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National Repository of Grey Literature 2 records found  Search took 0.01 seconds. 
Using gadget construction in structural convergence
 Hons, Tomáš ; Hartman, David (advisor) ; Ossona de Mendez, Patrice (referee) ; Pultr, Aleš (referee)
Structural convergence is a framework for convergence of graphs and relational struc- tures based on the probability of satisfaction of first-order formulas. We consider gadget construction, which is a ubiquitous tool in many areas of mathematics, as a method for constructing convergent sequences of structures. Both for elementary and local conver- gence, we investigate the behavior of a sequence created by gadget construction from convergent sequences of base structures and gadgets. We show that elementary conver- gence is always preserved while additional assumptions are necessary for local convergence as witnessed by several examples. We give various different conditions that ensure local convergence. One of them states that the resulting sequence is local convergent if the replaced edges are dense in the sequence of base structures. The sufficient conditions are partially complemented by inverse theorems. 1
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Modular tool for parametric analysis of dynamical systems using complex networks
 Hons, Tomáš ; Hartman, David (advisor) ; Hubička, Jan (referee)
Modelling of dynamical systems with complex internal structure is a complicated task which has more and more frequently been solved using complex networks capturing the structure of interactions among individual elements of the system. An important task of this process is the selection of suitable methods and their parameters by which we create the network and subsequently examine it. However, there is no tool that could automat- ically configure various parametrized analytical pipelines, enable executing all potential runs and compare their results. Such a tool would consequently allow selection of meth- ods and parameters most suitable for the system explored. This work presents the Neads library which is able to execute parametric analyses of general dynamical systems using complex networks, intermediate results being stored and available for subsequent calcula- tions as well as potential pipelines extensions. The tool has the potential to significantly accelerate scientific work in this area. 1
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