Search results for "Gauss"
showing 10 items of 701 documents
Random analysis of geometrically non-linear FE modelled structures under seismic actions
1990
Abstract In the framework of the finite element (FE) method, by using the “total Lagrangian approach”, the stochastic analysis of geometrically non-linear structures subjected to seismic inputs is performed. For this purpose the equations of motion are written with the non-linear contribution in an explicit representation, as pseudo-forces, and with the ground motion modelled as a filtered non-stationary white noise Gaussian process, using a Tajimi-Kanai-like filter. Then equations for the moments of the response are obtained by extending the classical Ito's rule to vectors of random processes. The equations of motion, and the equations for moments, obtained here, show a perfect formal simi…
Interpolation and approximation in L2(γ)
2007
Assume a standard Brownian motion W=(W"t)"t"@?"["0","1"], a Borel function f:R->R such that f(W"1)@?L"2, and the standard Gaussian measure @c on the real line. We characterize that f belongs to the Besov space B"2","q^@q(@c)@?(L"2(@c),D"1","2(@c))"@q","q, obtained via the real interpolation method, by the behavior of a"X(f(X"1);@t)@[email protected]?f(W"1)-P"X^@tf(W"1)@?"L"""2, where @t=(t"i)"i"="0^n is a deterministic time net and P"X^@t:L"2->L"2 the orthogonal projection onto a subspace of 'discrete' stochastic integrals x"[email protected]?"i"="1^nv"i"-"1(X"t"""i-X"t"""i"""-"""1) with X being the Brownian motion or the geometric Brownian motion. By using Hermite polynomial expansions the…
Stochastic differential equations with coefficients in Sobolev spaces
2010
We consider It\^o SDE $\d X_t=\sum_{j=1}^m A_j(X_t) \d w_t^j + A_0(X_t) \d t$ on $\R^d$. The diffusion coefficients $A_1,..., A_m$ are supposed to be in the Sobolev space $W_\text{loc}^{1,p} (\R^d)$ with $p>d$, and to have linear growth; for the drift coefficient $A_0$, we consider two cases: (i) $A_0$ is continuous whose distributional divergence $\delta(A_0)$ w.r.t. the Gaussian measure $\gamma_d$ exists, (ii) $A_0$ has the Sobolev regularity $W_\text{loc}^{1,p'}$ for some $p'>1$. Assume $\int_{\R^d} \exp\big[\lambda_0\bigl(|\delta(A_0)| + \sum_{j=1}^m (|\delta(A_j)|^2 +|\nabla A_j|^2)\bigr)\big] \d\gamma_d0$, in the case (i), if the pathwise uniqueness of solutions holds, then the push-f…
Distributed Learning Automata-based S-learning scheme for classification
2019
This paper proposes a novel classifier based on the theory of Learning Automata (LA), reckoned to as PolyLA. The essence of our scheme is to search for a separator in the feature space by imposing an LA-based random walk in a grid system. To each node in the grid, we attach an LA whose actions are the choices of the edges forming a separator. The walk is self-enclosing, and a new random walk is started whenever the walker returns to the starting node forming a closed classification path yielding a many-edged polygon. In our approach, the different LA attached to the different nodes search for a polygon that best encircles and separates each class. Based on the obtained polygons, we perform …
Pharmacological distribution diagrams: a tool for de novo drug design.
1996
Abstract Discriminant analysis applied to SAR studies using topological descriptors allows us to plot frequency distribution diagrams: a function of the number of drugs within an interval of values of discriminant function vs. these values. We make use of these representations, pharmacological distribution diagrams (PDDs), in structurally heterogeneous groups where generally they adopt skewed Gaussian shapes or present several maxima. The maxima afford intervals of discrimianant function in which exists a good expectancy to find new active drugs. A set of β-blockers with contrasted activity has been selected to test the ability of PDDs as a visualizing technique, for the identification of n…
Information Decomposition: A Tool to Dissect Cardiovascular and Cardiorespiratory Complexity
2017
This chapter reports some recent developments of information-theoretic concepts applied to the description of coupled dynamical systems, which allow to decompose the entropy of an assigned target system into components reflecting the information stored in the system and the information transferred to it from the other systems, as well as the nature (synergistic or redundant) of the information transferred to the target. The decomposition leads to well-defined measures of information dynamics which in the chapter will be defined theoretically, computed in simulations of linear Gaussian systems and implemented in practice through the application to heart period, arterial pressure and respirat…
A Survey of Active Learning for Quantifying Vegetation Traits from Terrestrial Earth Observation Data
2021
The current exponential increase of spatiotemporally explicit data streams from satellite-based Earth observation missions offers promising opportunities for global vegetation monitoring. Intelligent sampling through active learning (AL) heuristics provides a pathway for fast inference of essential vegetation variables by means of hybrid retrieval approaches, i.e., machine learning regression algorithms trained by radiative transfer model (RTM) simulations. In this study we summarize AL theory and perform a brief systematic literature survey about AL heuristics used in the context of Earth observation regression problems over terrestrial targets. Across all relevant studies it appeared that…
A Survey on Gaussian Processes for Earth-Observation Data Analysis: A Comprehensive Investigation
2016
Gaussian processes (GPs) have experienced tremendous success in biogeophysical parameter retrieval in the last few years. GPs constitute a solid Bayesian framework to consistently formulate many function approximation problems. This article reviews the main theoretical GP developments in the field, considering new algorithms that respect signal and noise characteristics, extract knowledge via automatic relevance kernels to yield feature rankings automatically, and allow applicability of associated uncertainty intervals to transport GP models in space and time that can be used to uncover causal relations between variables and can encode physically meaningful prior knowledge via radiative tra…
Latent force models for earth observation time series prediction
2016
We introduce latent force models for Earth observation time series analysis. The model uses Gaussian processes and differential equations to combine data driven modelling with a physical model of the system. The LFM presented here performs multi-output structured regression, adapts to the signal characteristics, it can cope with missing data in the time series, and provides explicit latent functions that allow system analysis and evaluation. We successfully illustrate the performance in challenging scenarios of crop monitoring from space, providing time-resolved time series predictions.
Statistical biophysical parameter retrieval and emulation with Gaussian processes
2019
Abstract Earth observation from satellites poses challenging problems where machine learning is being widely adopted as a key player. Perhaps the most challenging scenario that we are facing nowadays is to provide accurate estimates of particular variables of interest characterizing the Earth's surface. This chapter introduces some recent advances in statistical bio-geophysical parameter retrieval from satellite data. In particular, we will focus on Gaussian process regression (GPR) that has excelled in parameter estimation as well as in modeling complex radiative transfer processes. GPR is based on solid Bayesian statistics and generally yields efficient and accurate parameter estimates, a…