Search results for " space"

Optimal rates of convergence for persistence diagrams in Topological Data Analysis

2013

Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field. In this paper, we study topological persistence in general metric spaces, with a statistical approach. We show that the use of persistent homology can be naturally considered in general statistical frameworks and persistence diagrams can be used as statistics with interesting convergence properties. Some numerical experiments are performed in various contexts to illustrate our results.

Multistate active spaces from local CAS-SCF molecular orbitals: the photodissociation of HFCO as an example.

2005

A recently developed algorithm to generate localized molecular orbitals (LMO) is applied to the study of excited states along a photodissociation process. The LMOs allow for the selection of a consistent complete active space (CAS) for the simultaneous description of all the electronic states involved in a multistate process on the basis of simple chemical criteria. The local nature of the orbitals is used to label them in a unique way that does not depend on the molecular geometry. The selection of the electronic configurations of interest for the set of target states on only the basis of the dominant excitations required by the simplest configuration interaction (CI) descriptions for both…

Vertical spectrum of the C2H 2+ system. An open shell (SC)2-CAS-SDCI study

2003

The open shell (SC)(2)-CAS-SDCI method along with a basis set of atomic natural orbitals (ANO) has been applied for calculating the main ionization potentials of acetylene, as well as the manifold of excited states of the different symmetries up to 32 eV. In this method, the single and double excitations of a CAS space are generated and the corresponding CI matrix is corrected by means of the (SC)(2) procedure that cancels the size-extensivity error and adds some high order contributions. The mean absolute error for the outer-valence X (2)Pi(u)(1pi(u) (-1)), A (2)Sigma(g) (+)(3sigma(g) (-1)), and B (2)Sigma(u) (+)(2sigma(u) (-1)) states, and the inner-valence C (2)Sigma(g) (+)(2sigma(g) (-1…

State-specific multireference coupled-cluster theory

2012

The multireference problem is considered one of the great challenges in coupled-cluster (CC) theory. Most recent developments are based on state-specific approaches, which focus on a single state and avoid some of the numerical problems of more general approaches. We review various state-of-the-art methods, including Mukherjee's state-specific multireference coupled-cluster (Mk-MRCC) theory, multireference Brillouin–Wigner coupled-cluster (MR-BWCC) theory, the MRexpT method, and internally contracted multireference coupled-cluster (ic-MRCC) theory. Related methods such as extended single-reference schemes [e.g., the complete active space coupled-cluster (CASCC) theory] and canonical transfo…

Third-order iterative methods without using any Fréchet derivative

2003

AbstractA modification of classical third-order methods is proposed. The main advantage of these methods is they do not need to evaluate any Fréchet derivative. A convergence theorem in Banach spaces, just assuming the second divided difference is bounded and a punctual condition, is analyzed. Finally, some numerical results are presented.

Parallel finite element splitting-up method for parabolic problems

1991

An efficient method for solving parabolic systems is presented. The proposed method is based on the splitting-up principle in which the problem is reduced to a series of independent 1D problems. This enables it to be used with parallel processors. We can solve multidimensional problems by applying only the 1D method and consequently avoid the difficulties in constructing a finite element space for multidimensional problems. The method is suitable for general domains as well as rectangular domains. Every 1D subproblem is solved by applying cubic B-splines. Several numerical examples are presented.

On the structure of certain ultradistributions

2009

Let "o" be a nonempty open subset of the k-dimensional euclidean space Rk. In this paper we show that, if S is an ultradistribution in "o", belonging to a class of Roumieu type stable under differential operators, then there is a family f, 2 Nk 0, of elements of L1 loc("o") such that S is represented in the formP2Nk 0 D"a"f "a". Some other results on the structure of certain ultradistributions of Roumieu type are also given.

New dimension indices for the characterization of the solvent-accessible surface

2001

New super-orthogonal space-time trellis codes using differential M-PSK for noncoherent mobile communication systems with two transmit antennas

2010

Published version of an article in the journal: Annals of Telecommunications-Annales Des Telecommunications. Also available from the publisher at: http://dx.doi.org/10.1007/s12243-010-0191-1 In this paper, we develop super-orthogonal space-time trellis codes (SOSTTCs) using differential binary phase-shift keying, quadriphase-shift keying and eight-phase shift keying for noncoherent communication systems with two transmit antennas without channel state information at the receiver. Based on a differential encoding scheme proposed by Tarokh and Jafarkhani, we propose a new decoding algorithm with reduced decoding complexity. To evaluate the performance of the SOSTTCs by way of computer simulat…

Learning Automata-based Misinformation Mitigation via Hawkes Processes

2021

AbstractMitigating misinformation on social media is an unresolved challenge, particularly because of the complexity of information dissemination. To this end, Multivariate Hawkes Processes (MHP) have become a fundamental tool because they model social network dynamics, which facilitates execution and evaluation of mitigation policies. In this paper, we propose a novel light-weight intervention-based misinformation mitigation framework using decentralized Learning Automata (LA) to control the MHP. Each automaton is associated with a single user and learns to what degree that user should be involved in the mitigation strategy by interacting with a corresponding MHP, and performing a joint ra…