We show that Durr-Hoyer’s quantum algorithm of searching for extreme point of integer function can not be sped up for functions chosen randomly. Any other algorithm acting in substantially shorter time o( √ 2n) (n −→ ∞) gives incorrect answer for the functions φ with the single point of maximum chosen randomly with probability Perror −→ 1. The lower bound as Ω( √ 2n/b) is established for the qu...

We propose an Extreme Point Tabu Search (EPTS) algorithm that constructs globally optimal decision trees for classiication problems. Typically, decision tree algorithms are greedy. They optimize the misclassiication error of each decision sequentially. Our non-greedy approach minimizes the misclassiication error of all the decisions in the tree concurrently. Decision trees are ideal for data-mi...

Determinantal (a.k.a. fermion) random point processes were introduced in probability theory by Macchi about thirty years ago ([13], [14], [3]). In the last ten years the subject has attracted a considerable attention due to its rich connections to Random Matrix Theory, Combinatorics, Representation Theory, Random Growth Models, Number Theory and several other areas of mathematics. We refer the ...

This paper considers the robust strict positive real (SPR) problem for a family of plants of the form G(s; q) = N(s; q n)D ?1 (s; q d)?, where N(s; q n) and D(s; q d) are multiaane in uncertain parameters q n and q d , respectively , and > 0. In the discrete-time setting, this problem plays an important role in digital quantiza-tion. Several results are presented. First, we prove that this plan...

This short note lists my scientific results in 2013. Two main research topics are addressed: High dimensional statistical learning and Extreme-value analysis. 1 High dimensional statistical learning Copula provides a relevant tool to build multivariate probability laws, from fixed marginal distributions and required degree of dependence. From Sklar’s Theorem, the dependence properties of a cont...

Within econometrics, probability theory and statistics, an enormous literature exists on the topic of Extremes in Economics. See for instance Mikosch [47] and Klüppelberg [36] in this volume, and the numerous references listed in those contributions. For a long time, econometric research has shown that, for instance logarithmic returns of financial data are non–normal. Extremal moves up or down...

Next Generation Data Mining-NGDM 07 2 Introduction • Petascale simulations may require significant time to debug / understand. • Interesting regions in the simulation are generally a small part of the whole. • " Lookmarks " that point designers and users to interesting or anomalous regions greatly increase productivity.

We consider a point process sequence induced by a stationary symmetric α-stable (0 < α < 2) discrete parameter random field. It is easy to prove, following the arguments in the one-dimensional case in Resnick and Samorodnitsky (2004), that if the random field is generated by a dissipative group action then the point process sequence converges weakly to a cluster Poisson process. For the conserv...

In this study, the authors consider the asymptotic capacity of wireless multicast and unicast transmission schemes in a spectrum-sharing system. In these schemes, a secondary access point (SAP) utilises the licensed spectrum of an active primary user (PU) to send a common information to multiple secondary users simultaneously, as long as the interference power inflicted on the PU is less than a...