Topology of Windows in the High-Dimensional Parameter Space of Chaotic Maps

2003 ◽  
Vol 13 (09) ◽  
pp. 2681-2688 ◽  
Author(s):  
Murilo S. Baptista ◽  
Celso Grebogi ◽  
Ernest Barreto
Keyword(s):  
Parameter Space ◽  
Chaotic Systems ◽  
Chaotic Maps ◽  
High Dimensional ◽  
Dimensional Parameter ◽  
Different Shapes ◽  
Dynamical Quantity

Periodicity is ubiquitous in nature. In this work, we analyze the dynamical reasons for which periodic windows, that appear in parameter space diagrams, have different shapes and structures. For that, we make use of a dynamical quantity, called spine — the skeleton of the window, in order to explain a conjecture that describes the presence of periodic windows in the parameter space of high-dimensional chaotic systems.

scholarly journals Optimization and model reduction in the high dimensional parameter space of a budding yeast cell cycle model

2013 ◽  
Vol 7 (1) ◽  
pp. 53 ◽  
Author(s):  
Cihan Oguz ◽  
Teeraphan Laomettachit ◽  
Katherine C Chen ◽  
Layne T Watson ◽  
William T Baumann ◽  
...  
Keyword(s):  
Cell Cycle ◽  
Yeast Cell ◽  
Model Reduction ◽  
Parameter Space ◽  
Budding Yeast ◽  
Yeast Cell Cycle ◽  
High Dimensional ◽  
Cycle Model ◽  
Dimensional Parameter ◽  
Budding Yeast Cell Cycle

scholarly journals A door to model reduction in high-dimensional parameter space

2018 ◽  
Vol 346 (7) ◽  
pp. 524-531 ◽  
Author(s):  
Charles Paillet ◽  
David Néron ◽  
Pierre Ladevèze
Keyword(s):  
Model Reduction ◽  
Parameter Space ◽  
High Dimensional ◽  
Dimensional Parameter

Bayesian updating of complex nonlinear FE models with high-dimensional parameter space using heterogeneous measurements and a batch-recursive approach

2019 ◽  
Vol 201 ◽  
pp. 109724 ◽  
Author(s):  
Rodrigo Astroza ◽  
Nicolás Barrientos ◽  
Yong Li ◽  
Erick I. Saavedra Flores ◽  
Zhenning Liu
Keyword(s):  
Parameter Space ◽  
Bayesian Updating ◽  
High Dimensional ◽  
Dimensional Parameter

scholarly journals Large random simplicial complexes, I

2016 ◽  
Vol 08 (03) ◽  
pp. 399-429 ◽  
Author(s):  
A. Costa ◽  
M. Farber
Keyword(s):  
Probability Measure ◽  
Simplicial Complex ◽  
Parameter Space ◽  
Simplicial Complexes ◽  
High Dimensional ◽  
Topological Properties ◽  
Convex Domains ◽  
Dimensional Parameter ◽  
Random Simplicial Complexes ◽  
Simply Connected

In this paper we introduce and develop the multi-parameter model of random simplicial complexes with randomness present in all dimensions. Various geometric and topological properties of such random simplicial complexes are characterised by convex domains in the high-dimensional parameter space (rather than by intervals, as in the usual one-parameter models). We find conditions under which a multi-parameter random simplicial complex is connected and simply connected. Besides, we give an intrinsic characterisation of the multi-parameter probability measure. We analyse links of simplexes and intersections of multi-parameter random simplicial complexes and show that they are also multi-parameter random simplicial complexes.

Chaotic Map Construction from Common Nonlinearities and Microcontroller Implementations

2016 ◽  
Vol 26 (07) ◽  
pp. 1650121 ◽  
Author(s):  
Günyaz Ablay
Keyword(s):  
Chaotic Systems ◽  
Pulse Width Modulation ◽  
Chaotic Maps ◽  
Chaotic Map ◽  
Experimental Studies ◽  
Cross Coupling ◽  
Electrical Machines ◽  
High Dimensional ◽  
Map Construction ◽  
Arduino Microcontroller

This work presents novel discrete-time chaotic systems with some known physical system nonlinearities. Dynamic behaviors of the models are examined with numerical methods and Arduino microcontroller-based experimental studies. Many new chaotic maps are generated in the form of [Formula: see text] and high-dimensional chaotic systems are obtained by weak coupling or cross-coupling the same or different chaotic maps. An application of the chaotic maps is realized with Arduino for chaotic pulse width modulation to drive electrical machines. It is expected that the new chaotic maps and their microcontroller implementations will facilitate practical chaos-based applications in different fields.

scholarly journals Hierarchical Bayes modelling of penalty conversion rates of Bundesliga players

2021 ◽  
Author(s):  
Christoph Hanck ◽  
Martin C. Arnold
Keyword(s):  
Parameter Space ◽  
Historical Data ◽  
Hierarchical Bayes ◽  
High Dimensional ◽  
Football Players ◽  
Professional Football ◽  
Inherent Difficulty ◽  
Dimensional Parameter ◽  
Single Action ◽  
Conversion Rates

AbstractJudging by its significant potential to affect the outcome of a game in one single action, the penalty kick is arguably the most important set piece in football. Scientific studies on how the ability to convert a penalty kick is distributed among professional football players are scarce. In this paper, we consider how to rank penalty takers in the German Bundesliga based on historical data from 1963 to 2021. We use Bayesian models that improve inference on ability measures of individual players by imposing structural assumptions on an associated high-dimensional parameter space. These methods prove useful for our application, coping with the inherent difficulty that many players only take few penalties, making purely frequentist inference rather unreliable.

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