scholarly journals Navigator function for the conformal bootstrap

2021 ◽  
Vol 11 (3) ◽  
Author(s):  
Marten Reehorst ◽  
Slava Rychkov ◽  
David Simmons-Duffin ◽  
Benoit Sirois ◽  
Ning Su ◽  
...  
Keyword(s):  
Parameter Space ◽  
Optimization Methods ◽  
High Dimensional ◽  
Dimensional Parameter ◽  
Parameter Spaces ◽  
Standard Methods ◽  
Conformal Bootstrap ◽  
Bootstrap Techniques ◽  
Binary Information ◽  
Quasi Newton

Current numerical conformal bootstrap techniques carve out islands in theory space by repeatedly checking whether points are allowed or excluded. We propose a new method for searching theory space that replaces the binary information "allowed"/"excluded" with a continuous "navigator" function that is negative in the allowed region and positive in the excluded region. Such a navigator function allows one to efficiently explore high-dimensional parameter spaces and smoothly sail towards any islands they may contain. The specific functions we introduce have several attractive features: they are well-defined in large regions of parameter space, can be computed with standard methods, and evaluation of their gradient is immediate due to an SDP gradient formula that we provide. The latter property allows for the use of efficient quasi-Newton optimization methods, which we illustrate by navigating towards the 3d Ising island.

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.

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.

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