English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

This paper investigates the self-similar solutions of theEinstein-axion-dilaton configuration from type IIB string theory and the globalSL(2,R) symmetry. We consider the Continuous Self Similarity (CSS), where thescale transformation is controlled by an SL(2, R) boost or hyperbolictranslation. The solutions stay invariant under the combination of space-timedilation with internal SL(2,R) transformations. We develop a new formalismbased on Sequential Monte Carlo (SMC) and artificial neural networks (NNs) toestimate the self-similar solutions to the equations of motion in thehyperbolic class in four dimensions. Due to the complex and highly nonlinearpatterns, researchers typically have to use various constraints and numericalapproximation methods to estimate the equations of motion; thus, they have tooverlook the measurement errors in parameter estimation. Through a Bayesianframework, we incorporate measurement errors into our models to find thesolutions to the hyperbolic equations of motion. It is well known that thehyperbolic class suffers from multiple solutions where the critical collapsefunctions have overlap domains for these solutions. To deal with thiscomplexity, for the first time in literature on the axion-dilaton system, wepropose the SMC approach to obtain the multi-modal posterior distributions.Through a probabilistic perspective, we confirm the deterministic $\alpha$ and$\beta$ solutions available in the literature and determine all possiblesolutions that may occur due to measurement errors. We finally proposed thepenalized Leave-One-Out Cross-validation (LOOCV) to combine the BayesianNN-based estimates optimally. The approach enables us to determine the optimumweights while dealing with the co-linearity issue in the NN-based estimates andbetter predict the critical functions corresponding to multiple solutions ofthe equations of motion.

Sequential Monte Carlo with Cross-validated Neural Networks for Complexity of Hyperbolic Black Hole Solutions in 4D