Computational complexity of the landscape: Part I

doi:10.1016/j.aop.2006.07.013

Abstract

We study the computational complexity of the physical problem of finding vacua of string theory which agree with data, such as the cosmological constant, and show that such problems are typically NP hard. In particular, we prove that in the Bousso-Polchinski model, the problem is NP complete. We discuss the issues this raises and the possibility that, even if we were to find compelling evidence that some vacuum of string theory describes our universe, we might never be able to find that vacuum explicitly. In a companion paper, we apply this point of view to the question of how early cosmology might select a vacuum.

Toward a fundamental theory of optimal feature selection: Part II - Implementation and computational complexity

Morgera, S.D. January 1987 - IEEE Trans. Pattern Anal. Mach. Intell.; (United States)

Certain algorithms and their computational complexity are examined for use in a VLSI implementation of the real-time pattern classifier described in Part I of this work. The most computationally intensive processing is found in the classifier training mode wherein subsets of the largest and smallest eigenvalues and associated eigenvectors of the input data covariance pair must be computed. It is shown that if the matrix of interest is centrosymmetric and the method for eigensystem decomposition is operator-based, the problem architecture assumes a parallel form. Such a matrix structure is found in a wide variety of pattern recognition and speech andmore »« less
DOI: 10.1109/TPAMI.1987.4767870
A computational study of yttria-stabilized zirconia: I. Using crystal chemistry to search for the ground state on a glassy energy landscape

Dong, Yanhao ; Qi, Liang ; Li, Ju ; ... April 2017 - Acta Materialia
Cited by 1
DOI: 10.1016/j.actamat.2017.01.006
Automating Embedded Analysis Capabilities and Managing Software Complexity in Multiphysics Simulation, Part I: Template-Based Generic Programming

Pawlowski, Roger P. ; Phipps, Eric T. ; Salinger, Andrew G. January 2012 - Scientific Programming

An approach for incorporating embedded simulation and analysis capabilities in complex simulation codes through template-based generic programming is presented. This approach relies on templating and operator overloading within the C++ language to transform a given calculation into one that can compute a variety of additional quantities that are necessary for many state-of-the-art simulation and analysis algorithms. An approach for incorporating these ideas into complex simulation codes through general graph-based assembly is also presented. These ideas have been implemented within a set of packages in the Trilinos framework and are demonstrated on a simple problem from chemical engineering.
DOI: 10.1155/2012/202071
Automating Embedded Analysis Capabilities and Managing Software Complexity in Multiphysics Simulation, Part I: Template-Based Generic Programming

Pawlowski, Roger P. ; Phipps, Eric T. ; Salinger, Andrew G. January 2012 - Scientific Programming

An approach for incorporating embedded simulation and analysis capabilities in complex simulation codes through template-based generic programming is presented. This approach relies on templating and operator overloading within the C++ language to transform a given calculation into one that can compute a variety of additional quantities that are necessary for many state-of-the-art simulation and analysis algorithms. An approach for incorporating these ideas into complex simulation codes through general graph-based assembly is also presented. These ideas have been implemented within a set of packages in the Trilinos framework and are demonstrated on a simple problem from chemical engineering.
DOI: 10.1155/2012/202071
Calculational methods for nuclear heating. Part I. Theoretical and computational algorithms

Abdou, M.A. ; Maynard, C.W. April 1975 - Nucl. Sci. Eng., v. 56, no. 4, pp. 360-380

Title: Computational complexity of the landscape: Part I

Abstract

Citation Formats

Toward a fundamental theory of optimal feature selection: Part II - Implementation and computational complexity

A computational study of yttria-stabilized zirconia: I. Using crystal chemistry to search for the ground state on a glassy energy landscape

Automating Embedded Analysis Capabilities and Managing Software Complexity in Multiphysics Simulation, Part I: Template-Based Generic Programming

Automating Embedded Analysis Capabilities and Managing Software Complexity in Multiphysics Simulation, Part I: Template-Based Generic Programming

Calculational methods for nuclear heating. Part I. Theoretical and computational algorithms