Sorting by shuffling methods and a queue

We consider sorting by a queue that can apply a permutation from a given set over its content. This gives us a sorting device $\mathbb{Q}_{\Sigma}$ corresponding to any shuffling method $\Sigma$ since every such method is associated with a set of permutations. Two variations of these devices are considered - $\mathbb{Q}_{\Sigma}^{\prime}$ and $\mathbb{Q}_{\Sigma}^{\text{pop}}$. These require the entire content of the device to be unloaded after a permutation is applied or unloaded by each pop operation, respectively. First, we show that sorting by a deque is equivalent to sorting by a queue that can reverse its content. Next, we focus on sorting by cuts. We prove that the set of permutations that one can sort by using $\mathbb{Q}_{\text{cuts}}^{\prime}$ is the set of the $321$-avoiding separable permutations. We give lower and upper bounds to the maximum number of times the device must be used to sort a permutation. Furthermore, we give a formula for the number of $n$-permutations, $p_{n}(\mathbb{Q}_{\Sigma}^{\prime})$, that one can sort by using $\mathbb{Q}_{\Sigma}^{\prime}$, for any shuffling method $\Sigma$, such that the permutations associated with it are irreducible. Next, we prove a generalization of the fact that $\mathbb{Q}_{\text{cuts}}^{\text{pop}}$ can sort all permutations. We also show that $p_{n}(\mathbb{Q}_{\Sigma}^{\text{pop}})$ is given by the odd indexed Fibonacci numbers $F_{2n-1}$, for any shuffling method $\Sigma$ having a specific back-front property. The rest of the work is dedicated to a surprising conjecture inspired by Diaconis and Graham which states that one can sort the same number of permutations of any given size by using the devices $\mathbb{Q}_{\text{In-sh}}^{\text{pop}}$ and $\mathbb{Q}_{\text{Monge}}^{\text{pop}}$, corresponding to the popular In-shuffle and Monge shuffling methods.Comment: 29 pages, 7 figure

Research on the variability of the burnishing force during processing surfaces with 3D shape by using simultaneous 5-axis ball-burnishing process implemented on CNC milling machine

oai:ojs2.aj-tuv.org:article/20The present research is focused on continuously measuring the variability of the burnishing force during conducting ball-burnishing process for specimens with surfaces with 3D shape, by using CNC milling machine with dual rotary table installed. For measuring the burnishing force and its variability, the specifically developed ball-burnishing tool with miniature force sensor was used. To assess the degree of influence of the main regime parameters on the variability of the burnishing force, the four factors full factorial experiment design with two levels per factor and four replications per run has been carried out. The experimental results are processed statisti-cally and techniques such as Pareto and ANOVA were used after that, for sorting them by degree of significance. Some conclusions about the magnitude and the causes of the obtained variability also are given.The present research is focused on continuously measuring the variability of the burnishing force during conducting ball-burnishing process for specimens with surfaces with 3D shape, by using CNC milling machine with dual rotary table installed. For measuring the burnishing force and its variability, the specifically developed ball-burnishing tool with miniature force sensor was used. To assess the degree of influence of the main regime parameters on the variability of the burnishing force, the four factors full factorial experiment design with two levels per factor and four replications per run has been carried out. The experimental results are processed statisti-cally and techniques such as Pareto and ANOVA were used after that, for sorting them by degree of significance. Some conclusions about the magnitude and the causes of the obtained variability also are given

Трансграничното сътрудничество на балканските страни

The article examines the role, prospects and policies of the cross-border cooperation in the Balkan countries border regions. The main goal is to define the reasons, due to which the cross-border cooperation between the enterprises can be considered as an "optimal" policy for the Balkan countries. The opportunities for development of mutually beneficial cross-border relations are presented based on information obtained by different studies. The potential and the barriers for the development of the cross-border relations are discussed, as well as the degree of institutions' readiness to support the regional and cross-border cooperation. Some aspects of the delocalization processes near the border regions are presented. Some generalizations are made at the end of the article and feasible prospects for development are envisaged

Трансграничното сътрудничество на балканските страни

The article examines the role, prospects and policies of the cross-border cooperation in the Balkan countries border regions. The main goal is to define the reasons, due to which the cross-border cooperation between the enterprises can be considered as an "optimal" policy for the Balkan countries. The opportunities for development of mutually beneficial cross-border relations are presented based on information obtained by different studies. The potential and the barriers for the development of the cross-border relations are discussed, as well as the degree of institutions' readiness to support the regional and cross-border cooperation. Some aspects of the delocalization processes near the border regions are presented. Some generalizations are made at the end of the article and feasible prospects for development are envisaged

A mathematical framework for combining decisions of multiple experts toward accurate and remote diagnosis of malaria using tele-microscopy.

We propose a methodology for digitally fusing diagnostic decisions made by multiple medical experts in order to improve accuracy of diagnosis. Toward this goal, we report an experimental study involving nine experts, where each one was given more than 8,000 digital microscopic images of individual human red blood cells and asked to identify malaria infected cells. The results of this experiment reveal that even highly trained medical experts are not always self-consistent in their diagnostic decisions and that there exists a fair level of disagreement among experts, even for binary decisions (i.e., infected vs. uninfected). To tackle this general medical diagnosis problem, we propose a probabilistic algorithm to fuse the decisions made by trained medical experts to robustly achieve higher levels of accuracy when compared to individual experts making such decisions. By modelling the decisions of experts as a three component mixture model and solving for the underlying parameters using the Expectation Maximisation algorithm, we demonstrate the efficacy of our approach which significantly improves the overall diagnostic accuracy of malaria infected cells. Additionally, we present a mathematical framework for performing 'slide-level' diagnosis by using individual 'cell-level' diagnosis data, shedding more light on the statistical rules that should govern the routine practice in examination of e.g., thin blood smear samples. This framework could be generalized for various other tele-pathology needs, and can be used by trained experts within an efficient tele-medicine platform

Experimental research of partial regular microreliefs formed on rotary body face surfaces

The basic regularities in the influence of processing parameters on the geometrical characteristics of the partially regular microreliefs, formed on the rotary body face surface, are established. Combinations of partially regular microreliefs are formed by using a contemporary CNC milling machine, and an advanced programing method, based on previously developed mathematical models. Full factorial experimental design is carried out, which consist of three factors, varied on three levels. Regression stochastic models in coded and natural form, which give the relations between the width of the grooves and the deforming force, feed rate and the pitch of the axial grooves, are derived as a result. Response surfaces and contour plots are built in order to facilitate the results analysis. Based on the dependencies of the derived regression stochastic models, it is found that the greatest impact on the width of the grooves has the magnitude of the deforming force,followed by the feed rate. Also, it is found that the axial pitch between adjacent toolpaths has the least impact on the width of the grooves. As a result of the full-factorial experiment, the average geometric parameters of the microrelief grooves were obtained on their basis. When used, these values will provide for the required value of the relative burnishing area of the surface with regular microreliefs, and, accordingly, the specified operational properties

Application of New Generation Geometrical Product Specifications—Position Tolerancing

The geometrical product specifications (GPSs) from new generation are composed of several standards issued by the ISO/TC 213. They are related to the way of denoting the requirements in the design engineering drawings, such as drawing indication, definition of tolerance and values of specifications, characteristic, parameters and definitions of actual features. They also include requirements relating to compare verification, measure instrument and calibrate size, distance, radius, angle, form and position of geometrical features, roughness profile, waviness profile, primary profile, surface imperfection and edges. A lot of new and mathematical terms, the size system, indications of dimensions other than linear sizes by using geometrical tolerances, uncertainty series, etc. are introduced in this chapter. The aim of this chapter is to explain the new requirements of new generation standards for geometrical product specifications related to positional deviation. The advantages and disadvantages of the possibility to indicate the accurate requirements for location of surfaces and axes are discussed