Precise Runtime Analysis for Plateau Functions

To gain a better theoretical understanding of how evolutionary algorithms (EAs) cope with plateaus of constant fitness, we propose the n -dimensional \textsc {Plateau} _k function as natural benchmark and analyze how different variants of the (1 + 1) EA optimize it. The \textsc {Plateau} _k function has a plateau of second-best fitness in a ball of radius k around the optimum. As evolutionary algorithm, we regard the (1 + 1) EA using an arbitrary unbiased mutation operator. Denoting by \alpha the random number of bits flipped in an application of this operator and assuming that \Pr [\alpha = 1] has at least some small sub-constant value, we show the surprising result that for all constant k \ge 2 , the runtime T follows a distribution close to the geometric one with success probability equal to the probability to flip between 1 and k bits divided by the size of the plateau. Consequently, the expected runtime is the inverse of this number, and thus only depends on the probability to flip between 1 and k bits, but not on other characteristics of the mutation operator. Our result also implies that the optimal mutation rate for standard bit mutation here is approximately k/(en) . Our main analysis tool is a combined analysis of the Markov chains on the search point space and on the Hamming level space, an approach that promises to be useful also for other plateau problems.

T-Maps based Tolerance Analysis of Composites Assembly Involving Compensation Strategies

Clamping force and shimming are two important compensation processes in the composites assembly. Their effects on variation propagation should be investigated in tolerance analysis. The paper presents a tolerance analysis method for composites assembly based on the T-Maps method, mainly concerning the anisotropic variations accumulation and propagation where there is the clamping force modification and the shimming. Variations of the composite parts in different directions are represented by the T-Maps. Since the different axial deviations are represented in the same Euclidean point-space, the T-Maps based tolerance analysis of the composite parts assembly provides more accurate and reliable results. Compensation processes, the clamping force, and the shimming, on assembly tolerance synthesis of the composite parts, are analyzed clearly in the T-Map. This procedure is found to be effective for the anisotropy oriented assembly tolerance analysis, especially concerning about effect of the clamping force and the shimming on variations accumulation and propagation. The assembly of an aircraft composite elevator is considered to demonstrate the effectiveness of the T-Maps based method. The procedures outlined in the paper are quite general and can be used for assembly tolerance analysis of anisotropic parts.

Theoretical Derivation of Mean Cutting-Point Space of Grinding Wheel

In a surface grinding process, a successive cutting-point space of grinding wheel affects the maximum abrasive grain depth of cut, which is a major factor affecting grinding characteristics such as the grinding forces and temperature. These characteristics degrade the productivity and machining accuracy. Therefore, we have to clearly define the successive cutting-point space. There are, however, few reports on the derivation method of the theoretical formula since abrasive grains inside the wheel are randomly distributed. This study aimed to theoretically derive the mean cutting-point space and to clarify the successive cutting-point space. We proposed a new derivation method for the mean cutting-point space, which was measured by mapping the diamond wheel surface using an EPMA. The theoretically derived mean cutting-point space was then compared with the measurement results.

Paracompact-type mappings

Recently a new direction of uniform topology called the uniform topology of uniformly continuous mappings has begun to develop intensively. This direction is devoted, first of all, to the extension to uniformly continuous mappings of the basic concepts and statements concerning uniform spaces. In this case a uniform space is understood as the simplest uniformly continuous mapping of this uniform space into a one-point space. The investigations carried out have revealed large uniform analogs of continuous mappings and made it possible to transfer to uniformly continuous mappings many of the main statements of the uniform topology of spaces. The method of transferring results from spaces to mappings makes it possible to generalize many results. Therefore, the problem of extending some concepts and statements concerning uniform spaces to uniformly continuous mappings is urgent. In this article, we introduce and study uniformly R-paracompact, strongly uniformly R-paracompact, and uniformly R-superparacompact mappings. In particular, we solve the problem of preserving R-paracompact (respectively, strongly uniformly R-paracompact, uniformly R-superparacompact) spaces towards the preimage under uniformly R-paracompact (respectively, strongly uniformly R-paracompact, uniformly R-superparacompact) mappings.

Population-Based Novelty Searches Can Converge

Novelty search is a powerful tool for finding sets of complex objects in complicated, open-ended spaces. Recent empirical analysis on a simplified version of novelty search makes it clear that novelty search happens at the level of the archive space, not the individual point space. The sparseness measure and archive update criterion create a process that is driven by a clear pair of objectives: spread out to cover the space, while trying to remain as efficiently packed as possible driving these simplified variants to converge to an

Anisotropy Oriented Tolerance Analysis of Composite Assembly With T-Maps Method

Anisotropy is an outstanding characteristic of the composite parts, and should be considered during the course of the tolerance analysis. The paper presents a tolerance analysis method for composite elevator assembly using T-Maps method, mainly concerning the variations originated from the anisotropy of the composite materials. The composite elevator is composed of the forward spar, the skin panels, and the ribs. Variations of the composite forward spar and the composite panels in different directions are represented by the T-Maps. Mating clearances of the composite spar and the metallic joints are mapped to the hypothetical Euclidean space. Since the different axial deviations are represented in the same Euclidean point-space, anisotropy oriented tolerance analysis of the composite parts assembly could be conducted with more accurate results. This procedure is found to be effective for anisotropy oriented tolerance analysis. The assembly of the composite elevator is investigated intensively by the proposed method. The procedures outlined in the paper are quite general and can be used for tolerance analysis of any anisotropic parts assembly process.

Physics from Axioms

We introduce a definition of Time and Photons from four Axioms. Basically you take a 4-dimensional manifold, transform them into two superimposed Riemann Spheres and isolate a circle (call this Pp) in one of the spheres. Then one specifies the circle to turn by a unit amount (the turn is an quantum rotation: turn from state A to state B without visiting the in between states) as measured along the circle, every time the Pp encounters a space point. Space fluctuates and expands so this does not give a static circle Pp. The circle's infinity point stays at the north pole of the Riemann Sphere for any finite rotation since: infinity - constant = infinity. Using this one can define basic spacetime and from basic spacetime, Time can be defined if we require special particles to be in the particles of a clock. We go on to define photons and antiphotons. The model predicts that there is a direction in which photons (from the same process) are never emitted. We continue to define a pi-minus.

Children-friendly design of urban public space based on the study of Shanghai, China

At present, more than 50% of children live in big cities. But with the increasing number of motor vehicles and shrinking public spaces , children have less and less opportunities for outdoor activities, resulting in obesity and sub-health problems. Therefore, it is very important to build children-friendly public spaces in metropolis. This study takes the Shanghai,china as an example.Firstly,through questionnaires,it is found that ensuring the safe movement of children and inspiring their spontaneous activities are key points to build children-friendly public spaces. Meanwhile, The public spaces near the home are the most used environment by children. Therefore, open spaces in metropolis areas need to be planned carefully for children near their homes. Then it is way much better to make sure children's places of daily life, such as homes, schools, green spaces, sports venues and so on, can be connected in a safe path. Secondly, for building the safe path for children ,the safety of each spot along the path is analyzed by SP method, which is a mathematical algorithm , in order to find the risk factors and to avoid them in the future. Then we establish the action plan of "line space + point space" to build the children-friendly urban public space system. Line space refers to meeting the basic safety space needs of children through the improvement of the routes to school, including reducing the impact of motor vehicles, safe road facilities, and enhancing road lighting system. "Point space" refers to the promotion of children's outdoor activities through the arrangement of multi-level outdoor children's playgrounds and green spaces, including safe green parks, security platforms and so on. Finally, it is hoped that the "Safety Line Space + Interesting Point Space" plan will establish a safe and inspiring path for children to travel, linking home, school, green space and sports venues, which they use mostly in their daily life. Then we can ensure the safe movement of children and inspire children's spontaneous games in big cities for a children-friendly goal