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A Tucker decomposition process for probabilistic modeling of diffusion magnetic resonance imaging [article]

Hernan Dario Vargas Cardona, Mauricio A. Alvarez, Alvaro A. Orozco
2016 arXiv   pre-print
In this work, we propose a novel stochastic process called Tucker decomposition process (TDP) for performing HOT data interpolation.  ...  Our model is based on the Tucker decomposition and Gaussian processes as parameters of the TDP. We test the TDP in 2nd, 4th and 6th rank HOT fields.  ...  Note that probabilistic approaches (GWP and TDP) exhibit better performance than direct interpolation and log-Euclidean interpolation. One would expect GWP and TDP to exhibit a similar performance.  ... 
arXiv:1606.07970v1 fatcat:i3yqlbfs3ngwdiwyr74zh35fyq

Tensor decomposition processes for interpolation of diffusion magnetic resonance imaging

Hernán Darío Vargas-Cardona, Álvaro A. Orozco, Andrés M. Álvarez, Mauricio A. Álvarez
2019 Expert systems with applications  
Specifically, we introduce two probabilistic models, that we refer to as the Tucker decomposition 75 process (TDP) and the canonical decomposition process (CDP).  ...  Specifically to define M, we employ the canonical (Carroll & Chang, 1970) and the Tucker decomposition (Gulliksen & Frederiksen, 1964) of tensors to construct the probabilistic model.  ... 
doi:10.1016/j.eswa.2018.10.005 fatcat:mww5dlz2ere6tbj5x6kc7x3yci

Parallel stochastic methods for PDE based grid generation

Alexander Bihlo, Ronald D. Haynes
2014 Computers and Mathematics with Applications  
Further improvements through the use of interpolation along the sub-domain interfaces and smoothing of mesh candidates are discussed.  ...  The meshes over the single sub-domains can then be obtained completely independently of each other using the probabilistically computed solutions along the interfaces as boundary conditions for the linear  ...  Interpolation along the interface If the number of compute cores is limited, a promising approach to further reduce the cost of the probabilistic part of the domain decomposition algorithm is to avoid  ... 
doi:10.1016/j.camwa.2014.07.017 fatcat:4g4l2g5ohbcuxenbovy2mghtbu

Parallel stochastic methods for PDE based grid generation [article]

Alexander Bihlo, Ronald D. Haynes
2014 arXiv   pre-print
In addition we show further improvements are possible using interpolation of the subdomain interfaces and smoothing of mesh candidates.  ...  The meshes over the single subdomains can then be obtained completely independently of each other using the probabilistically computed solutions along the interfaces as boundary conditions for the linear  ...  Interpolation along the interface If the number of compute cores is limited, a promising approach to further reduce the cost of the probabilistic part of the domain decomposition algorithm is to avoid  ... 
arXiv:1310.3435v2 fatcat:3lsbbhqxfrhvhfbdmf6m2mqivi

Holomorphic martingales and interpolation between Hardy spaces: the complex method

P. F. X. Müller
1995 Transactions of the American Mathematical Society  
A probabilistic proof is given to identify the complex interpolation space of Hl(T) and H°°(T) as HP(T).  ...  These notes are also a continuation of [M] where a probabilistic argument was given to identify the real interpolation spaces between H°°(T) and 7/'(T).  ...  His work also contains the description of the real interpolation spaces for the couple (//', H°°).  ... 
doi:10.1090/s0002-9947-1995-1264825-8 fatcat:mdvamv2ggjgiha433p6prkzylu

Interpolated Spectral NGram Language Models

Ariadna Quattoni, Xavier Carreras
2019 Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics  
In this work we employ a technique for scaling up spectral learning, and use interpolated predictions that are optimized to maximize perplexity.  ...  The second is that the loss function behind spectral learning, based on moment matching, differs from the probabilistic metrics used to evaluate language models.  ...  Introduction In the recent years we have witnessed the development of spectral methods based on matrix decompositions to learn Probabilistic Non-deterministic Finite Automata (PNFA) and related models  ... 
doi:10.18653/v1/p19-1594 dblp:conf/acl/QuattoniC19 fatcat:umjd54ixobcalfga6he45bypmu

Page 819 of Mathematical Reviews Vol. , Issue 87b [page]

1987 Mathematical Reviews  
Klaus-Dieter Bierstedt (Paderborn) Gomez, Marcelo (1-IASP); Milman, Mario (1-IASP) Interpolation complexe des espaces H? et théoréme de Wolff. (English summary) [Complex interpolation of H?  ...  Various sections of the paper consider so-called E-spaces, an analysis of the probabilistic Cauchy-Schwarz inequality, norms and metrics, and probabilistic orthogonality. E. R.  ... 

Jean Bourgain's analytic partition of unity via holomorphic martingales

Paul Müller
1995 Pacific Journal of Mathematics  
Bourgain's interpolation inequality.  ...  Here I wish to present a soft way to this construction which results from using probabilistic tools such as holomorphic martingales.  ... 
doi:10.2140/pjm.1995.169.161 fatcat:47fw2ymyqnendezloiccldwzam

Domain decomposition solution of nonlinear two-dimensional parabolic problems by random trees

Juan A. Acebrón, Ángel Rodríguez-Rozas, Renato Spigler
2009 Journal of Computational Physics  
A domain decomposition method is developed for the numerical solution of nonlinear parabolic partial differential equations in any space dimension, based on the probabilistic representation of solutions  ...  An interpolation is then carried out, in order to approximate interfacial values of the solution inside the domain. Thus, a fully decoupled set of sub-problems is obtained.  ...  We called our method "probabilistic domain decomposition method" (PDD method, for short). In [5] , we extended such method to treat nonlinear parabolic one-dimensional problems.  ... 
doi:10.1016/j.jcp.2009.04.034 fatcat:d6h4d2mg2zespicivvs6anok24

Stochastic sensitivity analysis by dimensional decomposition and score functions

Sharif Rahman
2009 Probabilistic Engineering Mechanics  
The proposed decomposition facilitates univariate and bivariate approximations of stochastic sensitivity measures, lower-dimensional numerical integrations or Lagrange interpolations, and Monte Carlo simulation  ...  Both the probabilistic response and its sensitivities can be estimated from a single stochastic analysis, without requiring performance function gradients.  ...  Therefore, a higher-order interpolation can be avoided by decomposition in the original space in this problem.  ... 
doi:10.1016/j.probengmech.2008.07.004 fatcat:2ipkecreyrgu7cosdharehooj4

Probabilistically induced domain decomposition methods for elliptic boundary-value problems

Juan A. Acebrón, Maria Pia Busico, Piero Lanucara, Renato Spigler
2005 Journal of Computational Physics  
This allows for a domain decomposition of the domain.  ...  A continuous approximation of the solution is obtained interpolating on such interfaces, and then used as boundary data to split the original problem into fully decoupled subproblems.  ...  This method can be called a "probabilistic domain decomposition"(PDD) method. We stress that it can fully exploit parallel architectures.  ... 
doi:10.1016/j.jcp.2005.04.014 fatcat:koq3ov6orjfohphkkhhp7sg4my

Page 5608 of Mathematical Reviews Vol. , Issue 2001H [page]

2001 Mathematical Reviews  
(English summary) Operator theory and interpolation (Bloomington, IN, 1996), 123-144, Oper. Theory Adv. Appl., 115, Birkhduser, Basel, 2000.  ...  In this paper, the characterizations of probabilistically uniformly bounded sets, probabilistically bounded sets, probabilistically semi-bounded sets and probabilistically unbounded sets in Menger probabilistic  ... 

A dimensional decomposition method for stochastic fracture mechanics

Sharif Rahman
2006 Engineering Fracture Mechanics  
This paper presents a new dimensional decomposition method for obtaining probabilistic characteristics of crack-driving forces and reliability analysis of general cracked structures subject to random loads  ...  The method involves a novel function decomposition permitting lower-variate approximations of a crack-driving force or a performance function, Lagrange interpolations for representing lower-variate component  ...  Section 4 describes how the function decomposition is exploited in solving a general probabilistic fracture-mechanics problem.  ... 
doi:10.1016/j.engfracmech.2006.04.010 fatcat:va4jx36bkvamzlapsgxwldrw5y

A stochastic domain decomposition method for time dependent mesh generation [article]

Alexander Bihlo, Ronald D. Haynes
2014 arXiv   pre-print
The method uses the probabilistic form of the exact solution of the linear mesh generator to provide the sub-domain interface values that serve as boundary conditions for the domain decomposition.  ...  We use a time-relaxed linear grid generator of Winslow type to propose a new deterministic-stochastic domain decomposition approach to the generation of adaptive moving meshes.  ...  In [3] we proposed a stochastic domain decomposition (DD) method to find adaptive meshes by solving a linear elliptic mesh generator.  ... 
arXiv:1402.0266v1 fatcat:7koup3ypx5dqfkbgpgw43njgly

Verification of solar irradiance probabilistic forecasts

Philippe Lauret, Mathieu David, Pierre Pinson
2019 Solar Energy  
irradiance probabilistic forecasts and by extension probabilistic forecasts of solar power generation.  ...  We propose a framework for evaluating the quality of solar irradiance probabilistic forecasts.  ...  -Can be used for Ensemble (uniform/non uniform CDF) Decomposition of the CRPS into reliability and resolution provides additional insight into the performance of a probabilistic model.  ... 
doi:10.1016/j.solener.2019.10.041 fatcat:tbvjeqmjobbydbqr4kc4ge6bti
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