What are the latest advance in hierarchical matrices?5 answersThe latest advances in hierarchical matrices include innovative parallel implementations for improved performance, enhanced methods for solving linear systems with oscillatory kernels, and novel approaches to alleviate computational bottlenecks by reducing ranks and memory requirements. Additionally, advancements in fast memory-efficient construction algorithms for Hierarchically Semi-Separable (HSS) representations and efficient matrix-matrix multiplication for the fast multipole method (FMM) have been introduced. These developments aim to enhance the efficiency, scalability, and applicability of hierarchical matrices in various computational tasks, ranging from numerical simulations to solving dense linear systems arising in mathematical physics and engineering applications.
Hierarchical decision models?5 answersHierarchical decision models are a popular means of coping with complex decision problems. They involve a hierarchical structure where subtasks are ordered hierarchically, and locally optimal solutions are determined at each level. These models are used in various fields such as technology evaluation, energy portfolio forecast, distributed data storage and processing, and protein melting-point estimation. The models utilize different techniques such as the analytic hierarchy process (AHP), weighted average methods, and genetic algorithms for optimization. They provide insights into decision-making processes, allow for the consideration of various parameters, and enable the identification of effective solutions at different levels of the hierarchy.
What is hierarchical network model?3 answersA hierarchical network model is a type of network model that represents the hierarchical relationships among entities in a network. It allows for the explicit representation of the stochastic dependence among the dyads (random ties) of the network. This is achieved through the use of a dependency graph, which defines conditional independence clauses among the dyads of the network. The hierarchical network model can be used to generalize existing network models, such as the Erdos-Renyi and β models, by incorporating the hierarchical structure. Parameter estimation methods and simulation studies have been developed for hierarchical network models with sparse dependency graphs.
How can batching problems be solved in various hierarchy levels?3 answersBatching problems can be solved in various hierarchy levels. At the process choice/design level, decisions are made regarding how to batch items in order to impact goods-flow systems performance. Activity planning, which includes aggregate planning and activity programming, is another level where batching decisions are made. Finally, at the activity control level, decisions are made on how to control the batching process in order to optimize performance. Different approaches can be used to solve batching problems depending on the specific context. For example, in the case of on-line batching problems, a solution approach based on decomposing the chopping and processing of batches has been proposed. In the case of batching jobs on a single machine, the greedy algorithm has been shown to solve the problem when all jobs are of one type.
What is hierarchical control?5 answersHierarchical control is an approach used to handle complex control problems by decomposing them into smaller subproblems and reassembling their solutions into a hierarchical structure. It involves multiple control layers operating on different time scales, with signals of different granularity. The specifications for each control layer need to be carefully chosen, considering the trade-off between ease of control synthesis and difficulty in higher-level control synthesis. Hierarchical control has been applied in various domains, including distribution systems, microgrids, and motor systems. It enables the coordination of different control devices and automation systems to achieve efficient and reliable control.
What properties do hierarchical structures have?5 answersHierarchical structures possess several properties. They provide improved toughness and economy of material. They also offer functionalities that are unattainable in simpler structures. Hierarchical structures can be organized in a coherent manner, helping to organize our knowledge of minerals and crystal structures. They can also result in precise control over geometric features and wetting states, leading to the fabrication of biomimetic functional surfaces. In complex systems, hierarchical structures explain the mechanical properties and structure-property relationships. These structures can enhance specific properties, such as tensile and impact properties in polymers, through microlayering technology. Overall, hierarchical structures provide mechanical advantages, unique functionalities, organization, control over properties, and improved understanding of structure-property relationships.