Nikolaos Samaras

A decision tree is an easy-to-understand tool that has been widely used for classification tasks. On the one hand, due to privacy concerns, there has been an urgent need to create privacy-preserving classifiers that conceal the user's input from the classifier. On the other hand, with the rise of cloud computing, data owners are keen to reduce risk by outsourcing their model, but want security guarantees that third parties cannot steal their decision tree model. To address these issues, Joye and Salehi introduced a theoretical protocol that efficiently evaluates decision trees while maintaining privacy by leveraging their comparison protocol that is resistant to timing attacks. However, their approach was not only inefficient but also prone to side-channel attacks. Therefore, in this paper, we propose a new decision tree inference protocol in which the model is shared and evaluated among multiple entities. We partition our decision tree model by each level to be stored in a new entity we refer to as a "level-site." Utilizing this approach, we were able to gain improved average run time for classifier evaluation for a non-complete tree, while also having strong mitigations against side-channel attacks.

The algorithm for solving the matrix equation Xⁿ = A is well-known, where A is an given matrix and A is the unknown square matrix. This paper is concerned with the general case of the polynomial matrix equation , where . The study of the general case help us to solve any polynomial matrix equation. The main difficulty to solve the polynomial matrix equation is that, in general, the function is not invertible. Even if the function h is invertible, it is difficult to find the type of the inverse function and its derivatives. We designed an algorithm, which enables us to bypass anything related with the inverse function of h. In our algorithm we just used the polynomial function h and its derivatives. As it is easily understood, this is a very effective procedure and our algorithm can be used for every polynomial function h and any square matrix A. All the possible cases concerning the Jordan canonical form of the matrix A are examined and a formula of the matrix hoq(A) is given where q(x) is the interpolating polynomial to the data (4.1.1, 4.1.2). Mathematical types to calculate the number of different roots of the polynomial matrix equation and their algebraic multiplicity are also presented (5). We want to point out that the general case helps us to solve any polynomial matrix equation, which play an important role in many applications.

This work presents a Variable Neighborhood Search (VNS) approach for solving the Return-To-Player (RTP) optimization problem. A large number of software companies in the gaming industry seek to solve the RTP optimization problem in order to develop modern virtual casino gambling machines. These slot machines have a number of reels (e.g., three or more) that spin once a button is pushed. Each slot machine is required to have an RTP in a particular range according to the legislation of each country. By using a VNS framework that guides two local search operators, we show how to control the distribution of the symbols in the reels in order to achieve the desired RTP. In this study, optimization refers only to base game, the core of slot machine games, and not in bonus games, since a bonus game is triggered once two, three, or more specific symbols occur in the gaming monitor. Although other researchers have tried to solve the RTP problem in the past, this is the first time that a VNS methodology is proposed for this problem in the literature with good computational results.