithm with two other monothetic clustering algorithms to demonstrate its superiority. Even though our algorithm is slightly more computationally intensive than one of the algorithms, it generates better hierarchies. Our user studies also show that the proposed algorithm is superior to the other algorithms as a summarizing and browsing tool.
34607469
On the Coleman indices of voting power
Coleman [1971. Control of collectives and the power of a collectivity to act. In: Lieberman, B. (Ed.), Social Choice. Gordon and Breach, New York, pp. 269-298] suggested two indices of voting power, power to prevent an action and power to initiate an action. This paper rigorously demonstrates relationship between the two indices and shows that they satisfy several attractive properties.
3191837
Active 3-D Object Recognition Using Appearance-Based Aspect Graphs
We present a new active active recognition scheme (using an uncalibrated camera) based on a new idea, appearancebased aspect graphs. The scheme is robust to background clutter, and affine transformations of the object. We use a probabilistic reasoning framework which helps in probability calculations and planning the next view (when a view of the object does not contain sufficient features to recognise it unambiguously), in conjunction with a new hierarchical knowledge representation scheme. Preliminary experiments with the system show encouraging results.