Search results for "Multivariable calculus"
showing 10 items of 21 documents
Identifying Prognostic SNPs in Clinical Cohorts: Complementing Univariate Analyses by Resampling and Multivariable Modeling
2016
Clinical cohorts with time-to-event endpoints are increasingly characterized by measurements of a number of single nucleotide polymorphisms that is by a magnitude larger than the number of measurements typically considered at the gene level. At the same time, the size of clinical cohorts often is still limited, calling for novel analysis strategies for identifying potentially prognostic SNPs that can help to better characterize disease processes. We propose such a strategy, drawing on univariate testing ideas from epidemiological case-controls studies on the one hand, and multivariable regression techniques as developed for gene expression data on the other hand. In particular, we focus on …
Extension of The Stochastic Differential Calculus To Complex Processes
1996
In structural engineering complex processes arise to predict the first excursion failure, fatigue failure, etc. Indeed to solve these problems the envelope function, which is the modulus of a complex process, is usually introduced. In this paper the statistics of the complex response process related to the envelope statistics of linear systems subjected to parametric stationary normal white noise input are evaluated by using extensively the properties of stochastic differential calculus.
Land surface air temperature retrieval from EOS-MODIS images
2014
The knowledge of the spatial and temporal patterns of surface air temperature (SAT) is essential to monitor a region's climate and meteorology, to quantify surface exchange processes, to improve climatic and meteorological model results, and to study health and economic impacts. This letter analyzed correlations between SAT and geophysical land surface variables, mainly land surface temperature (LST), to establish operative techniques to obtain spatially continuous land SAT maps from satellite data, unlike data provided by meteorological station networks. The correlations were analyzed by using EOS-MODIS images, meteorological station network data, and geographical variables. Linear regress…
Estrategias para la elaboración de modelos estadísticos de regresión
2011
Multivariable regression models are widely used in health science research, mainly for two purposes: prediction and effect estimation. Various strategies have been recommended when building a regression model: a) use the right statistical method that matches the structure of the data; b) ensure an appropriate sample size by limiting the number of variables according to the number of events; c) prevent or correct for model overfitting; d) be aware of the problems associated with automatic variable selection procedures (such as stepwise), and e) always assess the performance of the final model in regard to calibration and discrimination measures. If resources allow, validate the prediction mo…
Linear Regression Analysis
2010
SUMMARY Background: Regression analysis is an important statistical method for the analysis of medical data. It enables the identification and characterization of relationships among multiple factors. It also enables the identification of prognostically relevant risk factors and the calculation of risk scores for individual prognostication. Methods: This article is based on selected textbooks of statistics, a selective review of the literature, and our own experience. Results: After a brief introduction of the uni- and multivariable regression models, illustrative examples are given to explain what the important considerations are before a regression analysis is performed, and how the resul…
Control zeros and nonminimum phase LTI mimo systems
1999
Abstract The paper presents a new, general, inverse-model/output-zeroing approach to zeros of LTI discrete-time multivariable, possibly nonsquare systems. It is shown on simple examples that the existing definitions of multivariable zeros fail to detect certain important zeros which contribute to zeroing the system output. As a result, a concept of ‘control zeros’ is introduced, followed by a general redefinition of minimum/nonminimum phase systems, both new contributions being based on the notion of (generalized) inverse systems. Output-zeroing/inverse-model/minimum-variance control-related justifications of the new approach are presented.
Transforming RNA-Seq Data to Improve the Performance of Prognostic Gene Signatures
2014
Gene expression measurements have successfully been used for building prognostic signatures, i.e for identifying a short list of important genes that can predict patient outcome. Mostly microarray measurements have been considered, and there is little advice available for building multivariable risk prediction models from RNA-Seq data. We specifically consider penalized regression techniques, such as the lasso and componentwise boosting, which can simultaneously consider all measurements and provide both, multivariable regression models for prediction and automated variable selection. However, they might be affected by the typical skewness, mean-variance-dependency or extreme values of RNA-…
Empirical study of the dependence of the results of multivariable flexible survival analyses on model selection strategy
2008
Flexible survival models, which avoid assumptions about hazards proportionality (PH) or linearity of continuous covariates effects, bring the issues of model selection to a new level of complexity. Each ‘candidate covariate’ requires inter-dependent decisions regarding (i) its inclusion in the model, and representation of its effects on the log hazard as (ii) either constant over time or time-dependent (TD) and, for continuous covariates, (iii) either loglinear or non-loglinear (NL). Moreover, ‘optimal’ decisions for one covariate depend on the decisions regarding others. Thus, some efficient model-building strategy is necessary. We carried out an empirical study of the impact of the model …
A physical approach to the connection between fractal geometry and fractional calculus
2014
Our goal is to prove the existence of a connection between fractal geometries and fractional calculus. We show that such a connection exists and has to be sought in the physical origins of the power laws ruling the evolution of most of the natural phenomena, and that are the characteristic feature of fractional differential operators. We show, with the aid of a relevant example, that a power law comes up every time we deal with physical phenomena occurring on a underlying fractal geometry. The order of the power law depends on the anomalous dimension of the geometry, and on the mathematical model used to describe the physics. In the assumption of linear regime, by taking advantage of the Bo…
New Results in Generalized Minimum Variance Control of Computer Networks
2014
In this paper new results in adaptive (generalized) minimum variance control of packet switching computer networks are presented. New solutions, corresponding to the new inverses of the nonsquare polynomial matrices, can be used for design of robust control of multivariable systems with different number of inputs and outputs. Application of polynomial matrix inverses with arbitrary degrees of freedom creates the possibilities to optimal control of computer networks in terms of usage their maximal bandwidth. Simulation examples made in Matlab environment show big potential of presented approach. DOI: http://dx.doi.org/10.5755/j01.itc.43.3.6268