Abstract Latouche and Nguyen (2015b) constructed a sequence of stochastic fluid processes showed that it converges weakly to Markov-modulated Brownian motion (MMBM). Here, we construct different show strongly an MMBM. To the best our knowledge, this is first result on strong convergence motion. Besides implying weak convergence, such approximation constitutes powerful tool for developing deep r...

In this paper, we consider the problem of computing the weak visibility (WV ) of a query line segment inside a simple polygon. Our algorithm first preprocesses the polygon and creates data structures from which any WV query is answered efficiently in an output sensitive manner. In our solution, the preprocessing is performed in time O(n log n) and the size of the constructed data structure is O...

Choice functions on tournaments always select the maximal element (Condorcet winner), provided they exist, but this property does not hold in the more general case of weak tournaments. In this paper we analyze the relationship between the usual choice functions and the set of maximal elements in weak tournaments. We introduce choice functions selecting maximal elements, whenever they exist. Mor...

Current re-ranking algorithms for machine translation rely on log-linear models, which have the potential problem of underfitting the training data. We present BoostedMERT, a novel boosting algorithm that uses Minimum Error Rate Training (MERT) as a weak learner and builds a re-ranker far more expressive than log-linear models. BoostedMERT is easy to implement, inherits the efficient optimizati...

In the streaming model, the order of the stream can significantly affect the difficulty of a problem. A t-semirandom stream was introduced as an interpolation between random-order (t = 1) and adversarial-order (t = n) streams where an adversary intercepts a random-order stream and can delay up to t elements at a time. IITK Sublinear Open Problem #15 asks to find algorithms whose performance deg...

Given a simple polygon P in the plane, we present new algorithms and data structures for computing the weak visibility polygon from any query line segment in P . We build a data structure in O(n) time and O(n) space that can compute the visibility polygon for any query line segment s in O(k log n) time, where k is the size of the visibility polygon of s and n is the number of vertices of P . Al...

We prove that iid random vectors that satisfy a rather weak moment assumption can be used as measurement vectors in Compressed Sensing, and the number of measurements required for exact reconstruction is the same as the best possible estimate – exhibited by a random Gaussian matrix. We then show that this moment condition is necessary, up to a log log factor. In addition, we explore the Compati...

Kramkov and Schachermayer (1999) proved the existence of log-optimal portfolios under weak assumptions in a very general setting. For many – but not all – cases, Goll and Kallsen (2000) obtained the optimal solution explicitly in terms of the semimartingale characteristics of the price process. By extending this result, this paper provides a complete explicit characterization of log-optimal por...

Trevisan has shown that constructions of pseudo-random generators from hard functions (the Nisan-Wigderson approach) also produce extractors. We show that constructions of pseudo-random generators from one-way permutations (the Blum-Micali-Yao approach) can be used for building extractors as well. Using this new technique we build extractors that do not use designs and polynomial-based error-co...