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# Weighted Ridge Regression

I found that lm. ridge_regression taken from open source projects. However, by having adopted ∈ = 0 we have lost in model sparseness. 0 is the ridge regression estimator, the best estima- tor among the weighted average estimators considered here is the ridge regression estimator. edu Departments of Statistics and Electrical Engineering. 3 \Ridge Regression" with Dependent Parameters In the ordinary least squares (OLS) statistical model, we assume that the output Y is a linear function of the input, plus some Gaussian noise. Required packages: monomvn. This algorithm exploits the special structure of the lasso problem, and provides an efficient way to compute the solutions simulataneously for all values of "s". that the regression coefﬁcients have smooth spatial structure. ridge regression (KRR) to data subsets that are distributively stored on multiple servers to produce individual output functions, and then takes a weighted average of the individual output functions as a nal estimator. Regression analysis will provide you with an equation for a graph so that you can make predictions about your data. 2 y xx=++ +ββ β. We study one-shot methods that construct weighted combinations of ridge regression estimators computed on each machine. By adding a degree of bias to the regression estimates, ridge regression reduces the standard errors. Polynomial Regression Models. KNN has been used in statistical estimation and pattern recognition already in the beginning of 1970’s as a non-parametric technique. The formula for ridge regression is. Hence, the tendency of the lasso to produce either zero or large estimates. Lecture 6: The Method of Maximum Likelihood for Simple Linear Regression 36-401, Fall 2015, Section B 17 September 2015 1 Recapitulation We introduced the method of maximum likelihood for simple linear regression in the notes for two lectures ago. In R, multiple linear regression is only a small step away from simple linear regression. Geographically weighted regression (GWR) is drawing attention as a statistical method to estimate regression models with spatially varying relationships between explanatory variables and a response variable. The key difference between these two is the penalty term. method = 'bridge' Type: Regression. , when y is a 2d-array of. It works by examining the correlations between independent variables to generate the best linear. 1070 Partners Way. ECE5424:#Introduction#to# Machine#Learning Stefan’Lee Virginia’Tech Topics:(– Midterm(Review. 10 Ridge Regression In Ridge Regression we aim for nding estimators for the parameter vector ~with smaller variance than the BLUE, for which we will have to pay with bias. 8 Reduction of Collinearity in the Estimation Data 274 10. edu Departments of Statistics and Electrical Engineering. Ridge regression (RR) is an alternative technique to be employed when such ill-conditioning problems occur (Hoerl, 1962). (nl can also obtain weighted least squares estimates. I am using the library scikit-learn to perform Ridge Regression with weights on individual samples. lstsq() to solve an over-determined system. Bengaluru Area, India. We start with the statistical model, which is the Gaussian-noise simple linear. For motivational purposes, here is what we are working towards: a regression analysis program which receives multiple data-set names from Quandl. One Year RAPM and Weighted Ridge Regression Post by permaximum » Thu Jan 03, 2013 4:05 am EDIT (DSMok1): Split off of Permaximum Ratings and Rankings (Updated Often) , since this is a different topic. 1 Consider the linear model yi = α+β1 xi1 +β2 xi2 +···+βk xik +εi = x. We investigated the detection of gene-environment interactions in a simulation study and in a real data application in which we compare the performance of weighted GRS (with weights from the elastic net regression) to unweighted GRS and to the common single SNPs analysis with Bonferroni correction. Bayesian Ridge Regression. sales, price) rather than trying to classify them into categories (e. This paper gives the formulas for and derivation of ridge regression methods when there are weights associated with each observation. Theory of Ridge Regression Estimation with Applications offers a comprehensive guide to the theory and methods of estimation. Diagnostic Measures in Ridge Regression Model with AR(1) Errors under the Stochastic Linear Restrictions Article 6 , Volume 29, Issue 1 , Winter 2018 , Page 67-78 PDF ( 218. A Contour Plot from a Response Surface Regression Analysis in NCSS. Ridge regression was first used in the context of least square regression in [15] and later on used in the context of logistic regression in [16]. This function estimates penalized spatially varying coefficients using the GWR and ridge regression approaches. A method of weight optimization is introduced when fitting penalized ridge regression models. Ridge regression When Lis MSE, this is called the ridge regression: min 1 2N XN n=1 [y n ˚e(x n)T ]2 + 2N XM j=1 2 j Di erentiating and setting to zero: ridge = (e Te + I M) 1e T y 3. B = lasso(X,y) returns fitted least-squares regression coefficients for linear models of the predictor data X and the response y. It thus learns a linear function in the space induced by the respective kernel and the data. Spatial kernel weights are applied to observations using the estimated kernel bandwidth to estimate local models at each data point. • Ordinary Least Squares Regression-Online version-Normal equations-Probabilistic interpretation • Overfitting and Regularization • Overview of additional topics-L1 Regression-Quantile Regression-Generalized linear models-Kernel Regression and Locally Weighted Regression 45. (nl can also obtain weighted least squares estimates. 6 Biased Estimation of Regression Coefﬁcients 271 10. This will occur whenever one value of the dichotomous independent variable is coded as 0. Nonlinear regression. Abbreviation to define. I understood @SteveDenham mentioned that this functionality would be bundled in with the Lasso method, since the user was directly asking about *ridge* logistic regression. The L 1 norm encourages sparseness, while the. Finally we will provide visualizations of the cost functions with and without regularization to help gain an intuition as to why ridge regression is a solution to poor conditioning and numerical stability. Ridge Regression Multicollinearity In polynomial regression models, higher order terms One or several predictor variables may be dropped from the model in order to remove the multicollinearity. XTREGFEM: Stata module to estimate Fixed-Effects Panel Data: Ridge and Weighted Regression. Suppose further that in the data these attributes are correlated, perhaps because the temperature rose one degree each day data was collected. Linear Regression Introduction. , the required number of columns to be sampled) to the effective dimensionality of the problem. Spatial kernel weights are applied to observations using the estimated kernel bandwidth to estimate local models at each data point. Although the typical aim of ridge regression and L² shrinkage in general is to produce an estimator with a lower MSE, this ability carries over to the predictive MSE as well. Ridge regression is useful when the predictors are correlated. For instance, ridge regression can be interpreted as Bayesian regression under the prior assumption that the sum square weights are bounded; truncated SVD analysis can be interpreted as Bayesian regression under the prior assumption that the weights lie in the same space as the leading principal components of the predictors. Under this context a method to estimate the variance of a random effect in a mixed model can be employed to obtain an estimate of the penalization weight. Kernel regression addresses these issues. PCA is applied. Schaffrin and H. In R, the glmnet package contains all you need to implement ridge regression. In this article, I gave an overview of regularization using ridge and lasso regression. as a bias estimator, as. method = 'bridge' Type: Regression. Ridge Estimation and its Modi cations for Linear Regression with Deterministic or Stochastic Predictors James Younker Thesis submitted to the Faculty of Graduate and. Ridge Regression. Therefore, it is a supervised learning tool that optimizes the linear parameters of an analytical expression in order to fit a data. We will use the infamous mtcars dataset as an illustration, where the task is to predict miles per gallon based on car's other characteristics. Multinomial: We use a symmetric formulation for multi- class logistic: Pr(G = |x)= eβ0 +x T β K k=1 e β0k+xT βk. double geographically weighted ridge regression kriging Shilei Chen Wuhan University, School of Water Resources and hydropower engineering, Depart of hydrology and water resources, China ([email protected] Loess curves are can reveal trends and cycles in data that might be difficult to model with a parametric curve. Although the typical aim of ridge regression and L² shrinkage in general is to produce an estimator with a lower MSE, this ability carries over to the predictive MSE as well. The new robust logistic ridge regression (RLRR) employs robust initial coefficient and robust ridge parameter in iterative updating formula. Essentially, we “penalize” large values of the paramters in the quantity we’re seeking to minimize. This is a review of the Weighted Least Squares Regression Model research with NHL data conducted by Brian Macdonald. - Stepwise regression, Regularization methods (Ridge and Lasso), PCA Lecturer in the certificate of "Big Data and Public Policy" and online instructor for "Introduction to R for the social sciences". So the result of this kernel regression isn't very different from than what the fit would look like from weighted k-NN. Outline • Review regression diagnostics • Remedial measures –Weighted regression –Ridge regression Weighted regression. Also known as Ridge Regression or Tikhonov regularization. Ridge regression addresses the problem by estimating regression coefficients using. Real Statistics Data Analysis Tool: To use the Ridge Regression data analysis tool for Example 1 press Ctrl-m and double click on the Regression option in the dialog box that appears (or click on the Reg tab when using the. The user @GrantD71 seems to have implemented a GWD in python through hard-coding using Numpy/Scipy. Machine learning algorithms such as Ridge, Bayesian Ridge, and KNN were deployed. WRR is defined as weighted ridge regression rarely. , the required number of columns to be sampled) to the effective dimensionality of the problem. png) ### Introduction to Machine learning with scikit-learn # Linear Models for Regression Andreas C. One challenge in the application of ridge regression is the choice of the ridge parameter that controls the amount of shrinkage of the regression coefficients. I understood @SteveDenham mentioned that this functionality would be bundled in with the Lasso method, since the user was directly asking about *ridge* logistic regression. For non-linear kernels, this corresponds to a non-linear function in. In: Slatet EA, Tate JO (eds) Science and archaeology Glasgow, vol. least square, ridge regression and equal weighting, to predict the criterion variables in future samples. Suppose a linear regression model for average daily humidity contains attributes for the day-of-month and the temperature. This time, we'll use it to estimate the parameters of a regression line. regression in a distributed computing environment? Ridge regression is an extremely popular method for supervised learning, and has several optimality properties, thus it is important to study. GitHub Gist: instantly share code, notes, and snippets. There are several weighting functions that can be used for IRLS. RidgeCoeff(Rx, Ry, lambda) - returns an array with unstandardized Ridge regression coefficients and their standard errors for the Ridge regression model based on the x values in Rx, y values in Ry and designated lambda value. Müller ??? So today we'll talk about linear models for regression. Radiation outcomes prediction (ROP) plays an important role in personalized prescription and adaptive radiotherapy. regression," and calls (6) a method of moments estimator, although it differs from the method of moments estimator we will introduce in the next subsection. Multicollinearity Ridge regression 3. Ridge regression belongs a class of regression tools that use L2 regularization. The ridge regression utilizes the L2 penalty and is best used when there are high correlations between predictors. polypls - PLS regression with polynomial inner-relation. Then differentiate L=B'HB+"((BÐb)'X'X(BÐb)Ð! o) and set the result. offset terms are allowed. Questions (1) and (2) by Perloff (1951) were not dealt with in the present research even though they are important and interesting in themselves. Minitab's Nonlinear Regression Tool. Leading development of all machine learning models for the Bidding team. ", keywords = "Eigenanalysis, Multiple regression, Principal component analysis, Ridge regression", author = "Hawkins, {Douglas M. As a rule of thumb, weighted regression uses the normal equations XWX on the left and XWY on the right. Ridge regression adds “ squared magnitude ” of coefficient as penalty term to the loss function. The key difference between these two is the penalty term. double geographically weighted ridge regression kriging Shilei Chen Wuhan University, School of Water Resources and hydropower engineering, Depart of hydrology and water resources, China ([email protected] Multicollinearity is the term used to describe multivariate regression with correlated predictors. method = 'bridge' Type: Regression. , sets of equations in which there are more equations than unknowns. A data model explicitly describes a relationship between predictor and response variables. Hence we minimize a quantity which is the sum of the squared residuals, plus a term usually proportional to the sum (or often a weighted sum) of the squared parameters. Regression analysis is used in many other ﬁelds of application both in the natural, the technical and the social sciences. Chapter 12. We will use the infamous mtcars dataset as an illustration, where the task is to predict miles per gallon based on car's other characteristics. OLS regression with multiple explanatory variables The OLS regression model can be extended to include multiple explanatory variables by simply adding additional variables to the equation. 0 is the ridge regression estimator, the best estima- tor among the weighted average estimators considered here is the ridge regression estimator. It works by examining the correlations between independent variables to generate the best linear. How to do linear regression 1. As we have seen we need to evaluate this expression in classic logistic regression. For non-linear kernels, this corresponds to a non-linear function in. However, by having adopted ∈ = 0 we have lost in model sparseness. Predictive Analytics Methods & Tools All the current and future topics of LearnByMarketing are listed here. on the weighted stochastic restricted ridge regression and shrinkage estimators Article in Far East Journal of Mathematical Sciences 108(1):27-60 · December 2018 with 41 Reads How we measure 'reads'. Suppose we have asamplesetofpairs(xi,yi),i=1,···,N,wherexi∈Rd is the i-th feature vector and yi ∈{+1,−1} is the cor-responding label. RidgeCoeff(Rx, Ry, lambda) – returns an array with unstandardized Ridge regression coefficients and their standard errors for the Ridge regression model based on the x values in Rx, y values in Ry and designated lambda value. Kernel methods, kernel SVM and ridge regression Machine Learning II: Advanced Topics CSE 8803ML, Spring 2012 Le Song. Linear regression also tends to work well on high-dimensional, sparse data sets lacking complexity. (like ridge regression) we get ^lasso = the linear regression estimate when = 0, and ^lasso = 0 when = 1 For in between these two extremes, we are balancing two ideas: tting a linear model of yon X, and shrinking the coe cients. Key Words: geographically weighted regression, penalized regression, lasso, model selection, collinearity, ridge regression 1 Introduction In the field of spatial analysis, the interest of some researchers in modeling relationships between variables locally has lead to the development of regression models. The example data can be obtained here(the predictors) and here (the outcomes). Hence we minimize a quantity which is the sum of the squared residuals, plus a term usually proportional to the sum (or often a weighted sum) of the squared parameters. Cost function for Ridge Regression. 5) Weighted Least. quantile regression lines also reveals that the conditional distribution of food expenditure is skewed to the left: the narrower spacing of the upper quantiles indicating high density and a short upper tail and the wider spacing of the lower quantiles indicating a lower density and longer lower tail. I found that lm. Ridge regression Forward stepwise regression Generalized additive models Lasso and elastic net generalized linear models Local regression Non-Negative Least Squares (NNLS) Recursive partitioning and regression trees Regressive partitioning and regression trees with pruning Gradient boosting method Bagging classification trees Logistic regression. that the regression coefﬁcients have smooth spatial structure. Linear regression with Numpy Few post ago , we have seen how to use the function numpy. Ridge regression is an example of a shrinkage method : compared to least squares, it shrinks the parameter estimates in the hopes of reducing variance, improving prediction accuracy, and aiding interpetation. LINEAR METHODS FOR REGRESSION 4. class: center, middle ![:scale 40%](images/sklearn_logo. Lasso can also be used for variable selection. , SPSS, R, Minitab, SAS). fit(X, y, sample_weight=some_array). polypls - PLS regression with polynomial inner-relation. We now show how to use the Ridge Regression Regression data analysis tool to calculate the regression coefficients and other important statistics for Ridge regression. Box kernel. Lasso regression uses a slightly different regularisation term called an L1 penalty, instead of ridge regression's L2 penalty as shown here. • Linear and ridge regression (QR, SVD, LMS) 3 This time • Logistic regression • MLE • Perceptron algorithm • IRLS • Multinomial logistic regression. It can be used to balance out the pros and cons of ridge and lasso regression. 1 Ridge Regression Possibly the most elementary algorithm that can be kernelized is ridge regression. ,4mm Light Sapphire (211) blue Swarovski crystal 5328 XILION Loose Bicone Beads. In fact, we can use generalized linear models to model count data as well. Not all topics are available, and many won’t be for months to come. 20, August 23, 2018. One Year RAPM and Weighted Ridge Regression Post by permaximum » Thu Jan 03, 2013 4:05 am EDIT (DSMok1): Split off of Permaximum Ratings and Rankings (Updated Often) , since this is a different topic. Kernel Regression 26 Feb 2014. There is also a paper on caret in the Journal of Statistical Software. Loess regression is a nonparametric technique that uses local weighted regression to fit a smooth curve through points in a scatter plot. This can be done by: esimator. Now, lets understand ridge and lasso regression in detail and see how well they work for the same problem. Specifically, ridge regression modifies X'X such that its determinant does not equal 0; this ensures that (X'X)-1 is calculable. A polynomial term–a quadratic (squared) or cubic (cubed) term turns a linear regression model into a curve. BaalChIP: Bayesian analysis of allele-specific transcription factor binding in cancer genomes. 20, August 23, 2018. We start with the statistical model, which is the Gaussian-noise simple linear. where ω ^ j (j = 1,, p) are the adaptive data-driven weights, which can be estimated by ω ^ j = β ^ j i n i-γ, where γ is a positive constant and β ^ i n i is an initial consistent estimator of β obtained through least squares or ridge regression if multicolinearity is important []. Ridge Regression Lambda. If a weighted least squares regression actually increases the influence of an outlier, the results of the analysis may be far inferior to an unweighted least squares analysis. When multicollinearity occurs, least squares estimates are unbiased, but their variances are large so they may be far from the true value. I found that lm. In general a big advantage to ridge regression is that the solution always exists, as mentioned above. Y1 - 2010/12/1. It can run so much more than logistic regression models. Constructor for the RidgeWightedReg Object which uses *weighted* ridge regression to correlate click and mouse movement to eye patch features The weighting essentially provides a scheduled falloff in influence for mouse movements. Uses weighted soft thresholding. 11 Ridge Regression 279 10. Hello Readers, Here we will continue our R regression series and after working with ordinary, and robust regression, we will address partial least squares regression. 2 Ridge Regression. Since most of the ICD-9 codes are unevenly represented in the medical records, a weighted scheme is employed to balance positive and negative examples. The user @GrantD71 seems to have implemented a GWD in python through hard-coding using Numpy/Scipy. The emphasis continues to be on exploratory data analysis. ME] 23 Aug 2018 Lecture notes on ridge regression Version 0. Flow charts aid in the selection of the appropriate statistical method. Least Squares Adjustment: Linear and Nonlinear Weighted Regression Analysis Allan Aasbjerg Nielsen Technical University of Denmark Applied Mathematics and Computer Science/National Space Institute. The following is a basic list of model types or relevant characteristics. Modifying the matrix in this way effectively eliminates collinearity, leading to more precise, and. Multiple regression estimates the β's in the equation y =β 0 +β 1 x 1j +βx 2j + +β p x pj +ε j The X's are the independent variables (IV's). It also deals with collinearity among explanatory variables. In this respect, the robust ridge estimator, called weighted ridge estimator WR βˆ, can be computed using the following formula : (X'WX KI)-1 X'WY WR. We start with the statistical model, which is the Gaussian-noise simple linear. polypls - PLS regression with polynomial inner-relation. Suppose we have asamplesetofpairs(xi,yi),i=1,···,N,wherexi∈Rd is the i-th feature vector and yi ∈{+1,−1} is the cor-responding label. 2 Ridge Regression Solution to the ℓ2 problem Data Augmentation Approach Bayesian Interpretation The SVD and Ridge Regression 3 Cross Validation K-Fold Cross Validation Generalized CV 4 The LASSO 5 Model Selection, Oracles, and the Dantzig Selector 6 References Statistics 305: Autumn Quarter 2006/2007 Regularization: Ridge Regression and the. A friendly introduction to linear regression (using Python) A few weeks ago, I taught a 3-hour lesson introducing linear regression to my data science class. Hi guys, I am running Ridge regression on a dataset (predicted variable = y; GDP, HPA and FX are regressors). sales, price) rather than trying to classify them into categories (e. edu Abstract. 0, the risk increases monotonically as the value of w increases. Linear regression with Numpy Few post ago , we have seen how to use the function numpy. Multinomial: We use a symmetric formulation for multi- class logistic: Pr(G = |x)= eβ0 +x T β K k=1 e β0k+xT βk. ,4mm Light Sapphire (211) blue Swarovski crystal 5328 XILION Loose Bicone Beads. The weighted ridge regression algorithm is used to compute the algorithm solution. One Year RAPM and Weighted Ridge Regression Post by permaximum » Thu Jan 03, 2013 4:05 am EDIT (DSMok1): Split off of Permaximum Ratings and Rankings (Updated Often) , since this is a different topic. Ridge Regression : In ridge regression, the cost function is altered by adding a penalty equivalent to square of the magnitude of the coefficients. In this paper, we apply weighted ridge regression to tackle the highly unbalanced data issue in automatic largescale ICD-9 coding of medical patient records. This is a review of the Weighted Least Squares Regression Model research with NHL data conducted by Brian Macdonald. We introduce the weighted mixed almost unbiased ridge estimator (WMAURE) based on the weighted mixed estimator (WME) (Trenkler and Toutenburg 1990) and the almost unbiased ridge estimator (AURE) (Akdeniz and Erol 2003) in linear regression model. Issue: can yield μ < 0! Natural log link: $$log(\mu)=\beta_0+\beta_1 x_1$$ The Poisson regression model for counts is sometimes referred to as a “Poisson loglinear model”. Estimation and inference of parameters for a regression line. But the nature of the ‘ 1 penalty causes some coe cients to be shrunken tozero exactly. Linear regression also tends to work well on high-dimensional, sparse data sets lacking complexity. Redesigned end-of-chapter summaries are easier to use when reviewing and studying. As told in the previous post that a polynomial regression is a special case of linear regression. Linear regression models in notebooks. So far, the. The analyst. Multiple linear regression analysis is an extension of simple linear regression analysis, used to assess the association between two or more independent variables and a single continuous dependent variable. Building on this idea, we turn to kernel regression. A WEIGHT statement names a variable in the input data set with values that are relative weights for a weighted least squares fit. It is a natural generalization of the ordinary ridge regression estimate (Hoerl and Kennard, 1970) to the non-parametric setting. Ridge Regression. Toutenburg, Weighted mixed regression, Zeitschrift fur Angewandte Mathematik und Mechanik 70 (1990), pp. Along with Ridge and Lasso, Elastic Net is another useful techniques which combines both L1 and L2 regularization. on the weighted stochastic restricted ridge regression and shrinkage estimators Article in Far East Journal of Mathematical Sciences 108(1):27-60 · December 2018 with 41 Reads How we measure 'reads'. 1, in the text). How can we do weighted ridge regression in R? In MASS package in R, I can do weighted linear regression by passing a weight parameter to lm. WRR stands for weighted ridge regression. 2 Ridge Regression Solution to the ℓ2 problem Data Augmentation Approach Bayesian Interpretation The SVD and Ridge Regression 3 Cross Validation K-Fold Cross Validation Generalized CV 4 The LASSO 5 Model Selection, Oracles, and the Dantzig Selector 6 References Statistics 305: Autumn Quarter 2006/2007 Regularization: Ridge Regression and the. Kernel regression addresses these issues. Thus, ridge regression optimizes the following:. A second extension, called generalized ridge regression or gridge regression, adds a feature-specific modifier κ i to the regularization: (17) κ i ≥ 0 adjusts the regularization penalty individually for each feature (ridge regression is a special case where κ i = 1 ∀ i). Linear regression models in notebooks. Regression analysis will provide you with an equation for a graph so that you can make predictions about your data. • Ridge regression is an example of shrinkage estimation: The process will typically "shrink" the least-squares estimates toward zero because of the biasing constant. Arashi2, B. This study aimed to look at the performance of several well-known robust estimators; M, MM, RIDGE and robust ridge regression estimators, namely Weighted Ridge M-estimator (WRM), Weighted Ridge MM (WRMM), Ridge MM (RMM), in such a situation. Prediction of mean response and new observation. In reality, a regression is a seemingly ubiquitous statistical tool appearing in legions of scientific papers, and regression analysis is a method of measuring the link between two or more phenomena. Locally Weighted Regression Instructors: Sham Kakade and Greg Shakhnarovich 1 NN in a subspace A common pre-processing step is to project the data into a lower-dimensional subspace, before applying k-NN estimator. Spatial kernel weights are applied to observations using the estimated or supplied kernel bandwidth to estimate local models at each data point. Checking Assumptions for the Regression Model. regression model is Y = 0 + 1x 1 + :::+ px p= TX where = ( 0;:::; p) T and X= (1;x 1;:::;x p)T. R, closely related to the commercial package S-Plus, is the largest and most comprehensive public domain statistical computing environment. Ridge regression Lasso Comparison Limitations of ridge regression A di erent way of dealing with this problem is to use penalized regression However, the ridge regression penalty (P 2 j), although it helps with obtaining less variable estimates, has two big shortcomings in this setting: Heavy bias toward zero for large regression coe cients. This time, we'll use it to estimate the parameters of a regression line. If generalized either Weighted Linear Regression (WLR) or nonlinear ridge regression is used, the method is referred to as regression can be easily and reliably used to estimate model generalized ridge regression with spatial constraint (GRRSC). For simple linear regression, one can choose degree 1. Lasso regression uses a slightly different regularisation term called an L1 penalty, instead of ridge regression's L2 penalty as shown here. ridgecv - Ridge regression by cross validation. Hence, the objective function that needs to be minimized can be. and Hilbe, Joseph}, TITLE = {Generalized Linear Models and Extensions}, YEAR = {2001}, PAGES = {245. 10 Principal Components Regression: A Caution 277 10. BaalChIP: Bayesian analysis of allele-specific transcription factor binding in cancer genomes. Recall, the ridge regression estimator can be viewed as a Bayesian estimate of when imposing a Gaussian prior. WRR stands for weighted ridge regression. Regression analysis is ubiquitous in educational research. Statistical Software Components from Boston College Department of Economics. exp(r) corresponds to Euler’s number e elevated to the power of r. One approach to this problem in regression is the technique of ridge regression, which is available in the sklearn Python module. First, we propose a kernelized ridge regression model wherein the kernel value is defined as the weighted sum of similarity scores of all pairs of patches between two samples. Tuning parameters: lambda (Regularization Parameter) qval (q) degree (Polynomial Degree) scale (Scale) Required packages: kerndwd. Bayesian Regression & Classiﬁcation Bayesian Kernel Ridge Regression = Gaussian Process GPs have become a standard regression method on a re-weighted data. Robust Locally Weighted Regression (LOWESS) ROC Curve. The smoothness constraint is imposed using a novel approach based on the eigenvectors of the Laplace operator over the domain, which results in a con-strained optimization problem equivalent to either ridge regression or least absolute shrinkage and selection. LINEAR METHODS FOR REGRESSION 4. Ridge regression allows you to analyze data even when severe multicollinearity is present and helps prevent overfitting. Note that confidence intervals cannot currently be drawn for this kind of model. This is why there can be an infinitude of solutions to the ordinary least squares problem when. Kernel ridge regression (KRR) [M2012] combines Ridge Regression (linear least squares with l2-norm regularization) with the kernel trick. Along with Ridge and Lasso, Elastic Net is another useful techniques which combines both L1 and L2 regularization. In R, the glmnet package contains all you need to implement ridge regression. solveRidgeRegression: Solve ridge regression or logistic regression problems in zinbwave: Zero-Inflated Negative Binomial Model for RNA-Seq Data. How can we do weighted ridge regression in R? In MASS package in R, I can do weighted linear regression by passing a weight parameter to lm. In fact, the same lm() function can be used for this technique, but with the addition of a one or more predictors. Like ridge regression, lasso regression adds a regularisation penalty term to the ordinary least-squares objective, that causes the model W-coefficients to shrink towards zero. Tutorial Files. 2: Ridge regression Before considering ridge regression, recall that even serious multicollinearitydoes not present a problem when the focus is on prediction, and prediction is limited to the overall pattern of predictors in the data. This study aimed to look at the performance of several well-known robust estimators; M, MM, RIDGE and robust ridge regression estimators, namely Weighted Ridge M-estimator (WRM), Weighted Ridge MM (WRMM), Ridge MM (RMM), in such a situation. 3 DiscretetoConnuousLabels' Sports% Science% News% Classification Regression% Anemiccell% Healthy%cell% Stock%Market% Predicon% Y'=?' X'=Feb01''. Leading development of all machine learning models for the Bidding team. OLS estimation. On Ridge Regression and Least Absolute Shrinkage and Selection Operator by Hassan AlNasser B. and Hilbe, Joseph}, TITLE = {Generalized Linear Models and Extensions}, YEAR = {2001}, PAGES = {245. If you want to fit a model of higher degree, you can construct polynomial features out of the linear feature data and fit to the model too. A Bayesian motivation is used and various choices of k. An advantage of the (kernel) ridge regression, compared to the robust statistics regression, is that a neat closed form solution results. GitHub Gist: instantly share code, notes, and snippets. When multicollinearity occurs, least squares estimates are unbiased. Worldwide, it is estimated to cause about 25% of lung cancer deaths, 8% of chronic obstructive pulmonary disease (COPD) deaths, and about 15% of ischaemic heart disease and stroke (World Health Organisation, 2017b). In this paper I describe a diagnostic method for assessing the local influence on the constant variance perturbation on the transformation in the Box-Cox biased ridge regression linear model. Lasso can also be used for variable selection. Contrary to lm. Note also that the slope of the regression line is the difference between the two means (16. Machine learning algorithms such as Ridge, Bayesian Ridge, and KNN were deployed. I am using the library scikit-learn to perform Ridge Regression with weights on individual samples. Required packages: monomvn. The WHO estimates that of all the air pollutants, fine airborne particulates (PM 2. We learned a lot by from running Excel regression and Studio experiments in parallel. Uses weighted soft thresholding. Y1 - 2010/12/1. exp(r) corresponds to Euler’s number e elevated to the power of r. Ridge regression (or Tikhonov regularization) When , i. Penalized regression methods, such as the ridge (Hoerl and Kennard, 1970), lasso (Tibshirani, 1996), elastic net (Zou and Hastie, 2005), and bridge (Frank and Friedman, 1993), have been proposed to solve the problem. How to derive tests 4. It is based on locally ﬁtting a line rather than a constant. Consider a technique called ridge regression, which is an alternative to OLS (ordinary least squares) methods of estimating regression coefficients that is intended to reduce the problems in regression analysis associated with multicollinearity. Root Mean Square (RMS. For each of these patients, the individual regression models were built and compared based on the two factors that evaluate the model prediction ability. Both data and model are known, but we'd like to find the model parameters that make the model fit best or good enough to the data according to some metric. Locally Weighted Regression Instructors: Sham Kakade and Greg Shakhnarovich 1 NN in a subspace A common pre-processing step is to project the data into a lower-dimensional subspace, before applying k-NN estimator. Outline • Review regression diagnostics • Remedial measures –Weighted regression –Ridge regression Weighted regression. Optimization of ridge parameters in multivariate generalized ridge regression by plug-in methods Nagai, Isamu, Yanagihara, Hirokazu, and Satoh, Kenichi, Hiroshima Mathematical Journal, 2012 Multivariate regression through affinely weighted penalized least squares Beran, Rudolf, From Probability to Statistics and Back: High-Dimensional Models and Processes -- A Festschrift in Honor of Jon A. VivaScan calibration data for seven patients were analyzed in this project. 9 Constraints on the Regression Coefﬁcients 276 10. The regression models include various for data with Gaussian, logistic and Poisson structures, as well as ridge regression for dealing with correlated predictors. In this paper, we focus on ridge regression, a penalised regression approach that has been shown to offer good performance in multivariate prediction problems. Abbreviation to define. - Ridge regression • Proc GLMSelect - LASSO - Elastic Net • Proc HPreg - High Performance for linear regression with variable selection (lots of options, including LAR, LASSO, adaptive LASSO) - Hybrid versions: Use LAR and LASSO to select the model, but then estimate the regression coefficients by ordinary weighted least squares. Thus you can get equivalent results by multiplying each observation by the square-root of the weight and using ordinary regression (in Excel, for example). Ayinde and Lukman (2014) proposed some generalized linear estimator (CORC. Spatial kernel weights are applied to observations using the estimated kernel bandwidth to estimate local models at each data point. A penalty term added to a likelihood may be viewed in the light of a hierarchical likelihood. Kernel Regression • Kernel regressions are weighted average estimators that use kernel functions as weights. One such model that has been widely applied is geographically weighted regression (GWR). Right Censoring. Statistical Software Components from Boston College Department of Economics. 2 Broughton Drive Campus Box 7111 Raleigh, NC 27695-7111 (919) 515-3364. It's not the fanciest machine learning technique, but it is a crucial technique to learn for many reasons:. Checking Assumptions for the Regression Model.


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# What is the 'sense' of a vector?

In my country we are taught of vectors as if they have three components, module (the length), direction (slope of the line that contains the vector), and 'sense' (sentido), which indicates the "way" or "sense" that the vector "goes". The vector $\vec{u}(5,6)$ has the same sense as $\vec{v}(10,12)$, and the opposite of $\vec{w}(-5,-6)$. My question is: What is really the thing that we're talking about? Is it a number? What are the values that 'sense' can be? Is it either 'the same', 'opposite', or 'different'? What is the sense of $\vec{z}(5,4)$ compared to the first vector? Does it only exist while we're comparing vectors?

• I would usually consider “sense” as part of the direction of a vector: e.g., $(5,6)$ and $(-5,-6)$ point in different directions. Sense the way you’re using it only really makes sense when comparing parallel vectors. (What is the sense of $(-5,6)$ compared to $(6,5)$, say?) – amd Apr 5 '18 at 23:21
• @amd That's what I'm asking about, from the exercises and the (short) material that I've seen, they would be just "different". – Nick Cassol Apr 5 '18 at 23:33
• The answer could just as well be “undefined.” Alternatively, you could look at the projection of the second vector onto the first and use that to determine if the have the “same” sense, i.e., if they loosely point in the same direction relative to a boundary that’s perpendicular to the first vector. – amd Apr 5 '18 at 23:37
• The answer could just as well be “undefined.” Alternatively, you could look at the projection of the second vector onto the first and use that to determine if the have the “same” sense, i.e., if they loosely point in the same direction relative to a boundary that’s perpendicular to the first vector. – amd Apr 5 '18 at 23:37

Sense is a set of all half lines who have the same orientation and by pairs belong to the same part of the half plane they define.

What is really the thing that we're talking about?

It is a set of half lines. A vector has sense A if the half line taken by extending the line segment from the end belongs to A.

Is it a number?

No.

What are the values that 'sense' can be?

This makes no sense (haha) if we define it as a set.

Is it either 'the same', 'opposite', or 'different'?

You need to rephrase those in terms of set relations and/or new relations you define.

What is the sense of 𝑧⃗ (5,4) compared to the first vector?

A disjoint set and whatever else you want to define.

Does it only exist while we're comparing vectors?

No.

PS: I found this topic really interesting since I was taught the same thing and had a similar question.

The best mathematical translation of the Spanish sentido is direction rather than sense.

It makes sense to say that two collinear vectors have the same or have opposite directions, but, absent some additional external reference, it does not make sense to speak of the direction of a vector or to say that two noncollinear vectors have or have not the same direction.

Given a vector, $$(x, y)$$, one can regard the unit vector $$\tfrac{(x, y)}{\sqrt{x^{2} + y^{2}}}$$ having the same direction as $$(x, y)$$ as its direction vector (or its sense).

format: plain


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# Homework Help: Contraction Mapping Theorem Question

1. May 3, 2010

### nugget

1. The problem statement, all variables and given/known data

Consider the function g : [0,∞) → R defined by g(x) = x + e−2x.

Given |g(x2) − g(x1)| < |x2 − x1| for all x1, x2 ∈ [0,∞) with x1 ≠ x2.

Is g a contraction on [0,∞)? Why?

2. Relevant equations

I think we are intended to use the given equation and the CMT

CMT states that |f(x)-f(y)|=c|x-y|, where x,y∈R.

Which is similar to |g(x2) − g(x1)|<|x2 − x1|

3. The attempt at a solution

I really don't know where to begin with this; I'm not simply after the answer though, just a prod in the right direction would be great

2. May 3, 2010

### Tedjn

On my computer, the formula for g(x) displays an unreadable symbol before the e-2x. Also, I confess that I have only seen CMT from browsing my friend's analysis book, and it doesn't exactly say
.
Are they equivalent?

EDIT: The actual statement I read is at http://en.wikipedia.org/wiki/Banach_fixed_point_theorem

Last edited: May 3, 2010
3. May 3, 2010

### gauss^2

g is a contraction precisely when there is some positive real number c < 1 with

$$|g(y) - g(x)| < c |y-x|$$

for all x,y in the domain.

You have to either find a positive c < 1 that satisfies the inequality above for all $$x,y \in [0,\infty)$$ or show no positive c < 1 exists which satisfies the inequality. Note that

$$|g(y) - g(x)| < |y-x|$$

does not show g is a contraction. The constant 0 < c < 1 really is needed (check the proof of the contraction mapping theorem to see why if you're interested; it's a really cool piece of mathematics).

Last edited: May 3, 2010
4. May 3, 2010

### HallsofIvy

No, it doesn't. That is simply the definition of "contraction map". The CMT states that if f is a contraction map that take set S into itself, then it has exactly one fixed point in S.


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# INFRARED SPECTRUM OF THE INTERACTION OF EXCITED NEON ATOMS WITH NO AND ITS MULTIMERS TRAPPED IN SOLID NEON

Please use this identifier to cite or link to this item: http://hdl.handle.net/1811/19118

Files Size Format View
1998-TJ-06.jpg 95.21Kb JPEG image

 Title: INFRARED SPECTRUM OF THE INTERACTION OF EXCITED NEON ATOMS WITH NO AND ITS MULTIMERS TRAPPED IN SOLID NEON Creators: Lugez, Catherine L.; Thompson, Warren E.; Jacox, Marilyn E. Issue Date: 1998 Publisher: Ohio State University Abstract: When a Ne:NO sample is codeposited at approximately 5 K with a beam of excited neon atoms, the infrared spectrum of the resulting deposit includes absorptions which can be assigned to several ionic products. The close correspondence of transitions observed in the gas-phase photoelectron spectrum of $(NO)_{2}^{a}$ with infrared absorptions previously assigned to trans-ONNO anion requires the reassignment of these absorptions to the cation. Results of detailed studies of the isotopic substitution pattern and photodestruction behavior of other absorptions which may be contributed by $(NO)_{2}$ anions will be presented. The possible presence of ionic species of composition $(NO)_{3}$ will also be considered. Description: $^{a}$ A. Strobel, N. Knoblauch, J. Agreiter, A.M. Smith, G. Niedner-Schatt***urg, and V.E. Bondybey, J. Phys. Chem. 99, 872 (1995). Author Institution: National Institute of Standards and Technology URI: http://hdl.handle.net/1811/19118 Other Identifiers: 1998-TJ-06


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Tag Info

Hot answers tagged signal-identification

3

If you approximate the yellow trace as a rectangular function: $$\text{rect}(ax)$$ then the Fourier transform of this is: $${1 \over |a|} \cdot \text{sinc}\left(\xi \over a\right )$$ Of course, a lightning impulse isn't exactly a rectangular pulse, but I suspect that does not substantially change the character of the frequency response: infinite, with ...

3

You have to provide the -i option to invert the signal in order to decode it properly. The lowpass filter is not really required as this is a quite strong signal (but does not harm either). \$ ./rs41ptu -i --crc -vx wav/20140717_402MHz.wav sample_rate: 48000 bits : 8 channels : 1 samples/bit: 10.00 [ 5047] (K1930308) Do 2014-07-17 12:32:13.999 lat: ...

3

There's multiple way that multiple signals can be sent at the same time on the same frequency. One is to have multiple antennas, where even though the antennas themselves can be omnidirectional, they can be used to "beam form" by carefully offsetting the signal. And likewise the receiver can do this trick. Also see this article on MIMO. Wifi can ...

3

Transmission between antennas is "two port in to two port out". But: in between there is a transmission path with reflections. Some frequencies are attenuated and some other frequencies are even stronger than average. That is called Rayleigh path (sorry, not complete for the moment). The transfer is frequency-dependent AND antenna position ...

3

From the wide spectrum screenshot it's evident your receiver is seriously overloaded. Note: the signal around 445.982 which appears to be identical other than being "flipped", and a little stronger. This comes from IQ imbalance in the receiver. additional copies of the signal all over the place. These are caused by intermodulation and harmonic ...

2

A Wi-Fi transmitter, like a lightbulb, throws out photons in a lot of directions. Only some of them will be captured by the receiver. Most will go elsewhere, eventually being absorbed by walls, atmospheric water vapor, and so on to be converted to heat. The Friis transmission equation explains this in more rigorous terms. Even if the two antennas are ...

1

Yes, multiple signals can exist on the same frequency at once. In a net, this could happen if two people tried to talk at the same time. This is called a "double". When this happens, the signals mix, or add together. If the two signals are AM, the amplitudes of the radio waves add, which corresponds to the amplitudes of the audio, so you get ...

1

First, the router power will be +20 or +22 dBm. Subtract a few dB on the way to the antenna, more if it's an internal antenna. Second, the free space path loss will be at least 20 dB, from phone to router, a few cm apart. This means that even held close by, the phone antenna only captures 1% of the transmitted signal. This will be made worse by the ...

Only top voted, non community-wiki answers of a minimum length are eligible


text:
시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 128 MB 0 0 0 0.000%

## 문제

For one of their clients, ACM prepares a TV advertisement that features ancient heroes, for example Prometheus, Achilles, Odysseus and many others. To demonstrate how difficult was life for these heroes, ACM runs computer simulations of their most famous tasks. In this problem, we will try to solve the problem of Theseus.

Theseus was an Athenian hero who killed Minotaur, the half-man, half-bull monster residing in an inescapable Labyrinth constructed by Daedalus. The hardest part of Theseus’ task was not killing the monster — the legend says Minotaur was just sleeping when Theseus came to him. Thus, the hero was able to batter the monster with his bare hands. But then the real challenge came: to find the way out. As you may know, Ariadne, beautiful daughter of king Minos, played an important role in this part. But that’s a different story.

As the technology advanced a lot since the ancient times, there are several important differences in today’s simulations:

1. Labyrinth-making skills advanced as well. Two-dimensional labyrinths are not a big challenge anymore. Thus, our labyrinth is d-dimensional. It looks like a regular ”grid” of n1×n2×...×nd (hyper)cubes, each of them being either empty (corridor) or filled with a rock (wall). Theseus moves in steps, each step means travelling between two neighboring empty hypercubes in any dimension. Two hypercubes are considered neighboring, if and only if the difference in their space coordinates is exactly one in one dimension, and zero in all other dimensions.

2. Our Minotaur is stronger, thus, it is no more possible to batter him with bare hands. Theseus must use a sword which lies somewhere inside the labyrinth. Note that before he takes the sword, he cannot go through the hypercube where Minotaur resides!

## 입력

The input consists of several labyrinth descriptions. Each description begins with a line containing a single integer number d (2 ≤ d ≤ 20) — the number of dimensions. On the second line of each description, there are d integer numbers n1, n2, ..., nd separated by spaces. These numbers give the size of the labyrinth in every dimension, measured in unit hypercubes (∀i : 2 ≤ ni). You may assume that the total number of hypercubes in any labyrinth will not exceed 220 = 1048576.

Then a labyrinth map follows, the description is defined recursively: Two-dimensional labyrinth (of the size n1 × n2) is described by n2 lines containing n1 characters each. Every character describes a single hypercube (”square” in the case of 2 dimensions) and is either “#” (rock), “.” (free space), or one of uppercase letters “T” (Theseus’ position), “M” (Minotaur), and ’S’ (sword). Each of these three objects will appear exactly once in the whole labyrinth. The hypercubes containing the letters are considered ”empty” otherwise, i.e., Theseus can walk (and must walk) through them.

For better clarity of the input, each two-dimensional map is followed by one empty line.

For d > 2, any d-dimensional labyrinth is a sequence of nd ”layers”, each layer being a description of a (d − 1)-dimensional labyrinth.

The last labyrinth description is followed by a line containing zero. This line terminates the input and no output should be produced for it.

## 출력

For each labyrinth, output the sentence “Theseus needs S steps.”, where S is the smallest possible amount of steps needed to reach the hypercube with the sword, the hypercube with Minotaur, and then back to the original Theseus’ position (where the exit is supposed to be). It is not possible to leave the labyrinth area, i.e., all hypercubes outside the labyrinth are considered rocks. Exit may appear in an inner hypercube, it may not reside on the “border”.

If it is not possible to solve the situation at all, output sentences “No solution. Poor Theseus!”

## 예제 입력

2
3 3
T..
M#.
S..

2
3 2
T#S
..M

3
4 4 3
#S..
###.
#M..
###.

.###
.###
.###
....

....
###.
###T
####

0

## 예제 출력

Theseus needs 8 steps.
No solution. Poor Theseus!
Theseus needs 40 steps.


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# Implicit 'higher' differentiation

1. Jun 29, 2008

### City88

Hi,
I'm working on a cal III problem involving implicit differentiation.
I have to find the second order partial derivative of an implicit function, basically:
$$\partial$$2f
$$\partial$$x2

now, I know that for a single order $$\partial$$f/$$\partial$$x, I would simply use the chain rule property:
$$\partial$$f = -$$\partial$$F/$$\partial$$x
$$\partial$$x ... $$\partial$$F/$$\partial$$f

But now, how would I find
$$\partial$$2f
$$\partial$$x2
for an implicit equation?

Last edited: Jun 29, 2008
2. Jun 29, 2008

### Defennder

What is the implicit function you are given?

3. Jun 30, 2008

### HallsofIvy

Do the same thing again. For example, if the function were z, given by 3xz+ yez= 1, then the partial derivative, with respect to x, would be given by 3z+ 3xzx+ yezzx= 0.

Differentiating that a second time, with respect to x, 3zx+ 3zx+ 3xzxx+ yez(zx)2+ yezzxx= 0.

You can solve that for zxx in terms of x, y, z, and zx.


text:
Silvrback is hands down the best blogging platform for tech bloggers and definitely one of the best blogging platforms overall. Let it be clear that this article is to demonstrate how your Silvrback blog (or really any website for that matter) can utilise a CDN. It is not meant to point out any flaws or infer that Silvrback is inadequate in any way.

If this has (or will) inspire you to get your own domain, I would highly recommend iwantmyname.com. Apart from the fact it lets you search hundreds of new gTLDs it also has a custom page for Silvrback!

This article looks much longer than it actually is because it contains many screenshots and some explanation to try and make it as simple to follow as possible. Let's begin...

When it came time to add my own domain (elliot.land) I wanted the following - in order of highest importance first:

1. HTTP and HTTPS support.
2. With and without www.
3. Faster.
4. Allow the domain to be used for other things in future.

The Existing Solution

I bought my domain through Godaddy and fortunately there is already a setup guide on Silvrback for this exact scenario:

Unfortunately this doesn't tick any of my 4 requirements. Time for a CDN...

What is a CDN?

A Content Delivery Network (CDN) is one or more data centres that can serve out static content very fast. It's fast because the pages do not have to be generated (at least not after the first time, we'll get to this). Furthermore, routing is done on a geographic basis so the assets come from the nearest data centre. Here is a pretty visualisation:

In a nutshell the pages are served from the data centre and rarely have to back to the origin server where the content is generated until such a time that the CDN decides that the content is now to too old and needs to be refreshed. This is called the TTL (Time-to-live) and is specified as the number of seconds the page (or asset, these are interchangeable) can be delivered to clients without getting the latest version from the origin.

What You Will Need

I chose to use the Amazon CDN product called CloudFront because I'm quite familiar with other AWS services; they are rock solid, reliable and cheap. We will also be using Route 53 for DNS to route the domain to CloudFront. Heres what you'll need:

1. An SSL certificate. This is optional if you want your domain to have HTTPS.
2. An AWS account to create and use the services. You are only billed for your usage. I have more information about cost below this.

These would be the steps taken. They shouldn't take more than an hour if this is the first time you've done this, probably less if your savvy with sort of this stuff.

1. Create a CloudFront Distribution.
2. Setup distribution Behaviors. These are the rules dictating how to serve the content.
3. Create a Hosted Zone in Route 53. To setup all the DNS records for you domain.
4. Update the name servers for your domain to point to Route 53.

There will be no effect on your existing domain until the last step when the name servers are changed over. The is a test checklist at the end before you change over the name servers.

Cost

If you chose to use AWS there will be a cost involved. What it really comes down to is:

• US$0.50 per month for Route 53 to pay for one Hosted Zone. • US$0.085 per GB for CloudFront. It's very hard to determine how much traffic you would be doing before hand but unless your doing a lot you should be fine. There is no contract and the stats of usage are almost realtime, turn off at any time.

If everything looks good so far you should take the time to read all the rest of the article before you begin. This is a good way to really understand how the steps will happen to prevent any unnecessary confusion.

1. Create the CloudFront Distribution

Log into the AWS console, navigate to CloudFront and click Create Distribution:

You will be presented two choices, you want to select Get Started under the first choice, Web.

For the Origin Settings we need to fill in:

• Origin Domain Name: This is the custom domain you will be using (without a subdomain).
• Origin ID: Just a identifier for when your have multiple origins. You may change the auto-generated value if you like.
• Origin Protocol Policy: The recommended value here is Match Viewer to allow both. You must use HTTP Only if you do not have an SSL certificate for your domain. We will add the certificate later if you do have one.

• Viewer Protocol Policy: Use whatever you prefer here, but as above you must have an SSL certificate if you want to use HTTPS.

• Price Class: This is up to you. You can read more about price classes here.
• Alternate Domain Names: Here you want to add any subdomains that you will be using, for example the www subdomain. You can change these later but CloudFront will only respond to the domains specified here.
• SSL Certificate: If you have an SSL certificate for you domain you must upload it here. Otherwise CloudFront will not be able to serve content over HTTPS. If you only care about HTTP you need not use this.

The final rules do not need to be changed just yet. We will setup more behaviours for the distribution next:

Finally click Create Distribution. It will take 10 minutes or so to propagate around to all the data centers and you can see the progress in the main CloudFront panel.

When the Status is Deployed we can test that the CloudFront endpoint is working by going to the Domain specified; which will be *.cloudfront.net.

You should see your blog, don't worry if the styles are not displaying correctly this is just because we're acting it through the CloudFront endpoint and some of the relative paths for resources cannot be found. This will not occur with you custom domain.

2. Setup CloudFront Behaviors

CloudFront "behaviors" are the rules for URLs based on regular expressions. You can use behaviours to fetch content from a different origin (like an S3 bucket, or another domain) and override the TTLs that come from the origin server. You may want both but the latter is the most useful right now.

We will create several behaviors. Navigate into the distribution and you will see a Behaviors tab. Click Create Behavior. I'll explain the first one in detail for mathjax/*.

• Path Pattern: mathjax/* will match any url starting with mathjax/.
• Origin: Where the content comes from. You will only have one origin.
• Viewer Protocol Policy: Select the most appropriate one for if you have a SSL certificate installed or not.
• Object Caching: This is where we can override the TTLs from Silvrback; by selecting Customize. I've set this to 1 day (86400 seconds).

To summarise the TTL for each:

• email_subscriptions/*. Important: you must disable all caching here. This includes forwarding all headers and cookies. Otherwise it will return the error "The content could not be loaded." when clicking on subscribe.
• mathjax/* is 86400. Despite not having MathJax turned on, it still serves all the assets for these out. They are by far the biggest assets served out.
• assets/* is 86400. These are versioned (unique URLs) so you could set the TTL to a year if you want.
• feed is 3600. This is the RSS feed. Adding new posts will not show in peoples feed readers for up to and hour. Fine for me since I post once per week.
• favicon.ico is 86400. The little Silvrback icon in the location bar. I quite like the logo and love the fact it promotes Silvrback subtly.
• / is 3600. One important thing here is you must Forward Query Strings because it uses query parameters to page through older posts in your archive. Unlike the other URLs that are not affected by URL parameters.
• static/* is a route I setup to point to another origin, an S3 bucket. Anything requested on this URL will fetch from the S3 bucket. I know that these objects will never be changed under the same URL so i've added a bold 1 year TTL.
• * is the default (catch all) rule. In this case, since it's the fallback, you will want it to pass the headers as-is straight through from the origin.

3. Create the Hosted Zone in Route 53

Log into the AWS console, navigate to Route 53 and click Create Hosted Zone:

The only field here you need to fill in is the domain (we will deal with subdomains later):

You can now click on the newly created hosted zone, and then click Create Record Set. This is the A record for the domain.

• Name: Leave blank.
• Alias: Yes
• Alias Target: When you focus on this field you should see the CloudFront Distribution listed. If you do not see it click on the menu again, sometimes it sticks. If it still isn't on the menu it could be because the distribution is not ready yet. Try again in a couple of minutes.

And finally click Create.

You will create another A record the same way except this time add "www" into the Name field; assuming you want www.youdomain.com to point to your blog as well. You could point these A records to another server (allowing for different subdomains in the future), for example.

Once both A records have been created you should have four records in total in the hosted zone:

4. Update the Name Servers For Your Domain

This is the final stage where you will point your custom domain to Route 53. Before you do this you should run through this checklist:

1. Make sure your blog comes up on the http://*.cloudfront.net URL. As stated earlier, some of the styles (such as the custom font) may not appear correctly. This is only while your accessing it through the CloudFront endpoint.
2. If you are using an SSL certificate, check the https://*.cloudfront.net works as well. You will see the same thing as the http:// version.

Once everything looks good we need to get the name servers from Route 53. Under the record set will be an NS record containing the name servers:

Some registrars require you provide the IP only. You can use ping to lookup the IP for each name server:

\$ ping ns-1778.awsdns-30.co.uk
PING ns-1778.awsdns-30.co.uk (205.251.198.242): 56 data bytes

Which ever registrar you are using for your domain will have their own name servers, you need to replace them with the name servers above. Here is an example of the name servers set on a Godaddy domain:

The changes will not be immediate. Computers around the world will be using their DNS cache for a while until it's looked up again. It's hard to know when this is fully propegated but the general rule is up to 24 hours. However, it's likely you will see the new domain in a couple of hours or less.

Here is the finished product, if your not looking at it already:


text: From: Cindy Parker on 20 May 2010 13:24 Ok, I know. In a batch file I can change environment variables temporarily (=for the current, remaining session) be entering e.g. set CLASSPATH=D:\newpath;%CLASSPATH% However these changes are not visible outside of the current session and furthermore they are lost after a reboot. Is there a(nother) way to change them PERMANENTLY from batch script? I can imagine that there is a way by a regedit or VisualBasic script or 3rd party cmdline tool. Again: I don't want to edit them manually e.g. in the "System" dialog in control panel. The change should take place on cmdline from a script Cindy From: John John - MVP on 20 May 2010 13:33 Cindy Parker wrote:> Ok, I know. In a batch file I can change environment variables temporarily (=for the > current, remaining session) be entering e.g. > > set CLASSPATH=D:\newpath;%CLASSPATH% > > However these changes are not visible outside of the current session and furthermore they > are lost after a reboot. > > Is there a(nother) way to change them PERMANENTLY from batch script? > > I can imagine that there is a way by a regedit or VisualBasic script or 3rd party cmdline tool. > > Again: I don't want to edit them manually e.g. in the "System" dialog in control panel. > The change should take place on cmdline from a script Use SetX (a Resource Kit tool). John From: John John - MVP on 20 May 2010 13:45 Cindy Parker wrote:> Ok, I know. In a batch file I can change environment variables temporarily (=for the > current, remaining session) be entering e.g. > > set CLASSPATH=D:\newpath;%CLASSPATH% > > However these changes are not visible outside of the current session and furthermore they > are lost after a reboot. > > Is there a(nother) way to change them PERMANENTLY from batch script? > > I can imagine that there is a way by a regedit or VisualBasic script or 3rd party cmdline tool. > > Again: I don't want to edit them manually e.g. in the "System" dialog in control panel. > The change should take place on cmdline from a script You can use the Resource Kit's SetX for this. John From: Marcello on 20 May 2010 14:41 REG ADD "HKLM\SYSTEM\ControlSet001\Control\Session Manager\Environment" /v MyVar /t REG_SZ /d "Good Morning" (Restart required.) Lg Marcello From: John John - MVP on 20 May 2010 15:04 Should be put in the CurrentControlSet, for all we know the ControlSet001 could be a failed control set... Placing it in the CurrentControlSet will ensure that it is written to the proper corresponding nnn Control Set. John Marcello wrote:> REG ADD "HKLM\SYSTEM\ControlSet001\Control\Session Manager\Environment" /v > MyVar /t REG_SZ /d "Good Morning" > > (Restart required.) > > Lg > Marcello > >


text:
# Revision history [back]

For some reason (which i do not know), FunctionField only works in one variable (see the doc with FunctionField?). So you have to create it as a fraction field of a polynomial ring:

sage: aInv_poly = PolynomialRing(QQ,'a2,a4,a6')
sage: aInv_poly
Multivariate Polynomial Ring in a2, a4, a6 over Rational Field
sage: aInv = aInv_poly.fraction_field()
sage: aInv.inject_variables()
Defining a2, a4, a6

sage: R.<X> = PolynomialRing(aInv); R
Univariate Polynomial Ring in X over Fraction Field of Multivariate Polynomial Ring in a2, a4, a6 over Rational Field

sage: f = X^3 + a2*X^2 + a4*X + a6 ; f
X^3 + a2*X^2 + a4*X + a6

sage: fprim = f.derivative()
sage: fprim
3*X^2 + 2*a2*X + a4


text:
Langmuir-Slow Extraordinary Mode Magnetic Signature Observations with Parker Solar Probe by A. Larosa et al

2022-05-03

Langmuir-Slow extraordinary mode (L-SE) waves have been routinely observed in the Solar wind and in Earth’s electron foreshock since the early age of the space exploration. They are intimately connected to the plasma emission mechanism for the type III and type II radio emissions. In fact, the generally accepted scenario is that L-SE waves are mode-converted to freely propagating electromagnetic emission at the plasma frequency. However,  the details of the […]

LOFAR size and shape measurements of solar metric radio burst sources by Gordovskyy et al

2022-04-19

The plasma density and magnetic field in the upper solar corona and inner heliosphere are not sufficient to produce detectable bremsstrahlung hard X-ray or gyrosynchrotron microwave emissions, making metric and decametric coherent radio emissions the only tool for probing energetic electrons in these layers of the solar atmosphere (e.g. McLean & Labrum 1985; Pick & Vilmer 2008 as reviews). This source of information is vital to understanding the underlying mechanisms […]

Fundamental electromagnetic emissions by a weak electron beam in solar wind plasmas with density fluctuations by C. Krafft and P. Savoini

2022-04-05

Solar radio bursts of Type III were currently observed since decades in the interplanetary space (Reid and Ratcliffe, 2014). They result from a series of successive processes arising in solar coronal and wind plasmas where Langmuir wave turbulence is radiated by electron beams generated during flares, leading ultimately to the emission of electromagnetic waves at the fundamental plasma frequency $\omega _{p}$ and its second harmonic. The Letter by Krafft and […]

New results from the spectral observations of solar coronal type II radio bursts by R. Ramesh et al.*

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While it is widely accepted that the type II radio bursts observed in the interplanetary medium are due to the coronal mass ejections (CMEs), the energetic disturbance responsible for the shocks that generate the type II bursts observed in the near-Sun corona is still being debated.  Several studies indicate that CMEs are responsible for the coronal type II bursts too, but flares and various other eruptive activity have also been […]

Spectral Analysis of Solar Radio Type III Bursts from 20 kHz to 410 MHz by K. Sasikumar Raja et al.*

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Solar type III radio bursts are produced by electron beams that are propagating along open magnetic field lines in the corona and interplanetary medium (IPM). Type III bursts drift from high frequency (~1 GHz) to 20 kHz at 1 AU and sometimes even beyond. It has been known for a long time that type IIIs are extremely variable, both in radio flux density and in observing frequency range. A statistical […]

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For a mission that has just entered its primary science phase, Solar Orbiter has already produced many remarkable results. Released on December 14, 2021, a special issue of Astronomy and Astrophysics brings together a wealth of studies and observations obtained during the mission’s cruise phase. Of the 56 articles published, 25 are based on data from the Radio & Plasma Waves (RPW) instrument (Maksimovic et al., A&A, 2020). The RPW […]

Signatures of Type III Solar Radio Bursts from Nanoflares: Modeling by Sherry Chhabra et al.*

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Nanoflares are impulsive energy releases due to small breaks in coronal magnetic fields that have become stressed by photospheric convection. They are too small to be detected individually, but several lines of evidence suggest that they may be a primary candidate of coronal heating. But, whether nanoflares excite particles like full-sized flares is unknown (Vievering et al. 2021). A leading theory of particle acceleration predicts that the efficiency of acceleration […]

Radio Probing of Solar Wind Sources in Coronal Magnetic Fields  by A. Koval et al.*

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The magnetic fields of the Sun govern the solar corona structure where the solar wind emanates and further accelerates supersonically. Therefore, the accurate observational data about the topology, and more significantly, quantities of the coronal magnetic field are pivotal for identifying the solar wind sources as well as for the Space Weather modeling where these data specify initial conditions. Magnetic-field strength values in the solar wind sources are derived from […]

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text:
# SkyRegion¶

class regions.SkyRegion[source]

Bases: regions.Region

Base class for all regions defined in celestial coordinates

Methods Summary

 contains(skycoord, wcs) Check whether a sky coordinate falls inside the region intersection(other) Returns a region representing the intersection of this region with other. symmetric_difference(other) Returns the union of the two regions minus any areas contained in the intersection of the two regions. to_pixel(wcs) Returns the equivalent region defined in pixel coordinates. union(other) Returns a region representing the union of this region with other.

Methods Documentation

contains(skycoord, wcs)[source]

Check whether a sky coordinate falls inside the region

Parameters: skycoord : SkyCoord The position or positions to check wcs : WCS instance The world coordinate system transformation to assume
intersection(other)[source]

Returns a region representing the intersection of this region with other.

symmetric_difference(other)[source]

Returns the union of the two regions minus any areas contained in the intersection of the two regions.

to_pixel(wcs)[source]

Returns the equivalent region defined in pixel coordinates.

Parameters: wcs : WCS instance The world coordinate system transformation to assume pixel_region : PixelRegion object.
union(other)[source]

Returns a region representing the union of this region with other.


text:
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#### DJ Omnimaga

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##### Re: Post your Nspire routines here!
« Reply #60 on: July 06, 2010, 10:00:29 pm »
How do you prevent the flickering, though?
In case you are wondering where I went, I left Omni back in 2015 to form CodeWalrus due to various reasons explained back then, but I stopped calc dev in 2016 and am now mostly active on the CW Discord server at https://discord.gg/cuZcfcF

#### bwang

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##### Re: Post your Nspire routines here!
« Reply #61 on: July 06, 2010, 10:01:55 pm »
Hmmm...interesting.
I remember my raycaster flickering like crazy until I got double-buffering working.
Are you doing anything special?

#### calc84maniac

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##### Re: Post your Nspire routines here!
« Reply #62 on: July 06, 2010, 10:04:07 pm »
Hmmm...interesting.
I remember my raycaster flickering like crazy until I got double-buffering working.
Are you doing anything special?
Well, in my emulators I'm not clearing the buffer and then drawing new graphics. I draw the graphics over the current buffer line-by-line (which is how the systems I'm emulating tend to operate anyway)
"Most people ask, 'What does a thing do?' Hackers ask, 'What can I make it do?'" - Pablos Holman

#### DJ Omnimaga

• Former TI programmer
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##### Re: Post your Nspire routines here!
« Reply #63 on: July 06, 2010, 10:06:41 pm »
oooh I see, that explains why sprites won't flicker while the map is getting displayed. I assume they're drawn at the same time as the map, right?
In case you are wondering where I went, I left Omni back in 2015 to form CodeWalrus due to various reasons explained back then, but I stopped calc dev in 2016 and am now mostly active on the CW Discord server at https://discord.gg/cuZcfcF

#### calc84maniac

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##### Re: Post your Nspire routines here!
« Reply #64 on: July 06, 2010, 10:10:28 pm »
oooh I see, that explains why sprites won't flicker while the map is getting displayed. I assume they're drawn at the same time as the map, right?
That's right. It's how some sprites are able to be displayed behind the map.

Actually, now that I think about it, I do have a very minimal form of double-buffering. In my GBC emulator, I draw the 160 pixels in a line to a small buffer, then copy it to the screen buffer (1 or 2 lines depending on the position, for aspect ratio purposes). In the TI-83+ and TI-89 emulators, there is stored an internal buffer of the emulated screen contents, and it is upscaled onto the screen buffer.
"Most people ask, 'What does a thing do?' Hackers ask, 'What can I make it do?'" - Pablos Holman

#### DJ Omnimaga

• Former TI programmer
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##### Re: Post your Nspire routines here!
« Reply #65 on: July 06, 2010, 10:57:17 pm »
Aaah I see ^^

Nice job on the emus regardless, though
In case you are wondering where I went, I left Omni back in 2015 to form CodeWalrus due to various reasons explained back then, but I stopped calc dev in 2016 and am now mostly active on the CW Discord server at https://discord.gg/cuZcfcF

#### fb39ca4

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##### Re: Post your Nspire routines here!
« Reply #66 on: July 07, 2010, 11:39:38 am »
I've got the buffering all figured out, but it seems like nmath.h is missing from the skeleton. When I tried to compile a program using line, I got an error saying nmath.h doesn't exist.

#### apcalc

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##### Re: Post your Nspire routines here!
« Reply #67 on: July 07, 2010, 11:56:48 am »
I've got the buffering all figured out, but it seems like nmath.h is missing from the skeleton. When I tried to compile a program using line, I got an error saying nmath.h doesn't exist.

I am assuming that the abs( function is from nmath.h (that is the only one that did not "exist").  A simple solution would be to write your own abs( function, get rid of the "#include "nmath.h"" at the top and add your own abs( to the header.  Here is a very basic one I wrote.  I am sure that a smaller and faster version could be written:

Code: [Select]
int abs(int x) {if (x<0) {x*=-1;}return x;}
« Last Edit: July 07, 2010, 11:58:13 am by apcalc »

#### fb39ca4

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##### Re: Post your Nspire routines here!
« Reply #68 on: July 07, 2010, 01:03:52 pm »
How do I use the sprite function, specifically, how would I define the sprite?

#### apcalc

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##### Re: Post your Nspire routines here!
« Reply #69 on: July 07, 2010, 01:09:29 pm »
Declare a sprite like this:

Code: [Select]
               char sprite[32]={15,15,15,0,0,15,15,15,                                 15,15, 0, 0,0, 0,15,15,                                15, 0, 0, 0, 0, 0, 0,15,                                 0 , 0, 0, 0, 0, 0, 0, 0};
The number of elements in the array should be equal to the height*width of the sprite.  Each element should be the color you want the pixel to be.  Bwang's sprite drawing functoin takes the syntax:

Code: [Select]
void sprite(char* scrbuf, char* sprite, int x, int y, int w, int h);
Where scrbuf is the buffer, sprite is the spite you want to draw, x is the x coordinate of the sprite, y is the y coordinate, w is the width, and h is the heigth

If you read my first, unedited post, please disregard it b/c some of the info was wrong.
« Last Edit: July 07, 2010, 02:09:26 pm by apcalc »

#### fb39ca4

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##### Re: Post your Nspire routines here!
« Reply #70 on: July 07, 2010, 02:51:36 pm »
Unfortunately, apcalc, I read you unedited post, but now it's all sorted out, and I can play pong on my nspire.

#### apcalc

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##### Re: Post your Nspire routines here!
« Reply #71 on: July 07, 2010, 04:22:34 pm »
Unfortunately, apcalc, I read you unedited post, but now it's all sorted out, and I can play pong on my nspire.

Thats great to hear! I was used to the way you draw sprites on the 89, so I just assumed it was the same way. Feel free to ask if you have any more questions!

#### bwang

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##### Re: Post your Nspire routines here!
« Reply #72 on: July 07, 2010, 05:50:04 pm »
That sprite routine is not production ready. It works, but don't use it for anything fancy!
I need to change it to a proper sprite function that copies blocks of memory one row at a time.
I also attached nmath.h/c. Please please please don't use this in sensitive programs! Its slow, poorly written, and not all that accurate (e.g. sine and cosine are approximated with a couple of power series terms) - I was just collecting some routines for personal use. Your mileage with this file will vary, depending on the program.
Here's a nice way to do abs():
Code: [Select]
#define abs(a) (a) > 0 ? (a) : -(a)
« Last Edit: July 07, 2010, 05:56:40 pm by bwang »

#### apcalc

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##### Re: Post your Nspire routines here!
« Reply #73 on: July 07, 2010, 09:41:24 pm »
I've been having a very odd bug with an Nspire C program.  Every time I exit the program pressing ESC (for some reason my loss detection dosen't work) the calculator reboots (the emulator says "CPU Reset") (I have only tried this on the emulator).  All of the other ASM programs I have on the emulator (ncaster, gbc4nspire, ndless demo) work correctly. Also in my code you will see that I have the loss detection commented out.  When I have this part of the code, the calc reboots right after the dialog box displays.  Here is the code:

Code: [Select]
#include <os.h>#include "utils.h"asm(".string \"PRG\"\n");int main(void) {  char marker[32]={15,15,15,0,0,15,15,15,15,15,0,0,0,0,15,15,15,0,0,0,0,0,0,15,0,0,0,0,0,0,0,0};  short int leftx,length,ycord,lengthchange;  float spritepos;  char* scrbuf = (char*) malloc(SCREEN_BYTES_SIZE);  char* tempbuf = (char*) malloc(SCREEN_BYTES_SIZE);  showSimpleDialogBox("TI-Nspire Tunnel","TI-Nspire Tunnel\nWritten in C by Danny Clark\n\nUse the arrow keys to control ship");  clearScreen();  leftx=120,length=120,lengthchange=1000,ycord=0;  spritepos=180;  clearBuf(scrbuf);  for(ycord=0;ycord<SCREEN_HEIGHT;ycord++) {  horizontalline(scrbuf,0,leftx,ycord,0);  horizontalline(scrbuf,leftx+length,319,ycord,0);}  sprite(scrbuf,marker,150,236,8,4);  refresh(scrbuf);  leftx=120;  ycord=0;  while (!isKeyPressed(KEY_NSPIRE_ESC)) {  if (isKeyPressed(KEY_NSPIRE_LEFT)) {  sprite(scrbuf,marker,spritepos,236,8,4);  spritepos-=0.7;  sprite(scrbuf,marker,spritepos,236,8,4);}  if (isKeyPressed(KEY_NSPIRE_RIGHT)) {  sprite(scrbuf,marker,spritepos,236,8,4);  spritepos+=0.7;  sprite(scrbuf,marker,spritepos,236,8,4);}  sprite(scrbuf,marker,spritepos,236,8,4);  lengthchange--;  if (lengthchange==0) {length--;lengthchange=1000;}  scrollScreen(scrbuf,tempbuf,1);  horizontalline(scrbuf,0,leftx,ycord,0);  horizontalline(scrbuf,leftx,leftx+length,ycord,15);  horizontalline(scrbuf,leftx+length,319,ycord,0);  sprite(scrbuf,marker,spritepos,236,8,4);  refresh(scrbuf);  //if (getPixel(spritepos-1,ycord-3)||getPixel(spritepos+8,ycord-3)) {free(scrbuf);free(tempbuf);return 0;}  }free(scrbuf);free(tempbuf);return 0;}
Also, I don't have the code for the function horizontal line there but I am sure that is not the problem because it was defined and used well before I experienced this problem.  This program was working fine earlier today, but I made a few small additons and now I have no idea what is causing this.  Also, I made one small modification to the function "scrollScreen(".  I changed the two signs in the function (+ to - and - to +) to make the screen go down instead of up.
« Last Edit: July 07, 2010, 09:44:11 pm by apcalc »

#### calc84maniac

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##### Re: Post your Nspire routines here!
« Reply #74 on: July 07, 2010, 09:54:57 pm »
Are you supposed to be able to use floats as arguments to the sprite routine?
"Most people ask, 'What does a thing do?' Hackers ask, 'What can I make it do?'" - Pablos Holman


text:
# Usual distances on DFAs (Deterministic Finite Automata)?

I've been searching in the literature for examples of distances defined on the set of the DFAs (or on the set of minimal DFAs) that are defined on a given alphabet sigma.

Since the languages they describe (regular languages) can potentially have an infinite size, defining a distance is not a trivial matter.

Nevertheless, having a distance on these objects can be useful, in order to fit these in metric spaces, which allows for a range of things (in my case to assess the performance of an algorithm).

My only consistent idea so far is to create a distance similar to the edit-distance in labeled graphs on the minimized DFAs.

Does someone have ever heard of other distances ?

• I haven’t, but I’d agree you’d have to define it on the set of minimal DFAs, or you risk comparing one worst-case automaton to a best-case automaton for two languages. Mar 27 '20 at 12:54
• There are many ways to define a distance that is probably useless for most purposes. What did you have in mind for what you want to use the distance for, or what you want it to capture? That should probably influence the choice of distance.
– D.W.
Mar 27 '20 at 16:24
• @D.W. The kind of distance I'm looking for should reflect the distance between the languages recognized as much as possible. For instance, the problem with the edit-distance ont the minimal DFA is that it gives a greater distance between (a*) and (a+) than between (a*) and (b+). My use case is to assess performance on regular language inference algorithms by comparing the 'ground truth' DFA to the infered DFA. Mar 28 '20 at 9:19
• @m.raynal Not sure if it helps, but you can encode the language defined by DFA with an infinite binary sequence ($0$ stands for lack of the word, $1$ for presence) and then choose any metric for infinite sequences, for instance $\Sigma_{i}{\frac{|x_i - y_i|}{2^i}}$ Mar 28 '20 at 17:33
• But what do you mean by distance between languages? How do you want to use this distance metric? You say assess performance, but what aspect of performance? To ask it another way: How will you evaluate answers? We need criteria we can use to evaluate answers -- for instance, we need a way to vote on answers. This is not just for you, but also for others who might have a similar question. So, we need a well-defined question -- if you were hoping we would share as many ideas as we could think of and you'd pick one, I'm afraid this site isn't intended for brainstorming exercises.
– D.W.
Mar 28 '20 at 17:37

There are many possible distance metrics, and without any criteria, we have no basis to choose. Here are two plausible ones.

Let $$L_1,L_2$$ be the languages of the two DFAs. Let $$L$$ be the symmetric difference of those languages (i.e., $$(L_1 \setminus L_2) \cup (L_2 \setminus L_1)$$).

One dissimilarity measure is $$d(L_1,L_2) = 2^{-n}$$ where $$n=\min\{|x| : x \in L\}$$, i.e., $$n$$ is the length of the shortest word in $$L$$. This is not a distance metric, because it does not satisfy the triangle inequality.

Another possibility is to use the density of $$L$$, i.e.,

$$d(L_1,L_2) = \sum_{n=0}^\infty {|L \cap \Sigma^n| \over 2^n |\Sigma|^n}.$$

This one is a distance metric.

These can be computed given DFAs for $$L_1,L_2$$. You can easily compute a DFA for $$L$$. Then, it is easy to find the length of the shortest word in $$L$$ using breadth-first search.

Computing the density is a bit trickier, but can be done efficiently using a little more math. Let $$A$$ denote the transition matrix of the DFA for $$L$$, i.e., $$A_{ij}=1$$ if there is a transition (on any input symbol) from state $$i$$ to state $$j$$, or $$A_{ij}=0$$ if not. Let $$s$$ denote the one-hot vector indicating the start state, i.e., $$s_i=1$$ iff $$i$$ is the start state, and $$f$$ denote the one-hot vector indicating the final states, i.e., $$f_i=1$$ iff $$i$$ is an accepting state. Now $$|L \cap \Sigma^n| = s^\top A^n f$$, so the distance is given by

$$d(L_1,L_2) = \sum_{n=0}^\infty {s^\top A^n f \over 2^n |\Sigma|^n} = s^\top C f$$

where

$$C = \sum_{n=0}^\infty B^n = {1 \over I - B} = (I - B)^{-1}$$

where $$B={1 \over 2|\Sigma} A$$ and $$I$$ represents the identity matrix. This can be computed in time proportional to the cube of the number of states in the DFA for $$L$$ using standard algorithms for matrix inversion.

I finally found in the literature a paper answering my question precisely, as well as providing a framework to define distances between languages.

The method is very similar to the one explained by @D.W in his answer (it is based on defining a distance by computing a density on the symmetric difference), it only provides a slightly more formal and more general framework, and also provides several examples of possible metrics.

The paper can be found here, it is 'Approximate Language Identification' by R.M. Wharton (1974).
It is one of the founding papers for grammatical inference of languages though probabilistic language models.


text:
An experimental investigation was conducted to study the effects of increased ambient pressure (up to $6.89MPa$) and increased nozzle pressure drop (up to $2.8MPa$) on the cone angles for sprays produced by pressure-swirl atomizers having varying amounts of initial swirl. This study extends the classical results of DeCorso and Kemeny, (1957, “Effect of Ambient and Fuel Pressure on Nozzle Spray Angle,” ASME Transactions, 79(3), pp. 607–615). Shadow photography was used to measure cone angles at $x∕D0=10$, 20, 40, and 60. Our lower pressure results for atomizer swirl numbers of 0.50 and 0.25 are consistent with those of DeCorso and Kemeny, who observed a decrease in cone angle with an increase in nozzle pressure drop, $ΔP$, and ambient density, $ρair$, until a minimum cone angle was reached when $ΔPρair1.6∼100MPa(kg∕m3)1.6$ (equivalent to $200psi(lbm∕ft3)1.6$). Results for atomizers having higher initial swirl do not match the DeCorso and Kemeny results as well, suggesting that their correlation be used with caution. Another key finding is that an increase in $ΔPρair1.6$ to a value of $600MPa(kg∕m3)1.6$ leads to continued decrease in cone angle, but that a subsequent increase to $2000MPa(kg∕m3)1.6$ has little effect on cone angle. Finally, there was little effect of nozzle pressure drop on cone angle, in contrast to findings of previous workers. These effects are hypothesized to be due to gas entrainment.

1.
DeCorso
,
D. E.
, and
Kemeny
,
G. A.
, 1957, “
Effect of Ambient and Fuel Pressure on Nozzle Spray Angle
,”
Trans. ASME
0097-6822,
79
(
3
), pp.
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615
.
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Ortman
,
J.
, and
Lefebvre
,
A. H.
, 1985, “
Fuel Distributions from Pressure-Swirl Atomizers
,”
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0748-4658,
1
(
1
), pp.
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.
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Preussner
,
C.
,
Döring
,
C.
,
Fehler
,
S.
, and
Kampmann
,
S.
, 1998, “
GDI: Interaction Between Mixture Preparation, Combustion System and Injector Performance
,” SAE Technical Paper No. 980498.
4.
Satapathy
,
M. R.
, 1997, “
The Effect of Ambient Density on the Performance of an Effervescent Diesel Injector: A Thesis
,” MSME thesis, Purdue University, West Lafayette.
5.
Zeaton
,
G. W. P.
, 2004, “
An Experimental Study of Supercritical Fluid Jets: A Thesis
,” MSME thesis, Purdue University, West Lafayette.
6.
Syred
,
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,
Gupta
,
A. K.
, and
Beer
,
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, 1954, “
Temperature and Density Gradient Changes Arising With the Processing Vortex Core and Vortex Breakdown in Swirl Burners
,”
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, pp.
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597
.
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Lefebvre
,
A. H.
, 1989,
Atomization and Sprays
,
Hemisphere
,
New York
.
8.
Ohrn
,
T. R.
, 1989, “
The Effects of Internal Geometry and Injection Pressure on the Flow and Spray Characteristics of a Plain Orifice Atomizer: A Thesis
,” MSME thesis, Purdue University, West Lafayette.
9.
Dodge
,
L. G.
, and
Biaglow
,
J. A.
, 1986, “
Effect of Elevated Temperature and Pressure on Sprays From Simplex Swirl Atomizers
,”
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0742-4795,
108
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215
.
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Jang
,
C.
,
Bae
,
C.
, and
Choi
,
C.
, 2000, “
Characterization of Prototype High-Pressure Swirl Injector Nozzles—Part I: Prototype Development and Initial Characterization of Sprays
,”
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1044-5110,
10
, pp.
159
178
.
11.
Chen
,
S. K.
,
Lefebvre
,
A. H.
, and
Rollbuhler
,
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, 1992, “
Factors Influencing the Effective Spray Cone Angle of Pressure Swirl Atomizers
,”
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Kline
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, and
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,
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, and
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Influence of Ambient Air Pressure on Pressure-Swirl Atomization
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Effect of Air Pressure Upon Spray Angle∕Width Characteristics of Simplex Pressure Swirl Atomizers
,” ASME Paper No. 88-GT-176.


text:
# Fourier transform of a sum of 2 delta function

i have a channel impulse response $$\h(\tau,t)=\delta(\tau-1/4t)+b\delta(\tau-T)\$$

if I would like to take Fourier transform, I can take FT for each delta function and then sum up a result.

$$\FT(h(\tau,t))=FT(\delta(\tau-1/4t))+b FT(\delta(\tau-T))\$$

How to find FT for the first delta function is clear, but I don't understand how to find ft of the second delta function, $$\FT(\delta(\tau-T))\$$.

$$\mathcal{F}\{f(t-\tau)\} = e^{-j\omega\tau}\mathcal{F}\{f(t)\}\$$


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The Annals of Statistics

A characterization of marginal distributions of (possibly dependent) lifetime variables which right censor each other

Abstract

It is well known that the joint distribution of a pair of lifetime variables $X_1$ and $X_2$ which right censor each other cannot be specified in terms of the subsurvival functions $$P(X_2 > X_1 > x), \quad P(X_1 > X_2 > x) \quad \text{and} \quad P(X_1 = X_2 > x)$$ without additional assumptions such as independence of $X_1$ and $X_2$. For many practical applications independence is an unacceptable assumption, for example, when $X_1$ is the lifetime of a component subjected to maintenance and $X_2$ is the inspection time. Peterson presented lower and upper bounds for the marginal distributions of $X_1$ and $X_2$, for given subsurvival functions. These bounds are sharp under nonatomicity conditions. Surprisingly, not every pair of distribution functions between these bounds provides a feasible pair of marginals. Crowder recognized that these bounds are not functionally sharp and restricted the class of functions containing all feasible marginals. In this paper we give a complete characterization of the possible marginal distributions of these variables with given sub-survival functions, without any assumptions on the underlying joint distribution of $X_1, X_2$. Furthermore, a statistical test for an hypothesized marginal distribution of $(X_1$ based on the empirical subsurvival functions is developed.

The characterization is generalized from two to any number of variables.

Article information

Source
Ann. Statist., Volume 25, Number 4 (1997), 1622-1645.

Dates
First available in Project Euclid: 9 September 2002

https://projecteuclid.org/euclid.aos/1031594734

Digital Object Identifier
doi:10.1214/aos/1031594734

Mathematical Reviews number (MathSciNet)
MR1463567

Zentralblatt MATH identifier
0936.62014

Citation

Bedford, Tim; Meilijson, Isaac. A characterization of marginal distributions of (possibly dependent) lifetime variables which right censor each other. Ann. Statist. 25 (1997), no. 4, 1622--1645. doi:10.1214/aos/1031594734. https://projecteuclid.org/euclid.aos/1031594734

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