In the first part of this chapter we present existing work in center based clustering methods. In particular, we focus on the k-means and the k-median clustering which are two of the most widely used clustering objectives. We describe popular heuristics for these methods and theoretical guarantees associated with them. We also describe how to design worst case approximately optimal algorithms f...

For j = 4 and j = 5 and all d j, the maximum value of detXX , where X runs through all j d (0,1)-matrices, is determined along with a matrix X0 for which the maximum determinant is attained. In the theory of statistical designs, X0 is called a D-optimal design matrix. Design matrices that were previously thought to be D-optimal, are shown here to be D-optimal.

In this paper‎, ‎we model and solve the problem of optimal shaping and placing to put sensors for a 3-D wave equation with constant damping in a bounded open connected subset‎ ‎of 3-dimensional space‎. ‎The place of sensor is modeled by a subdomain‎ ‎of this region of a given measure‎. ‎By using an approach based on the embedding process‎, ‎first‎, ‎the system is formulated in variational form;...

We explore the use of Optimal Mixture Models to represent topics. We analyze two broad classes of mixture models: set-based and weighted. We provide an original proof that estimation of set-based models is NP-hard, and therefore not feasible. We argue that weighted models are superior to set-based models, and the solution can be estimated by a simple gradient descent technique. We demonstrate t...

this paper deals with optimal operation of a three-product dividing-wall column (dwc). the main idea is to design a control structure, through a systematic procedure for plantwide control, with an objective to achieve desired product purities with the minimum use of energy. exact local method is used to find the best controlled variables as single measurement or combination of measurements base...

Novel approach in the design of 2−D extremely narrow bandstop FIR filters is presented. The completely analytical design method is based on the 1−D optimal bandstop FIR filters. The 1−D FIR optimal bandstop filters are based on Zolotarev polynomial. Closed form formulas for the design of the filters are presented. One example demonstrates the design procedure. One application of the 2−D narrow ...

An A-optimal minimax design criterion is proposed to construct fractional factorial designs, which extends the study of the D-optimal minimax design criterion in Lin and Zhou (Canadian Journal of Statistics 41, 325–340, 2013). The resulting Aoptimal and D-optimal minimax designs minimize, respectively, the maximum trace and determinant of the mean squared error matrix of the least squares estim...

In this paper we study the optimal file-sharing mechanism in a peer-to-peer network with a mechanism design perspective. This mechanism improves upon existing incentive schemes. In particular, we show that peer-approved scheme is never optimal and service-quality scheme is optimal only under certain circumstances. Moreover, we find that the optimal mechanism can be implemented by a mixture of p...

Glibenclamide (GLIB) is a poorly soluble drug with formulation-dependent bioavailability. Therefore, we attempted in this study to improve GLIB dissolution rate by preparing drug solid dispersions by solvent evaporation (SE) and supercritical fluid solvent-antisolvent techniques (SCF-SAS). A D-optimal mixture design was used to investigate the effects of different ratios of HPMCE5 (50-100%), PE...