Top-Down Skiplists

We describe todolists (top-down skiplists), a variant of skiplists (Pugh 1990) that can execute searches using at most $\log_{2-\varepsilon} n + O(1)$ binary comparisons per search and that have amortized update time $O(\varepsilon^{-1}\log n)$. A variant of todolists, called working-todolists, can execute a search for any element $x$ using $\log_{2-\varepsilon} w(x) + o(\log w(x))$ binary comparisons and have amortized search time $O(\varepsilon^{-1}\log w(w))$. Here, $w(x)$ is the "working-set number" of $x$. No previous data structure is known to achieve a bound better than $4\log_2 w(x)$ comparisons. We show through experiments that, if implemented carefully, todolists are comparable to other common dictionary implementations in terms of insertion times and outperform them in terms of search times.Comment: 18 pages, 5 figure

A Nonparametric Ensemble Binary Classifier and its Statistical Properties

In this work, we propose an ensemble of classification trees (CT) and artificial neural networks (ANN). Several statistical properties including universal consistency and upper bound of an important parameter of the proposed classifier are shown. Numerical evidence is also provided using various real life data sets to assess the performance of the model. Our proposed nonparametric ensemble classifier doesn't suffer from the `curse of dimensionality' and can be used in a wide variety of feature selection cum classification problems. Performance of the proposed model is quite better when compared to many other state-of-the-art models used for similar situations

The combinatorics of scattering in layered media

Reflection and transmission of waves in piecewise constant layered media are important in various imaging modalities and have been studied extensively. Despite this, no exact time domain formulas for the Green's functions have been established. Indeed, there is an underlying combinatorial obstacle: the analysis of scattering sequences. In the present paper we exploit a representation of scattering sequences in terms of trees to solve completely the inherent combinatorial problem, and thereby derive new, explicit formulas for the reflection and transmission Green's functions.Comment: 24 pages. arXiv admin note: substantial text overlap with arXiv:1206.269

A Static Optimality Transformation with Applications to Planar Point Location

Over the last decade, there have been several data structures that, given a planar subdivision and a probability distribution over the plane, provide a way for answering point location queries that is fine-tuned for the distribution. All these methods suffer from the requirement that the query distribution must be known in advance. We present a new data structure for point location queries in planar triangulations. Our structure is asymptotically as fast as the optimal structures, but it requires no prior information about the queries. This is a 2D analogue of the jump from Knuth's optimum binary search trees (discovered in 1971) to the splay trees of Sleator and Tarjan in 1985. While the former need to know the query distribution, the latter are statically optimal. This means that we can adapt to the query sequence and achieve the same asymptotic performance as an optimum static structure, without needing any additional information.Comment: 13 pages, 1 figure, a preliminary version appeared at SoCG 201

Grounding the Unreal

The scientific successes of the last 400 years strongly suggest a picture on which our scientific theories exhibit a layered structure of dependence and determination. Economics is dependent on and determined by psychology; psychology in its turn is, plausibly, dependent on and determined by biology; and so it goes. It is tempting to explain this layered structure of dependence and determination among our theories by appeal to a corresponding layered structure of dependence and determination among the entities putatively treated by those theories. In this paper, I argue that we can resist this temptation: we can explain the sense in which, e.g., the biological truths are dependent on and determined by chemical truths without appealing to properly biological or chemical entities. This opens the door to a view on which, though there are more truths than just the purely physical truths, there are no entities, states, or properties other than the purely physical entities, states, and properties. I argue that some familiar strategies to explicate the idea of a layered structure of theories by appeal to reduction, ground, and truthmaking encounter difficulties. I then show how these difficulties point the way to a more satisfactory treatment which appeals to something very close to the notion of ground. Finally, I show how this treatment provides a theoretical setting in which we might fruitfully frame debates about which entities there really are