We consider the minimax estimation problem of a discrete distribution with support size k under locally differential privacy constraints. A privatization scheme is applied to each raw sample independently, and we need to estimate the distribution of the raw samples from the privatized samples. A positive number ǫ measures the privacy level of a privatization scheme. In our previous work (arXiv:...

We consider the problem of designing optimal M × N (M ≤ N ) sensing matrices which minimize the maximum condition number of all the submatrices of K columns. Such matrices minimize the worst-case estimation errors when only K sensors out of N sensors are available for sensing at a given time. For M = 2 and matrices with unit-normed columns, this problem is equivalent to the problem of maximizin...

Optimal design of beams subject to a combination of uncertain and deterministic transverse loads is presented using a min-max approach. The compliance of the beam is maximized to compute the worst case loading and minimized to determine the optimal cross-sectional shape. The uncertain component of the transverse load acting on the beam is not known a priori resulting in load uncertainty subject...

This study aims to develop a Multi-Attribute Decision-Making (MADM) method, the Best-Worst Tradeoff which draws on underlying principles of two popular MADM methods (the Method (BWM) and Tradeoff). The traditional procedure, is based axiomatic foundation multi-attribute value theory, considers ranges attributes, but decision-makers/analysts find it hard check consistency paired comparisons when...

Municipal solid waste (MSW) management is one of the most important issues in urban environments, especially developing countries. In this work, a comprehensive assessment framework for MSW proposed to evaluate and screen optimal scenario. The best-worst method (BWM) utilized determine weight each criterion disposal However, original BWM model difficult be solved globally. A linear presented so...

The main aim of this study, introduce a model todetermine the optimal values of the index value to minimize thetotal expected cost index and also the best decision making inselecting the industry and the region for investment by investors.For this purpose, the technique of linear programming to determinethe optimal values of the index value is used. Finally, FuzzyTOPSIS technique to prioritize ...

Recent work on online auctions for digital goods has explored the role of optimal stopping theory — particularly secretary problems — in the design of approximately optimal online mechanisms. This work generally assumes that the size of the market (number of bidders) is known a priori, but that the mechanism designer has no knowledge of the distribution of bid values. However, in many real-worl...

In this paper we describe a new efficient (in fact optimal) data structure for the top-K color problem. Each element of an array A is assigned a color c with priority p(c). For a query range [a, b] and a value K, we have to report K colors with the highest priorities among all colors that occur in A[a..b], sorted in reverse order by their priorities. We show that such queries can be answered in...

Efficient solution approaches for optimal control problems where the dynamics are described by uncertain differential equations are discussed in the present paper. Problems with uncertainties can be addressed by the robust worst-case formulation. In order to numerically solve the robust counterpart for the optimal control problem several approximation techniques can be employed. In this paper w...