Matrix Analysis of Repetitive Circulant Structures: New-block and Near Block Matrices

In many scientific fields and several problems, Block Circulant Matrices (BCM) have been used for a long period of time. Each row of the BCM is a cyclic shift of its upper row to the right. BCM has been studied widely and there are closed-form solutions for problems of BCM. In these problems, the properties of near-BCM and BCM lead to a significant decrease in computational cost and efforts. In other words, these matrices are useful to perform some computational operations at the low cost. This study introduces a method for transforming a structure into a new type of Block Circulant Structure (BCS) by applying minor modifications. Furthermore, transformation of structural matrices into Block Circulant Matrices is discussed, and the properties of these matrices are then described in details. The methods introduce calculating eigenvalues and eigenvectors of these matrices instead of calculating the inverse of their matrices. To achieve this goal, the properties of near-Block and Block Circulant Matrices are used to analyze the structural stiffness matrices. In addition, the inverse of stiffness matrices for structures are calculated and utilized in structural mechanics. For clarification of efficiency and accuracy of the method, some examples are presented

A multi-set charged system search for truss optimization with variables of different natures; element grouping

Optimization problems may include variables of different natures. In structural optimization for example different variables representing cross-sectional, geometrical, topological and grouping properties of the structure may be present. Having different interpretations, the effects of these variables on the objective function are not alike and their search spaces may represent different characteristics. Thus, it is helpful to take these variables apart and to control each set separately. Based on the above considerations, in this paper a multi set charged system search (MSCSS) is introduced for the element grouping of truss structures in a weight optimization process. The results are compared to those obtained through predefined grouping by different algorithms. The comparisons show the efficiency and the effectiveness of the proposed algorithm. Although this paper only considers size optimization of truss structures where sizing and grouping variables are present and regarded as variables of different natures, the algorithm can be extended to cover the simultaneous shape and size optimization and topology optimization of different types of structures

Magnetic charged system search for structural optimization

In this paper the Magnetic Charged System Search algorithm is applied to structural optimization. This algorithm uses the Biot-Savar law of electromagnetism to incorporate magnetic forces into the already existing Charged System Search algorithm and thus can be considered as an extension of it. Each search agent exerts magnetic forces on other agents based on the variation of its objective function value during its last movement. This additional force provides some additional information and enhances the performance of the Charged System Search. The efficiency of the Magnetic Charged System Search is examined by application of this algorithm to four structural optimization problems. The results are compared to those of CSS and some of the methods available in the literature

Phenotypic heterogeneity in modeling cancer evolution

The unwelcome evolution of malignancy during cancer progression emerges through a selection process in a complex heterogeneous population structure. In the present work, we investigate evolutionary dynamics in a phenotypically heterogeneous population of stem cells (SCs) and their associated progenitors. The fate of a malignant mutation is determined not only by overall stem cell and differentiated cell growth rates but also differentiation and dedifferentiation rates. We investigate the effect of such a complex population structure on the evolution of malignant mutations. We derive exact analytic results for the fixation probability of a mutant arising in each of the subpopulations. The analytic results are in almost perfect agreement with the numerical simulations. Moreover, a condition for evolutionary advantage of a mutant cell versus the wild type population is given in the present study. We also show that microenvironment-induced plasticity in invading mutants leads to more aggressive mutants with higher fixation probability. Our model predicts that decreasing polarity between stem and differentiated cells turnover would raise the survivability of non-plastic mutants; while it would suppress the development of malignancy for plastic mutants. We discuss our model in the context of colorectal/intestinal cancer (at the epithelium). This novel mathematical framework can be applied more generally to a variety of problems concerning selection in heterogeneous populations, in other contexts such as population genetics, and ecology.Comment: 28 pages, 7 figures, 2 table

Counselling training in Afghanistan: the long term development of the INSPIRE project

Between 2010 and 2014, the British Council funded a project under a scheme called INSPIRE, which involved training a group of 20 Afghan practitioners in counselling skills. The participants were from Kabul and Herat and the University of Herat were partners in the project. The ethos of the programme was based on co-constructing a model of transcultural training that could be applicable within the Afghan context (Berdondini et al., 2014). As an outcome, in 2016 the Afghan Ministry of Higher Education approved the launch of a Counselling Department and a Student Counselling Service within the University of Herat. This article aims to present and analyse the long term development of INSPIRE in Afghanistan from the perspective of some participants. Reflections on future implementation of this approach and training programs are also included

Chaotically Enhanced Meta-Heuristic Algorithms for Optimal Design of Truss Structures with Frequency Constraints

The natural frequencies of any structure contain useful information about the dynamic behavior of that structure, and by controlling these frequencies, the destructive effects of dynamic loads, including the resonance phenomenon, can be minimized. Truss optimization by applying dynamic constraints has been widely welcomed by researchers in recent decades and has been presented as a challenging topic. The main reason for this choice is quick access to dynamic information by examining natural frequencies. Also, frequency constraint relations are highly nonlinear and non-convex and have implicit variables, so using mathematical and derivative methods will be very difficult and time consuming. In this regard, the use of meta-heuristic algorithms in truss weight optimization with frequency constraints has good results, but with the introduction of form variables, these algorithms trap at local optima. In this research, by applying chaos map in meta-heuristic algorithms, suitable conditions have been provided to escape from local optima and access to global optimums. These algorithms include Chaotic Cyclical Parthenogenesis Algorithms (CCPA), Chaotic Biogeography-Based Optimization (CBBO), Chaotic Teaching-Learning-Based Optimization (CTLBO) and Chaotic Particle Swarm Optimization (CPSO), respectively. Also, by using different scenarios, a good balance has been achieved between the exploration and exploitation of the algorithms

Size/Layout Optimization of Truss Structures Using Shuffled Shepherd Optimization Method

The main purpose of this paper is to investigate the ability of the recently developed multi-community meta-heuristic optimization algorithm, shuffled shepherd optimization algorithm (SSOA), in layout optimization of truss structures. The SSOA is inspired by mimicking the behavior of shepherd in nature. In this algorithm, agents are first divided into communities which are called herd and then optimization process, inspired by the shepherd’s behavior in nature, is operated on each community. The new position of agents is obtained using elitism technique. Then communities are merged for sharing the information. The results of SSOA in layout optimization show that SSOA is competitive with other considered meta-heuristic algorithms

Fuzzy-multi-mode Resource-constrained Discrete Time-cost-resource Optimization in Project Scheduling Using ENSCBO

Construction companies are required to employ effective methods of project planning and scheduling in today's competitive environment. Time and cost are critical factors in project success, and they can vary based on the type and amount of resources used for activities, such as labor, tools, and materials. In addition, resource leveling strategies that are used to limit fluctuations in a project's resource consumption also affect project time and cost. The multi-mode resource-constrained discrete-time–cost-resource optimization (MRC-DTCRO) is an optimization tool that is developed for scheduling of a set of activities involving multiple execution modes with the aim of minimizing time, cost, and resource moment. Moreover, uncertainty in cost should be accounted for in project planning because activities are exposed to risks that can cause delays and budget overruns. This paper presents a fuzzy-multi-mode resource-constrained discrete-time–cost-resource optimization (F-MRC-DTCRO) model for the time-cost-resource moment tradeoff in a fuzzy environment while satisfying all the project constraints. In the proposed model, fuzzy numbers are used to characterize the uncertainty of direct cost of activities. Using this model, different risk acceptance levels of the decision maker can be addressed in the optimization process. A newly developed multi-objective optimization algorithm called ENSCBO is used to search non-dominated solutions to the fuzzy multi-objective model. Finally, the developed model is applied to solve a benchmark test problem. The results indicate that incorporating the fuzzy structure of uncertainty in costs to previously developed MRC-DTCRO models facilitates the decision-making process and provides more realistic solutions