scholarly journals Linear Models with Response Functions Based on the Laplace Distribution: Statistical Formulae and Their Application to Epigenomics

2013 ◽  
Vol 2013 ◽  
pp. 1-22
Author(s):  
C. Z. W. Hassell Sweatman ◽  
G. C. Wake ◽  
A. B. Pleasants ◽  
C. A. McLean ◽  
A. M. Sheppard
Keyword(s):  
Linear Model ◽  
Covariance Matrix ◽  
Response Function ◽  
Linear Models ◽  
Likelihood Ratio Statistic ◽  
Laplace Distribution ◽  
Simple Expression ◽  
Modulus Function ◽  
Response Functions ◽  
Statistical Application

The statistical application considered here arose in epigenomics, linking the DNA methylation proportions measured at specific genomic sites to characteristics such as phenotype or birth order. It was found that the distribution of errors in the proportions of chemical modification (methylation) on DNA, measured at CpG sites, may be successfully modelled by a Laplace distribution which is perturbed by a Hermite polynomial. We use a linear model with such a response function. Hence, the response function is known, or assumed well estimated, but fails to be differentiable in the classical sense due to the modulus function. Our problem was to estimate coefficients for the linear model and the corresponding covariance matrix and to compare models with varying numbers of coefficients. The linear model coefficients may be found using the (derivative-free) simplex method, as in quantile regression. However, this theory does not yield a simple expression for the covariance matrix of the coefficients of the linear model. Assuming response functions which are 𝒞2 except where the modulus function attains zero, we derive simple formulae for the covariance matrix and a log-likelihood ratio statistic, using generalized calculus. These original formulae enable a generalized analysis of variance and further model comparisons.

scholarly journals Analysis of a Linear Model for Non-Synchronous Vibrations Near Stall

2021 ◽  
Vol 6 (3) ◽  
pp. 26
Author(s):  
Christoph Brandstetter ◽  
Sina Stapelfeldt
Keyword(s):  
Linear Model ◽  
Linear Models ◽  
Structural Vibration ◽  
Experimental Investigations ◽  
Vibration Modes ◽  
Critical Problem ◽  
Safety Critical ◽  
Unstable Vibration ◽  
Aero Engines ◽  
Lock In

Non-synchronous vibrations arising near the stall boundary of compressors are a recurring and potentially safety-critical problem in modern aero-engines. Recent numerical and experimental investigations have shown that these vibrations are caused by the lock-in of circumferentially convected aerodynamic disturbances and structural vibration modes, and that it is possible to predict unstable vibration modes using coupled linear models. This paper aims to further investigate non-synchronous vibrations by casting a reduced model for NSV in the frequency domain and analysing stability for a range of parameters. It is shown how, and why, under certain conditions linear models are able to capture a phenomenon, which has traditionally been associated with aerodynamic non-linearities. The formulation clearly highlights the differences between convective non-synchronous vibrations and flutter and identifies the modifications necessary to make quantitative predictions.

Covariance matrix of the bias-corrected maximum likelihood estimator in generalized linear models

2013 ◽  
Vol 55 (3) ◽  
pp. 643-652
Author(s):  
Gauss M. Cordeiro ◽  
Denise A. Botter ◽  
Alexsandro B. Cavalcanti ◽  
Lúcia P. Barroso
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Covariance Matrix ◽  
Generalized Linear Models ◽  
Linear Models ◽  
Likelihood Estimator

IMPROVING EXTRACTION OF IMPULSE RESPONSE FUNCTIONS USING STATIONARY WAVELET SHRINKAGE IN TERAHERTZ REFLECTION IMAGING

2010 ◽  
Vol 09 (04) ◽  
pp. 387-394 ◽  
Author(s):  
YANG CHEN ◽  
YIWEN SUN ◽  
EMMA PICKWELL-MACPHERSON
Keyword(s):  
Experimental Data ◽  
Impulse Response ◽  
Response Function ◽  
Impulse Response Function ◽  
Terahertz Imaging ◽  
Impulse Response Functions ◽  
Response Functions ◽  
Inverse Filtering ◽  
Wavelet Shrinkage ◽  
Gaussian Filtering

In terahertz imaging, deconvolution is often performed to extract the impulse response function of the sample of interest. The inverse filtering process amplifies the noise and in this paper we investigate how we can suppress the noise without over-smoothing and losing useful information. We propose a robust deconvolution process utilizing stationary wavelet shrinkage theory which shows significant improvement over other popular methods such as double Gaussian filtering. We demonstrate the success of our approach on experimental data of water and isopropanol.

scholarly journals Application of Adjoint-Derived Forecast Sensitivities to the 24–25 January 2000 U.S. East Coast Snowstorm

2005 ◽  
Vol 133 (11) ◽  
pp. 3148-3175 ◽  
Author(s):  
Daryl T. Kleist ◽  
Michael C. Morgan
Keyword(s):  
Response Function ◽  
Initial Conditions ◽  
Forecast Error ◽  
Weather Prediction ◽  
Lower Troposphere ◽  
Vertical Motion ◽  
Initial Condition ◽  
Response Functions ◽  
Eastern United States ◽  
Surface Cyclone

Abstract The 24–25 January 2000 eastern United States snowstorm was noteworthy as operational numerical weather prediction (NWP) guidance was poor for lead times as short as 36 h. Despite improvements in the forecast of the surface cyclone position and intensity at 1200 UTC 25 January 2000 with decreasing lead time, NWP guidance placed the westward extent of the midtropospheric, frontogenetically forced precipitation shield too far to the east. To assess the influence of initial condition uncertainties on the forecast of this event, an adjoint model is used to evaluate forecast sensitivities for 36- and 48-h forecasts valid at 1200 UTC 25 January 2000 using as response functions the energy-weighted forecast error, lower-tropospheric circulation about a box surrounding the surface cyclone, 750-hPa frontogenesis, and vertical motion. The sensitivities with respect to the initial conditions for these response functions are in general very similar: geographically isolated, maximized in the middle and lower troposphere, and possessing an upshear vertical tilt. The sensitivities are maximized in a region of enhanced low-level baroclinicity in the vicinity of the surface cyclone’s precursor upper trough. However, differences in the phase and structure of the gradients for the four response functions are evident, which suggests that perturbations could be constructed to alter one response function but not necessarily the others. Gradients of the forecast error response function with respect to the initial conditions are used in an iterative procedure to construct initial condition perturbations that reduce the forecast error. These initial condition perturbations were small in terms of both spatial scale and magnitude. Those initial condition perturbations that were confined primarily to the midtroposphere grew rapidly into much larger amplitude upper-and-lower tropospheric perturbations. The perturbed forecasts were not only characterized by reduced final time forecast error, but also had a synoptic evolution that more closely followed analyses and observations.

scholarly journals A Cascaded Unsupervised Model for PoS Tagging

2021 ◽  
Vol 20 (1) ◽  
pp. 1-23
Author(s):  
Necva Bölücü ◽  
Burcu Can
Keyword(s):  
Linear Model ◽  
Language Processing ◽  
Bayesian Model ◽  
Linear Models ◽  
Syntactic Category ◽  
Semantic Parsing ◽  
Pos Tagging ◽  
Part Of Speech ◽  
Sentence Level ◽  
Log Linear

Part of speech (PoS) tagging is one of the fundamental syntactic tasks in Natural Language Processing, as it assigns a syntactic category to each word within a given sentence or context (such as noun, verb, adjective, etc.). Those syntactic categories could be used to further analyze the sentence-level syntax (e.g., dependency parsing) and thereby extract the meaning of the sentence (e.g., semantic parsing). Various methods have been proposed for learning PoS tags in an unsupervised setting without using any annotated corpora. One of the widely used methods for the tagging problem is log-linear models. Initialization of the parameters in a log-linear model is very crucial for the inference. Different initialization techniques have been used so far. In this work, we present a log-linear model for PoS tagging that uses another fully unsupervised Bayesian model to initialize the parameters of the model in a cascaded framework. Therefore, we transfer some knowledge between two different unsupervised models to leverage the PoS tagging results, where a log-linear model benefits from a Bayesian model’s expertise. We present results for Turkish as a morphologically rich language and for English as a comparably morphologically poor language in a fully unsupervised framework. The results show that our framework outperforms other unsupervised models proposed for PoS tagging.

scholarly journals Linear power-flow analysis method for AC-DC electric power networks

2021 ◽  
Author(s):  
Mohammadreza Vatani
Keyword(s):  
Power Systems ◽  
Linear Model ◽  
Power Flow ◽  
Linear Models ◽  
Power Converters ◽  
Power Balance ◽  
Balance Equations ◽  
Dc Power ◽  
Phase Angles ◽  
Dc Power Systems

AC-DC power systems have been operating more than sixty years. Nonlinear bus-wise power balance equations provide accurate model of AC-DC power systems. However, optimization tools for planning and operation require linear version, even if approximate, for creating tractable algorithms, considering modern elements such as DERs (distributed energy resources). Hitherto, linear models of only AC power systems are available, which coincidentally are called DC power flow. To address this drawback, linear bus-wise power balance equations are developed for AC-DC power systems and presented. As a first contribution, while AC and DC lines are represented by susceptance and conductance elements, AC-DC power converters are represented by a proposed linear relationship. As a second contribution, a three-step linear AC-DC power flow method is proposed. The first step solves the whole network considering it as a linear AC network, yielding bus phase angles at all busses. The second step computes attributes of the proposed linear model of all AC-DC power converters. The third step solves the linear model of the AC-DC system including converters, yielding bus phase angles at AC busses and voltage magnitudes at DC busses. The benefit of the proposed linear power flow model of AC-DC power system, while an approximation of the nonlinear model, enables representation of bus-wise power balance of AC-DC systems in complex planning and operational optimization formulations and hence holds the promise of phenomenal progress. The proposed linear AC-DC power systems is tested on numerous IEEE test systems and demonstrated to be fast, reliable, and consistent.

scholarly journals Experimental validation of wind energy estimation

2020 ◽  
Vol 24 (6 Part A) ◽  
pp. 3795-3806
Author(s):  
Predrag Zivkovic ◽  
Mladen Tomic ◽  
Vukman Bakic
Keyword(s):  
Wind Speed ◽  
Linear Model ◽  
Linear Models ◽  
Stokes Equations ◽  
Momentum Conservation ◽  
Electricity Production ◽  
Navier Stokes ◽  
Energy Estimation ◽  
Navier Stokes Equations ◽  
Non Linear

Wind power assessment in complex terrain is a very demanding task. Modeling wind conditions with standard linear models does not sufficiently reproduce wind conditions in complex terrains, especially on leeward sides of terrain slopes, primarily due to the vorticity. A more complex non-linear model, based on Reynolds averaged Navier-Stokes equations has been used. Turbulence was modeled by modified two-equations k-? model for neutral atmospheric boundary-layer conditions, written in general curvelinear non-orthogonal co-ordinate system. The full set of mass and momentum conservation equations as well as turbulence model equations are numerically solved, using the as CFD technique. A comparison of the application of linear model and non-linear model is presented. Considerable discrepancies of estimated wind speed have been obtained using linear and non-linear models. Statistics of annual electricity production vary up to 30% of the model site. Even anemometer measurements directly at a wind turbine?s site do not necessarily deliver the results needed for prediction calculations, as extrapolations of wind speed to hub height is tricky. The results of the simulation are compared by means of the turbine type, quality and quantity of the wind data and capacity factor. Finally, the comparison of the estimated results with the measured data at 10, 30, and 50 m is shown.

scholarly journals A linear model for leaf area measurement to screen potential leaf material for herbal drug in Adhatoda vasica L.

2016 ◽  
Vol 8 (1) ◽  
pp. 140-143
Author(s):  
J. V. Thaker ◽  
R. P. Kuvad ◽  
V. S. Thaker
Keyword(s):  
Water Content ◽  
Leaf Area ◽  
Linear Model ◽  
Plant Species ◽  
Linear Models ◽  
Dry Weight ◽  
Nondestructive Method ◽  
Area Measurement ◽  
Adhatoda Vasica ◽  
Linear Correlations

Leaf area is an important parameter in physiology and agronomy studies. Linear models for leaf area measurement are developed for plant species as a nondestructive method. The plant Adhatoda vasica L. (a medicinal plant) was selected and the leaves of this plant were used for development of linear model for leaf area using Leaf Area Meter (LAM) software. Planimetric parameters (length, length2, width and width2) and gravimetric (dry weight and water content) parameters are considered for the development of linear model for this plant species. Single factor ANOVA and linear correlations were worked out using these parameters and leaf area. The plant was showed significant relationship with the parameters studied. The best correlation as represented by regression coefficient (R2) was used and improved R2 is worked out. It is observed that with increase in leaf area, water content is also increased and showed best correlation with the leaf area. Thus water content can be taken as a parameter for developing linear model for leaf area is concluded.

scholarly journals The Application of Log-Linear Model to Selected Poison Patients

2020 ◽  
pp. 1-7
Author(s):  
Fatin N.S.A. ◽  
Norlida M.N. ◽  
Siti Z.M.J.
Keyword(s):  
Linear Model ◽  
Linear Models ◽  
Demographic Data ◽  
Contingency Tables ◽  
Categorical Variables ◽  
State Variables ◽  
Exposure Route ◽  
Higher Dimensional ◽  
Route Of Exposure ◽  
Log Linear

Log-linear model is a technique used to analyze the cross-classification categorical data or the contingency table. It is used to obtain the parsimony models that describe the interaction between the categorical variables in contingency tables. Log-linear models are commonly used in evaluating higher dimensional contingency tables that involves more than two categorical variables. This study focuses on analyzing data of poisoned patients from 2012 to 2014 using log-linear model. There are two model analyzed; model for demographic data of patients and model of poisoning information. For the first model, the variables involved are gender, age, race and state. Variables for the second model are circumstance of exposure, type of exposure, location of exposure, route of exposure and types of poison. Both log-linear models are developed to investigate the association between variables in the model. As a result of this study, the best model for demographic data and poisoning information are the model with three-ways interaction. For the best model of demographic data, there is an association between gender, age and race, race, gender and state as well as age, race and state. Meanwhile, the best model for poisoning information reveals that there is relationship between circumstance of exposure, route of exposure and type of poison, location of exposure, route of exposure and type of poison, circumstance of exposure, type of exposure and route of exposure, circumstance of exposure, location of exposure and route of exposure, circumstance of exposure, type of exposure and type of poison and also type of exposure, location of exposure and type of poison. Keywords: log-linear; demographic; gender; age; race; state; circumstance of exposure; type of exposure; location of exposure; route of exposure; types of poison

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