Search results for "Computational Mathematic"
showing 10 items of 987 documents
Exploring chemical reactivity of complex systems with path-based coordinates: role of the distance metric.
2014
Path-based reaction coordinates constitute a valuable tool for free-energy calculations in complex processes. When a reference path is defined by means of collective variables, a nonconstant distance metric that incorporates the nonorthonormality of these variables should be taken into account. In this work, we show that, accounting for the correct metric tensor, these kind of variables can provide iso-hypersurfaces that coincide with the iso-committor surfaces and that activation free energies equal the value that would be obtained if the committor function itself were used as reaction coordinate. The advantages of the incorporation of the variable metric tensor are illustrated with the an…
Network structure and optimal technological innovation
2019
The role of networks in the emergence, diffusion and evolution of technological innovations has attracted much theoretical and empirical attention. Yet, much of the work has explored the role of undirected and homogeneous networks. In real cases, many networks are directed. The flow of information, benefits or observations is directed from one node towards another node. Real networks are also heterogeneous, for example, few nodes have a high degree while many others have a low degree. In this article, we report on the results of an evolutionary agent-based model in which a group of agents, in our case firms, collectively search a complex (rugged) technological landscape and observe each oth…
An automatic L1-based regularization method for the analysis of FFC dispersion profiles with quadrupolar peaks
2023
Fast Field-Cycling Nuclear Magnetic Resonance relaxometry is a non-destructive technique to investigate molecular dynamics and structure of systems having a wide range of ap- plications such as environment, biology, and food. Besides a considerable amount of liter- ature about modeling and application of such technique in specific areas, an algorithmic approach to the related parameter identification problem is still lacking. We believe that a robust algorithmic approach will allow a unified treatment of different samples in several application areas. In this paper, we model the parameters identification problem as a con- strained L 1 -regularized non-linear least squares problem. Following…
An analysis of Ralston's quadrature
1987
Ralston's quadrature achieves higher accuracy in composite rules than analogous Newton-Cotes or Gaussian formulas. His rules are analyzed, computable expressions for the weights and knots are given, and a more suitable form of the remainder is derived.
Residuenabschätzung für Polynom-Nullstellen mittels Lagrange-Interpolation
1970
If, for each zero of a polynomial, an approximation is known, estimates for the errors of these approximations are given, based on the evaluation of the polynomial at these points. The procedure can be carried over to the case of multiple roots and root clusters using derivatives up to the orderk - 1, wherek is the multiplicity of the cluster.
A symmetric tangent stiffness approach to cohesive mechanical interfaces in large displacements
2022
The present article proposes a formulation for a cohesive interface element in large displacement conditions. Theoretical and computational aspects, useful for an effective and efficient finite element implementation, are examined in details. A six-node (or higher) isoparametric interface element for two dimensional cohesive fracture propagation problems is developed. The element operators are consistently derived by a variational approach enforced in the current configuration, where a current frame is defined with axes tangential and normal to the middle line of the interface opening displacement gap. Under the constitutive assumption of small value of the modulus of the vector product bet…
How Low Can Approximate Degree and Quantum Query Complexity Be for Total Boolean Functions?
2012
It has long been known that any Boolean function that depends on n input variables has both degree and exact quantum query complexity of Omega(log n), and that this bound is achieved for some functions. In this paper we study the case of approximate degree and bounded-error quantum query complexity. We show that for these measures the correct lower bound is Omega(log n / loglog n), and we exhibit quantum algorithms for two functions where this bound is achieved.
Comparison of implementations of the lattice-Boltzmann method
2008
AbstractSimplicity of coding is usually an appealing feature of the lattice-Boltzmann method (LBM). Conventional implementations of LBM are often based on the two-lattice or the two-step algorithm, which however suffer from high memory consumption and poor computational performance, respectively. The aim of this work was to identify implementations of LBM that would achieve high computational performance with low memory consumption. Effects of memory addressing schemes were investigated in particular. Data layouts for velocity distribution values were also considered, and they were found to be related to computational performance. A novel bundle data layout was therefore introduced. Address…
[Editorial] Special issue on computational intelligence and nature-inspired algorithms for real-world data analytics and pattern recognition
2018
Cagnoni, S., & Castelli, M. (2018). [Editorial]. Special issue on computational intelligence and nature-inspired algorithms for real-world data analytics and pattern recognition. Algorithms, 11(3), 1-2. DOI: 10.3390/a11030025 This special issue of Algorithms is devoted to the study of Computational Intelligence and Nature-Inspired Algorithms for Real-World Data Analytics and Pattern Recognition. The special issue considered both theoretical contributions able to advance the state-of-the-art in this field and practical applications that describe novel approaches for solving real-world problems. published
On the stability of spline-collocation methods of multivalue type
1987
In this paper the general classV of spline-collocation methods for first order systems of ordinary differential equations is investigated. The methods can in part be regarded as so-called multivalue methods. This type contains the generalized singly-implicit methods treated by Butcher.