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# If a solid right circular cylinder with height 9 and radius 2 is cut

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If a solid right circular cylinder with height 9 and radius 2 is cut  [#permalink]

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19 Sep 2018, 22:00
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If a solid right circular cylinder with height 9 and radius 2 is cut as shown into three new cylinders, each of equal and uniform height, how much new surface area is created?

(A) $$4\pi$$

(B) $$12\pi$$

(C) $$16\pi$$

(D) $$24\pi$$

(E) $$36\pi$$

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Re: If a solid right circular cylinder with height 9 and radius 2 is cut  [#permalink]

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19 Sep 2018, 22:03
4 new circle surfaces were created.

hence 4 x π(2)^2 = 16π

My guess is c.
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Re: If a solid right circular cylinder with height 9 and radius 2 is cut  [#permalink]

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19 Sep 2018, 22:20
Bunuel wrote:

If a solid right circular cylinder with height 9 and radius 2 is cut as shown into three new cylinders, each of equal and uniform height, how much new surface area is created?

(A) $$4\pi$$

(B) $$12\pi$$

(C) $$16\pi$$

(D) $$24\pi$$

(E) $$36\pi$$

Attachment:
Capture (1).JPG

New surface areas added are the circular bases and tops.
when cut in 3 pieces it adds 4 circular areas each of radius 2.
Therefor the new added surface area will be = 4*π*r^2 = 4*4*π = 16*π
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Re: If a solid right circular cylinder with height 9 and radius 2 is cut  [#permalink]

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21 Sep 2018, 02:08
Please remember that the surface area of cylinder created by height will not change
But 4 new circle surfaces were created hence 4 x π(2)^2 = 16π

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Re: If a solid right circular cylinder with height 9 and radius 2 is cut &nbs [#permalink] 21 Sep 2018, 02:08
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Reoptimization Techniques in MIP Solvers

• Recently, there have been many successful applications of optimization algorithms that solve a sequence of quite similar mixed-integer programs (MIPs) as subproblems. Traditionally, each problem in the sequence is solved from scratch. In this paper we consider reoptimization techniques that try to benefit from information obtained by solving previous problems of the sequence. We focus on the case that subsequent MIPs differ only in the objective function or that the feasible region is reduced. We propose extensions of the very complex branch-and-bound algorithms employed by general MIP solvers based on the idea to warmstart'' using the final search frontier of the preceding solver run. We extend the academic MIP solver SCIP by these techniques to obtain a reoptimizing branch-and-bound solver and report computational results which show the effectiveness of the approach.

$Rev: 13581$

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# How can we extend the predictive interface so it can suggest new operations?

### Introduction

Mathematica 9 has introduced a new predictive interface. For each output, it suggest possible actions the user might want to take.

How can this interface be extended so that it will suggest additional, possibly user-defined, actions?

### The starting point

@Rojo mentioned in chat that he discovered that much of the functionality is contained in the Predictions and PredictiveInterface contexts. Many of the symbols have usage messages (but make sure that you trigger loading them by using the predictive interface at least once).

The PredictionsPredictionRule symbol seems to contain the rules on which the predictions are based, as downvalues (see its usage message).

The functionality seems to be defined in files found in the \$InstallationDirectory/AddOns/Applications/PredictiveInterface/ directory. The relevant part is in .mx files (not directly readable) and comments in the .m` files suggest that these may be updated automatically.

I posted this question as a starting point for people who want to figure out how this works, and to facilitate collaboration.

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Is this the same question as this one? –  Leonid Shifrin Dec 18 '12 at 21:28
@Leonid Oops... I guess I'll delete this soon and transfer the info to the other Q –  Szabolcs Dec 18 '12 at 21:30
@Leonid Actually, after looking at that question, I would suggest implementing a separate suggestion bar to the OP. Shall we keep this question as specific to the built-in predictive interface and keep the other one separate? –  Szabolcs Dec 18 '12 at 21:35
Perhaps it is a good idea. I was not sure whether or not yours is a dupe, from the start. Let's see what others think. –  Leonid Shifrin Dec 18 '12 at 21:38


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Vol 22, No 4

## Optical and X-Ray Observations of MAXI J1820+070 During the Early Outburst Phase in 2018: Zooming in the Low Frequency QPOs

#### Dong-Ming Mao, Wen-Fei Yu, Ju-Jia Zhang, Zhen Yan, Stefano Rapisarda, Xiao-Feng Wang, Jin-Ming Bai

Abstract

Abstract We report a further investigation of the optical low frequency quasi periodic oscillations (LF QPOs) detected in the black hole transient MAXI J1820+070 in the 2018 observations with the YFOSC mounted on Lijiang 2.4 m telescope (LJT). In addition, we make use of the Insight-HXMT/HE observations to measure the properties of the quasi-simultaneous X-ray LF QPOs of MAXI J1820+070 on the same day. We compared the centroid frequency, the full width at half maximum (FWHM) and the fractional rms of the LF QPOs in both wavelength ranges. We found that the centroid frequency of the optical QPO is at a frequency of 51.58 mHz, which is consistent with that of the X-ray LF QPO detected on the same day within 1 mHz. We also found that the FWHM of the optical LF QPO is significantly smaller than that of the X-ray LF QPO, indicating that the optical QPO has a higher coherence. The quasi-simultaneous optical and the X-ray LF QPO at a centroid frequency of about 52 mHz suggests that the actual mechanisms of these LF QPOs as the Lense–Thirring precession should work in the vicinity of a radius of about 80–117 gravitational radii ($$R_g=GM/c^2$$, M is the mass of the black hole) from the black hole if the QPO frequency is related to a proxy of the orbital frequency in the accretion flow as the Lense– Thirring precession model suggests. Furthermore, the apparent higher coherence of the optical QPO favors that it is a more original signal as compared with the X-ray QPO.

Keywords

Keywords X-ray stars – Low mass binary stars – X-ray transient sources

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# Ridge Regression Matlab

But the nature of the ' 1 penalty causes some coe cients to be shrunken tozero exactly. b = ridge(y,X,k) returns the ridge regression coefficients b for the linear model y = X +, where: X is an n-by-p matrix y is the n-by-1 vector of observations k is a scalar constant (the ridge parameter) The ridge estimator of is. leverage - Regression diagnostic. Marquardt and Snee [1970] suggested using the value of K for. An appendix describes the experimentalPLSprocedureofSAS/STAT software. Ridge Regression [Documentation PDF] Ridge regression is a technique for analyzing multiple regression data that suffer from multicollinearity. Magdon-Ismail CSCI 4100/6100. The code is inspired from these slides in the context of the course Kernel Methods in Machine Learning (Julien Mairal (INRIA)- Jean-Philippe Vert (ENS Paris & Mines ParisTech)), of the MVA. The simple Regression toolbox, simpleR, contains a set of functions in Matlab to illustrate the capabilities of several statistical regression algorithms. % modlgui - Graphical user interface for modlmker % % Non-Linear Regression Methods. Part 1: Overview and Case Study Using Generalized (Penalized) Regression. 09169v3 [stat. In this article, the Ridge–GME parameter estimator, which combines Ridge Regression and Generalized Maximum Entropy, is improved in order to eliminate the subjectivity in the analysis of the ridge trace. Elastic Net regression can also be solved using Matlab lasso function and elasticnet package in R [9]. DOWNLOAD HERE (the code we provided in this page is meant for reasearch and teaching purpose). Also try practice problems to test & improve your skill level. In the case of multicollinearity of the vectors of design matrix, LSE has very big variance, i. Hoerl A E and R W Kennard 1970a Ridge regression Biased estimation for non from ISYE 6421 at Georgia Institute Of Technology. Linear Regression is one of the easiest algorithms in machine learning. In each case, we have to begin the modeling , i. When $$q = 2$$, this model is called ridge regression. Simply, regularization introduces additional information to an problem to choose the "best" solution for it. Kernel Ridge Regression in Matlab Collaborative project with my friend Alexandre Hannebelle from master MVA to classify mnist using Kernel Ridge Regression. Your email address will not be published. 1 1 Learning Logistic Regressors by Gradient Descent Machine Learning – CSE446 Carlos Guestrin University of Washington April 17, 2013 ©Carlos Guestrin 2005-2013. Sample texts from an R session are highlighted with gray shading. % modlrder - Displays information from MODLMKER models. For alphas in between 0 and 1, you get what's called elastic net models, which are in between ridge and lasso. ridge treats NaN values in X or y as missing values. pdf: Song, Xiaonan and Lu, Haiping,. Note that it becomes the lasso when and the ridge regression when. The regression process depends on the model. Tipping Microsoft Research, 7 J J Thomson Avenue, Cambridge, CB3 0FB, U. Specifically, it replaces x in linear regression with polynomial basis [1, x, x2, … , xd]. MILLER CSIRO Division of Mathematics and Statistics, Melbourne, Australia [Read before the Royal Statistical Society on Wednesday, January 25th, 1984, the President, Professor P. Hi I am comparing MSE of OLS and ridge regression in order to determine which estimate is best. the paths are smooth, like ridge regression, but are more simi-lar in shape to the Lasso paths, particularly when the L1 norm is relatively small. Octave-Forge is a collection of packages providing extra functionality for GNU Octave. leverage - Regression diagnostic. In the Wolfram Language , LinearModelFit returns an object that contains fitting information for a linear regression model and allows for easy extraction of results and diagnostics. Strflab is a comprehensive set of matlab routines to estimate receptive fields using both ridge regression and gradient descent approaches. Regularization: Ridge Regression and Lasso Week 14, Lecture 2 1 Ridge Regression Ridge regression and the Lasso are two forms of regularized regression. Ridge Regression procedure. Lasso is a regularization technique for performing linear regression. Image quality and accuracy is the core factors of. An appendix describes the experimentalPLSprocedureofSAS/STAT software. % % General Regression Modelling. Therefore, it resembles ridge regression. Here we used default settings for cv. A variety of predictions can be made from the fitted models. Ask Question Asked 7 years, Browse other questions tagged matlab ridge-regression sparse or ask your own question. Stepwise regression and best subsets regression are both automatic tools that help you identify useful predictors during the exploratory stages of model building for linear regression. Each entry includes a short definition for the term along with a bibliography and links to related Web pages. If you need more info about LASSO and Ridge,. Example of a matlab ridge regression function:. ed u Editor: Ross Quinlan Abstract. L2 regularization / Ridge regression. Example of a matlab ridge regression function:. Lasso is a regularization technique for performing linear regression. Read Section 14. It takes the weighted average of Y for all observations near to > > the particular value of X, weighted using the kernel function. In particular, POGS can very efficiently solve problems that involve different objective functions, but the same data matrix (eg. This causes a challenge in notation, since we must somehow indicate whether the variables in a particular formula are standardized or not. The user in the linked thread clearly was asking for an implementation of ridge logistic regression, so your interpretation seems strange to me. Linear regression is still a good choice when you want a very simple model for a basic predictive task. Logistic Regression Model or simply the logit model is a popular classification algorithm used when the Y variable is a binary categorical variable. Ridge regression ! Second stage: 1-NN classification using knowledge base fMRI Prediction Results ©Emily Fox 2013 34 ! Leave-two-out-cross-validation " Learn ridge coefficients using 58 fMRI images " Predict semantic features of 1st heldout image " Compare whether semantic features of 1st or 2nd heldout image are closer. Ridge, LASSO and Elastic net algorithms work on same principle. inputs, linear regression ﬁts a 2-dim. This volume presents in detail the fundamental theories of linear regression analysis and diagnosis, as well as the relevant statistical computing techniques so that readers are able to actually model the data using the methods and techniques described in the book. Shuxiao Chen, Edgar Dobriban, Jane H Lee Invariance reduces Variance: Understanding Data Augmentation in Deep Learning and Beyond. Here the highlighted part represents L2. html , that ridge regression actually mean centers and make the std equal to 1 for the predictors. Mar´ın, and M. This is the 'Bayesian Linear Regression' entry in the machine learning glossary at Carnegie Mellon University. Gaussian kernel regression with Matlab code. In this paper the basic methods of obtaining of Ridge‐estimators and numerical procedures of its realization in MATLAB are considered. Logistic Regression is a type of regression that predicts the probability of ocurrence of an event by fitting data to a logit function (logistic function). While fitting a linear regression model to a given set of data, we begin with simple linear regression model. Shuxiao Chen, Edgar Dobriban, Jane H Lee Invariance reduces Variance: Understanding Data Augmentation in Deep Learning and Beyond. , Cary, NC Abstract Partial least squares is a popular method for soft modelling in industrial applications. Below is a diagram generated using a real data and a real fitted model:. Summer School at Technical University of Denmark) [Matlab scripts] 2013/7/10: PCA, k-means, and pLSA (数理情報工学演習第二). Selection of Subsets of Regression Variables By ALAN J. , learning algorithms, such as Support Vector Regression (SVR), Kernel Ridge Regression (KRR), Relevance Vector Regression (RVR) and Augmented Radial Basis Function (A-RBF) have been adopted in order to build different accurate predictors. Following the general vibe of responses, I changed the “Non-linear Regression / SPSS” field to “Limited” to avoid potential misinterpretations of the table. But I am unable to figure out how to calculate the score of my model i. However, ridge regression includes an additional 'shrinkage' term - the. If we apply ridge regression to it, it will retain all of the features but will shrink the coefficients. In this paper, the Ridge-GME parameter estimator, which combines Ridge Regression and Generalized Maximum Entropy, is improved in order to eliminate the subjectivity in the analysis of the ridge trace. Ridge Regression [Documentation PDF] Ridge regression is a technique for analyzing multiple regression data that suffer from multicollinearity. In this problem, we will examine and compare the behavior of the Lasso and ridge regression in the case of an exactly repeated feature. Magdon-Ismail CSCI 4100/6100. He uses sample data about diabetes patients and their disease progression to show how to use JMP Pro lasso and elastic net shrinkage techniques to reduce prediction variance, handle non-normal and zero-inflated responses, model mean responses and select the. This estimator has built-in support for multi-variate regression (i. Ridge regression adds “squared magnitude” of coefficient as penalty term to the loss function. Octave / Matlab Code. I did linear regression in google docs and I did it for python. This is a variant of ridge regression using the kernel trick (Mercers Theorem). 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. regstats - Regression diagnostics. where k is the ridge parameter and I is the identity matrix. 8, 363-368 (1985) Ridge Regression and Its Application to Medical Data R. Bishop and Michael E. Regularization Ridge regression, lasso, Run the command by entering it in the MATLAB Command Window. Elastic net is what I am calling a "flexible" regularization technique because it lets you play around with a second fudge parameter, alpha, to fluctuate between ridge regression and linear regression with LASSO that uses the L1 norm. (Contours illustrate constant RSS. We will use dataset which is provided in courser ML class assignment for regularization. Therefore, it resembles ridge regression. Linear regression一般只对low dimension适用，比如n=50, p=5，而且这五个变量还不存在multicolinearity. In this post, I'm going to walk you through an elementary single-variable linear regression with Octave (an open-source Matlab alternative). Linear Regression and Kernel Methods. A linear model predicts the value of a response variable by the linear combination of predictor variables or functions of predictor variables. Select a Web Site. 1 Predicting Pace Based on Previous Training Runs Tiffany Jin [email protected] Performing the Regression. In this paper, we focus on ridge regression, a penalised regression approach that has been shown to offer good performance in multivariate prediction problems. Mar´ın, and M. Fuzzy Ridge Regression with non symmetric membership functions and quadratic models S. Sample texts from an R session are highlighted with gray shading. April 03, 2014 Uniform PDF and CDF with MATLAB. 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. How to use Ridge Regression and Lasso in R. In R, multiple linear regression is only a small step away from simple linear regression. Strflab is available at strflab. Multinomial logistic regression is used to model nominal outcome variables, in which the log odds of the outcomes are modeled as a linear combination of the predictor variables. Kernel ridge regression Isabelle Guyon - [email protected] Ridge Logistic Regression •Minimize N𝐿𝐿+𝜆 2 σ𝑖=1 𝐾𝛽 𝑖 2 •(NLL = Negative Log-Likelihood) •𝜆=0is what we did before •𝜆>0means that we are not minimizing the NLL. Utilised a ridge regression scheme to reduce false-positives. 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. In R: Ridge function of the package MASS (use the lm. Instead, we are trying to make the NLL as small as possible, while still making sure that the 𝛽s are not too large. This paper considers the natural follow-up to the OLS problem, ridge regression, which solves $(\boldsymbol{X}^* \boldsymbol{X} + \lambda \boldsymbol{I}) \boldsymbol{\beta} = \boldsymbol{X}^* \boldsymbol{y}$. The lasso algorithm is a regularization technique and shrinkage estimator. An overfit model is one that is too complicated. Performing the Regression. We constrain to be in a hypersphere around 0. In Linear Regression these two variables are related through an equation, where exponent (power) of both these variables is 1. Forward and backward stepwise selection is not guaranteed to give us the best model containing a particular subset of the p predictors but that's the price to pay in order to avoid overfitting. This also hints at the possibility of parallelising the whole algorithm for use on large datasets. regstats - Regression diagnostics. Let us see a use case of the application of Ridge regression on the longley dataset. , the estimator is unstable. Pick the smallest value of k that produces a stable estimate of β. It implements a variety of ways to solve 'LASSO' problems (Least Squares with a penalty on the L1-norm of the parameters). Stepwise Regression Variable selection using stepwise regression Multivariate Regression Linear regression with a multivariate response variable Regularization Ridge regression, lasso, elastic nets. , ridge regression and generalized cross-validation) can be. In this post, I explain what an overfit model is and how to detect and avoid this problem. com, June 2005 The kernel ridge regression method (see e. Mathworks MatLab also has routines to do ridge regression and estimate elastic net models. inputs, linear regression ﬁts a 2-dim. (Contours illustrate constant RSS. Coefficient estimates for the models described in Linear Regression rely on the independence of the model terms. Online convex optimization: ridge regression, adaptivity 5 Since 8t, 1 2 kx t xk2 1 t+1 1 t H t 0, we have established R T 1 2 XT t=1 G2 t H 1:t: Note that our procedure does not require that we know the curvature of an adversary's functions in advance. Read Section 14. This tour studies linear regression method in conjunction with regularization. I tried MATLAB and other softwares. This tutorial will explore how R can be used to perform multiple linear regression. Strflab is available at strflab. • Ridge trace plot is a plot of parameter estimates vs k where k usually lies in the interval of [0,1]. particle_swarm, see ?cv. Response Variable: Estimated variable. • Rule of Thumb: 1. However, if you would like to have probability outputs, you may consider logistic regression. This also hints at the possibility of parallelising the whole algorithm for use on large datasets. Ridge and Lasso Regression are types of Regularization techniques Regularization techniques are used to deal with overfitting and when the dataset is large Ridge and Lasso Regression involve adding penalties to the regression function. van Wieringen1,2 1 Department of Epidemiology and Biostatistics, VU University Medical Center. Plus I will share my Matlab code for this algorithm. ) You need only supply the function f(); you do not need to supply the derivatives. And in using Graph Lab Create it's really simple to do the ridge regression modification because, as we mentioned before, there's this l2 penalty input. This situation of multicollinearity can arise, for example, when data are collected without an experimental design. Mathworks MatLab also has routines to do ridge regression and estimate elastic net models. In this paper the basic methods of obtaining of Ridge‐estimators and numerical procedures of its realization in MATLAB are considered. Realization of Ridge Regression in MATLAB. The method is not widely diffused among statisticians. • The value of k can be estimated by looking at the ridge trace plot. particle_swarm, see ?cv. Ridge Regression is a commonly used technique to address the problem of multi-collinearity. It's possible to write the ridge regression solution in terms of the SVD of the dataset. Linear Model, often called Linear Regression Model, is the model that de-scribes the relationship between response Y i and explanatory variables X ij. % modlmker - Develops PCR, PLS and RR models. As such, lasso is an alternative to stepwise regression and other model selection and dimensionality reduction techniques. MLlib: Scalable Machine Learning on Spark support vector regression (SVR), ridge Weak scaling for logistic regression MLbase VW Matlab 0 200 400 600 800 1000. As the title suggests, the book is about regression analysis. LinearRegression() # Train the model using the training sets regr. Elastic Net regression can also be solved using Matlab lasso function and elasticnet package in R [9]. Regression is the process of fitting models to data. 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. This tutorial will explore how R can be used to perform multiple linear regression. In the Bayesian view of lasso regression, the prior distribution of the regression coefficients is Laplace (double exponential), with mean 0 and scale , where is the fixed shrinkage parameter and. is an indicator function (it is 1 if its argument is true and 0 otherwise). Measuring speed and time complexity of these methods. An obvious question arises. Logistic Regression Model or simply the logit model is a popular classification algorithm used when the Y variable is a binary categorical variable. It contrasts ridge regression and the Lasso. Focus will be on classification and regression models, clustering methods, matrix factorization and sequential models. See Section 5 for details. @drsimonj here to show you how to conduct ridge regression (linear regression with L2 regularization) in R using the glmnet package, and use simulations to demonstrate its relative advantages over ordinary least squares regression. Read Section 14. The key to this estimation is that the linear interpolation. •[b,fitInfo] = lasso(X,y,ʹLambdaʹ,lambda) –b ‐Lasso coefficients. Ridge regression will not. Fit Bayesian Lasso Regression Model. An Introduction to Splines 1 Linear Regression Simple Regression and the Least Squares Method Least Squares Fitting in R Polynomial Regression 2 Smoothing Splines Simple Splines B-splines. Elastic net is a combination of ridge and lasso regression. Reminder: ridge regression and variable selection Recall our setup: given a response vector y2Rn, and a matrix X2Rn pof predictor variables (predictors on the columns) Last time we saw thatridge regression, ^ridge = argmin 2Rp ky X k2 2 + k k2 2 can have betterprediction errorthan linear regression in a variety of scenarios, depending on the. It is a combination of both L1 and L2 regularization. It can also fit multi-response linear regression. Development started in 2004 and the toolbox receives regular updates. Linear regression一般只对low dimension适用，比如n=50, p=5，而且这五个变量还不存在multicolinearity. 2 minutes read. MILLER CSIRO Division of Mathematics and Statistics, Melbourne, Australia [Read before the Royal Statistical Society on Wednesday, January 25th, 1984, the President, Professor P. Ridge Regression procedure. Kernel Ridge Regression in Matlab Collaborative project with my friend Alexandre Hannebelle from master MVA to classify mnist using Kernel Ridge Regression. is an indicator function (it is 1 if its argument is true and 0 otherwise). In this post, I’m going to implement standard logistic regression from scratch. Bharatendra Rai 20,435 views. The basic form of a formula is \[response \sim term_1 + \cdots + term_p. Ridge regression adds "squared magnitude" of coefficient as penalty term to the loss function. m' and 'run3DExample. Ridge regression addresses the problem of multicollinearity (correlated model terms) in linear regression problems. Using R for Linear Regression In the following handout words and symbols in bold are R functions and words and symbols in italics are entries supplied by the user; underlined words and symbols are optional entries (all current as of version R-2. Ridge, LASSO and Elastic net algorithms work on same principle. Regularization Ridge regression, lasso, Run the command by entering it in the MATLAB Command Window. This has the effect of shrinking the coefficient values (and the complexity of the model) allowing some coefficients with minor contribution to the response to get close to zero. 岭回归(Ridge Regression)是在平方误差的基础上增加正则项, 通过确定 的值可以使得在方差和偏差之间达到平衡：随着 的增大，模型方差减小而偏差增大。 对 求导，结果为. edu Abstract This is a note to explain kernel ridge regression. Stepwise Regression Variable selection using stepwise regression Multivariate Regression Linear regression with a multivariate response variable Regularization Ridge regression, lasso, elastic nets. Like many forms of regression analysis, it makes use of several predictor variables that may be either numerical or categorical. Different models, i. There is an option for the GCV criterion which is automatic. I did linear regression in google docs and I did it for python. (Editors), IOS Press, NATO Science Series III: Computer and Systems Sciences, volume 190. 1 Ridge Regression Possibly the most elementary algorithm that can be kernelized is ridge regression. ridge regression. Tutorial Files. Multiple linear regression attempts to model the relationship between two or more explanatory variables and a response variable by fitting a linear equation to observed data. This model solves a regression model where the loss function is the linear least squares function and regularization is given by the l2-norm. Ridge regression 5. inference; neural models, regression and feature selection. Ridge Regression Introduction to Ridge Regression. We ﬁrst review linear regres-. Kernel ridge Regression Max Welling Department of Computer Science University of Toronto 10 King's College Road Toronto, M5S 3G5 Canada [email protected] Ridge regression addresses the problem by estimating regression coefficients using. A serious concern with the visual inspection of the ridge trace to define the supports for the. Measuring speed and time complexity of these methods. Therefore, the lasso estimates share features of the estimates from both ridge and best subset selection regression since they both shrink the magnitude of all the coefficients, like ridge regression, but also set some of them to zero, as in the best subset selection case. Linear Regression. Method should be e ciently represented with a boolean circuit. Sample texts from an R session are highlighted with gray shading. Stepwise Regression Variable selection using stepwise regression Multivariate Regression Linear regression with a multivariate response variable Regularization Ridge regression, lasso, elastic nets. Lasso is a regularization technique for performing linear regression. A linear relationship between two variables x and y is one of the most common, effective and easy assumptions to make when trying to figure out their relationship. Be Your Own Boss! by Being a Digital Content Creator !! Ridge Algorithm. Ridge regression Selection of Ridge regression in R/SAS De nition and solution Properties Ridge regression: Solution (Cont'd) Corollary: In the special case of an orthonormal design matrix, ^ridge J = ^OLS J 1+ This illustrates the essential feature of ridge regression: shrinkage Applying the ridge regression penalty has the e ect of. RegEM; Referenced in 13 articles replaces the conditional maximum likelihood estimation of regression parameters in the conventional EM algorithm squares (with fixed truncation parameter) and ridge regression with generalized cross-validation as regularized estimation regularized estimation of regression parameters (e. Vila IDBIS Research Group - Dept. In order to use sklearn, we need to input our data in the form of vertical vectors. Regression in R: best subset, stepwise, ridge, lasso, and PCR # The following code is for the book The Elements of Statistical Learning , chapter 3 # Data was described on page 3. In particular, see glmnet at CRAN. If you already know the theory. Partial factor modeling: predictor-dependent shrinkage for linear regression P. y i 2f 1;1gis its class label. Uses the Akaike criterion for model selection, and is able to deal with weighted instances. squares (OLS) regression - ridge regression and the lasso. I tried to keep the math to a minimum, but I failed. In general, set scaled equal to 1 to produce plots where the coefficients are displayed on the same scale. You know that linear regression is a popular technique and you might as well seen the mathematical equation of linear regression. In the Wolfram Language , LinearModelFit returns an object that contains fitting information for a linear regression model and allows for easy extraction of results and diagnostics. If you got a project about implementing a non-linear regression for a complex functional form, you would use R, Matlab or a similar programming language. Magdon-Ismail CSCI 4100/6100. Linear Regression is one of the methods to solve that. 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. 2 Learning strategy We apply cascaded Ridge Regression [2] to train our regressor. (ANOCOVA), multiple linear regression, stepwise regression, response surface prediction, ridge regression, and one-way multivariate analysis of variance (MANOVA). Generalized Linear Models¶ The following are a set of methods intended for regression in which the target value is expected to be a linear combination of the input variables. Here we used default settings for cv. An overfit model is one that is too complicated. Another kind of regularized regression that you could use instead of ridge regression is called Lasso Regression. A regression model that uses L1 regularization technique is called Lasso Regression and model which uses L2 is called Ridge Regression. 3 Ridge Regression For ridge regression instead of minimizing least squares we penalize for having to many β that are big by considering the following minimization criteria: XN i=1 (y i −β 0 − p j=1 x ijβ j) 2 +λ j=1 β2 j. We will implement. transformations like ridge regression (Yuan and Lin, 2006). Figure 2 Quantile Regression rFunction. Ridge regression is used as an alternative model in the case when there is presence of multicollinearity in the model. I found R function ridge. Ridge regression addresses the problem by estimating regression coefficients using β ^ = ( X T X + k I ) − 1 X T y where k is the ridge parameter and I is the identity matrix. The plot shows the nonzero coefficients in the regression for various values of the Lambda regularization parameter. , Cary, NC Abstract Partial least squares is a popular method for soft modelling in industrial applications. Lasso solutions are quadratic programming problems, which are best solved with software (like Matlab). regress - Multiple linear regression using least squares. 1 Ridge Regression Possibly the most elementary algorithm that can be kernelized is ridge regression. Ridge regression Here, λ ≥ 0 is a tuning parameter for controlling the strength of the penalty • When λ = 0, we minimize only the loss  overfitting • When λ = ∞,we get that minimizes the penalty  underfitting. Ramanathan and Sharad D. 5 minute read. Ridge Regression Introducción a Ridge Regression. A serious concern with the visual inspection of the ridge trace to define the supports for the. Ridge Regression creates a linear regression model that is penalized with the L2-norm which is the sum of the squared coefficients. 00 1 2 #requests per minute. More information about the spark. Learning From Data Lecture 9 Logistic Regression and Gradient Descent Logistic Regression Gradient Descent M. Ridge Regression is a commonly used technique to address the problem of multi-collinearity. This page uses the following packages. As the name suggests this algorithm is applicable for Regression problems. ) You need only supply the function f(); you do not need to supply the derivatives. By using ridge regression where there are 5 ridge parameters k. • To demonstrate a nonparametric version of QR which outperforms the currently available nonlinear QR regression formations [9]. But the problem is that model will still remain complex as there are 10,000 features, thus may lead to poor model performance. The simple Regression toolbox, simpleR, contains a set of functions in Matlab to illustrate the capabilities of several statistical regression algorithms. Based on your location, we recommend that you select:. The name of package is in parentheses. In the case of multicollinearity of the vectors of design matrix, LSE has very big variance, i. ) •In MATLAB, the back-slash operator computes a least square solution. In this problem, we will examine and compare the behavior of the Lasso and ridge regression in the case of an exactly repeated feature. perform better than evaluating test points by Gaussian process regression using no lattice at all. Lasso and Elastic Net Details Overview of Lasso and Elastic Net. L2 regularization / Ridge regression. We also call this a regression problem; Predict continuous valued output (price) Shown that using MATLAB to prototype is a really good way to do this. The aim of this paper is to propose estimators of the unknown functional coefficients in the Functional Concurrent Model (FCM). The lasso algorithm is a regularization technique and shrinkage estimator. scikit-learn includes linear regression, logistic regression and linear support vector machines with elastic net regularization. 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. Welcome to STAT 508: Applied Data Mining and Statistical Learning! This course covers methodology, major software tools, and applications in data mining. This makes the Lasso far easier to interpret than the Ridge. LINEAR METHODS FOR REGRESSION 4. These two procedures use different methods and present you with different output. Focus will be on classification and regression models, clustering methods, matrix factorization and sequential models. This tour studies linear regression method in conjunction with regularization. It allows us to perform non-linear regression by construct-ing a linear regression function in a high di-mensional feature space. Ridge regression addresses the problem of multicollinearity (correlated model terms) in linear regression problems. Vito Ricci - R Functions For Regression Analysis – 14/10/05 ([email protected] Built a system to compute ridge regression preserving privacy ( nd best- t curve for a collection of encrypted data points). Logistic regression is a generalized linear model that we can use to model or predict categorical outcome variables. Listing 1: Demonstration code for logistic regression problem. The goal of learning a linear model from training data is to find the coefficients, β, that best explain the data. Ridge Regression. % modlrder - Displays information from MODLMKER models. Selection of Subsets of Regression Variables By ALAN J. Online convex optimization: ridge regression, adaptivity 5 Since 8t, 1 2 kx t xk2 1 t+1 1 t H t 0, we have established R T 1 2 XT t=1 G2 t H 1:t: Note that our procedure does not require that we know the curvature of an adversary's functions in advance. Lasso minimizes the sum of the squared errors plus the sum of the absolute value of the regression coefficients. Ridge Regression procedure. It's possible to write the ridge regression solution in terms of the SVD of the dataset. Partial Least Squares Regression Randall D. For alphas in between 0 and 1, you get what's called elastic net models, which are in between ridge and lasso. 8, 363-368 (1985) Ridge Regression and Its Application to Medical Data R. Expertise includes probabilistic modeling in medicine, biology, engineering, psychology and finance. Summary of ridge regression. 56 CHAPTER 4. , learning algorithms, such as Support Vector Regression (SVR), Kernel Ridge Regression (KRR), Relevance Vector Regression (RVR) and Augmented Radial Basis Function (A-RBF) have been adopted in order to build different accurate predictors. The related elastic net algorithm is more suitable when predictors are highly correlated. 所以没法做variable selection。. Vila IDBIS Research Group - Dept. Support Vector Machine - Regression (SVR) Support Vector Machine can also be used as a regression method, maintaining all the main features that characterize the algorithm (maximal margin). The Gaussian Kernel can be changed to any desired kernel. I encourage you to explore it further. In this article, I gave an overview of regularization using ridge and lasso regression. b = ridge(y,X,k) returns the ridge regression coefficients b for the linear model y = X +, where: X is an n-by-p matrix y is the n-by-1 vector of observations k is a scalar constant (the ridge parameter) The ridge estimator of is. We present particular variants of RK and RGS for solving this system and derive their convergence rates. Ridge regression #.


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# All the pairs ( x, y ) that satisfy the inequality $2^{\sqrt{sin^{2}x-2sinx+5}\cdot \frac{1}{4^{sin^{2}y}}}\leq 1$  also satisfy the equation :  Option 1) $2|sinx|=3siny$ Option 2) $2 sinx=siny$ Option 3) $sinx=2siny$ Option 4) $sinx=|siny|$

$2^{\sqrt{sin^{2}x-2sinx+5}\cdot \frac{1}{4^{sin^{2}y}}}\leq 1$

$2^{\sqrt{sin^{2}x-2sinx+5}}\leq 2^{2sin^{2}y}$

$\sqrt{{sin^{2}x-2sinx+5}}\leq 2 sin^{2}y$

$\sqrt{{(sinx-1)^{2}+4}}\leq 2 sin^{2}y$

=> $sinx=1$ & $|siny|=1$

So, correct option is (4).

Option 1)

$2|sinx|=3siny$

Option 2)

$2 sinx=siny$

Option 3)

$sinx=2siny$

Option 4)

$sinx=|siny|$

Exams
Articles
Questions


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# Looking for feedback (my new C++ TinyXML Serialization code)

This topic is 4166 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

Greetings, I've spent the last few days working on some code to help automate the process of loading/saving data to XML files. (Using TinyXml in C++.) The code has blown up into something much bigger than what I originally had in mind. In fact, it's probably the most complicated piece of software I've ever written. (And that's something, considering that it's not really that much code, and I've worked on some really big projects at work.) While the code is probably more complicated than it needs to be (with lots of templates and operator overloads) its use is relatively simple. Here's a quick example:
#include "XmlBind.hpp"

using namespace XmlBind;

struct Test
{
int a;
float b;
};

void GetBinding(OuterBinding<Test> &binding)
{
if(!binding.Initialized())
{
binding.Define()
[
Bind("a", &Test::a),
Bind("b", &Test::b)
];
}
}

int main()
{
Test t;
t.a = 42;
t.b = 17.2f;

TiXmlElement element("Test");
ToXml(element, t);
element.Print(stdout, 0);

return 0;
}

And its output:
<Test>
42
17.2
</Test>

Note: You may notice the similarity in the registration code to how a function is registered with LuaBind. This is intentional. I really like that library, and after writing this code, I have even more respect for its authors than I did before. I figured I could do alot worse than to imitate them. (It's also why I chose the name XmlBind, though a google search showed me that there's a library already using that name. Ah well.) Here's the code (and a slightly more complicated demo): XmlBind.hpp demo.cpp It requires both TinyXml and Boost. (Though it just requires some boost headers, it does require foreach.hpp, which isn't in the latest release. You'll have to get that from CVS. You can use the Sourceforge CVS web interface to get it. It's no sweat.) What it can do: 1) Automatically handles the following types: (signed and unsigned where appropriate) char, short, int, long, float, double, bool, and std::string. 2) After registering them, it handles user defined types composed of the basic types or other registered types. (Classes inside of classes is no problem.) 3) Getter/setter class member functions. 4) Standard C++ containers (vector, list, deque.) So, here's what I'm looking for. 1) Is this useful to anyone? 2) Do you see a way to improve the code? 3) Does it compile properly in your favorite C++ compiler? (I've tried VC8 and g++/mingw.) 4) Are there any other features that you think would be worth adding? If you don't feel like commenting in this public forum for whatever reason, feel free to shoot me an email. jessechounard@gmail.com

##### Share on other sites
I've made some substantial changes to the code, based on feedback I've received.

These were the requests that I decided to work on.
1) Don't use BOOST_FOREACH, so that people who don't get Boost from CVS can use the code.
2) Separate the class binding code from the TinyXml code, so that it can be used with other XML libraries, or for other intentions completely.
3) Fix the Getter/Setter functionality so that passing/returning by const reference works properly.

All of those are done.

1) I had some trouble getting boost::bind and std::for_each to work properly with some of the templated functions, which is why I was using BOOST_FOREACH, but I've replaced that with a simple for-loop. Looking deeper into the bind issue is on my todo list, but there's not really a problem with the way it's done now.

2) Separating the Binding code from TinyXml specific code pretty much required a rewrite, but that's okay, as the code is much cleaner for it. Now there's a set of virtual functions in the base class, called DependantFunction# (where # is 1, 2, 3, and 4) that can be overloaded in a derived class to give whatever functionality is required.

3) Fixing this one was pretty simple. Instead of function pointers, I'm now passing and storing Boost::function objects. Now if you pass (or return) by value or reference, everything should compile and run properly. Passing/returning by pointers still isn't supported, though.

4) The software is now released under the MIT (X11) License. Basically, I want people to be free to do anything they want with it. If anybody has a problem with that license and has a recommendation, please let me know.

Here's the new header files and a source for a simple test:
Binding.hpp
TinyXmlBinding.hpp
test.cpp

There's still zero documentation. I'll get to that sooner or later. :)

Thanks to everybody who sent feedback. Please feel free to tell me what you think. (Comment here or email me at jessechounard@gmail.com)


text:
# Laplace operator

In mathematics and physics, the Laplace operator or Laplacian, denoted by Δ, is a differential operator, specifically an important case of an elliptic operator, with many applications in mathematics and physics. In physics, it is used in modeling of wave propagation and heat flow, forming the Helmholtz equation. It is central in electrostatics, anchoring in Laplace's equation and Poisson's equation. In quantum mechanics, it represents the kinetic energy term of the Schrödinger equation. In mathematics, functions with vanishing Laplacian are called harmonic functions; the Laplacian is at the core of Hodge theory and the results of de Rham cohomology.

## Definition

The Laplace operator is a second order differential operator in the n-dimensional Euclidean space, defined as the divergence of the gradient:

$\Delta =\nabla ^{2}=\nabla \cdot \nabla .$

Equivalently, the Laplacian is the sum of all the unmixed second partial derivatives:

$\Delta =\sum _{{i=1}}^{n}{\frac {\partial ^{2}}{\partial x_{i}^{2}}}.$

Here, it is understood that the $x_{i}$ are Cartesian coordinates on the space; the equation takes a different form in spherical coordinates and cylindrical coordinates, as shown below.

In the three-dimensional space the Laplacian is commonly written as

$\Delta ={\frac {\partial ^{2}}{\partial x^{2}}}+{\frac {\partial ^{2}}{\partial y^{2}}}+{\frac {\partial ^{2}}{\partial z^{2}}}.$

As we shall see later, the Laplacian can be generalized to non-Euclidean spaces, where it may be elliptic or hyperbolic. For example, in the Minkowski space the Laplacian becomes the d'Alembert operator or d'Alembertian

$\square ={\partial ^{2} \over \partial x^{2}}+{\partial ^{2} \over \partial y^{2}}+{\partial ^{2} \over \partial z^{2}}-{\frac {1}{c^{2}}}{\partial ^{2} \over \partial t^{2}}.$

The D'Alembert operator is often used to express the Klein-Gordon equation and the four-dimensional wave equation. The sign in front of the fourth term is negative, while it would have been positive in the Euclidean space. The additional factor of c is required because space and time are usually measured in different units; a similar factor would be required if, for example, the x direction was measured in inches, and the y direction was measured in centimeters. Indeed, physicists usually work in units such that c=1 in order to simplify the equation.

### Coordinate expressions

In three dimensions, it is common to work with the Laplacian in a variety of different coordinate systems. Given a function f, in cylindrical coordinates, one has:

$\Delta f={1 \over r}{\partial \over \partial r}\left(r{\partial f \over \partial r}\right)+{1 \over r^{2}}{\partial ^{2}f \over \partial \theta ^{2}}+{\partial ^{2}f \over \partial z^{2}}.$
$\Delta f={1 \over r^{2}}{\partial \over \partial r}\left(r^{2}{\partial f \over \partial r}\right)+{1 \over r^{2}\sin \theta }{\partial \over \partial \theta }\left(\sin \theta {\partial f \over \partial \theta }\right)+{1 \over r^{2}\sin ^{2}\theta }{\partial ^{2}f \over \partial \phi ^{2}}.$

The spherical coordinates Laplacian can also be written in this form:

$\Delta f={1 \over r}{\partial ^{2} \over \partial r^{2}}\left(rf\right)+{1 \over r^{2}\sin \theta }{\partial \over \partial \theta }\left(\sin \theta {\partial f \over \partial \theta }\right)+{1 \over r^{2}\sin ^{2}\theta }{\partial ^{2}f \over \partial \phi ^{2}}.$

### Identities

If f and g are functions, then the Laplacian of the product is given by

$\Delta (fg)=(\Delta f)g+2(\nabla f)\cdot (\nabla g)+f(\Delta g).$

## Laplace-Beltrami operator

The Laplacian can be exteneded to functions defined on surfaces, or more generally, on Riemannian and pseudo-Riemannian manifolds. This more general operator goes by the name Laplace-Beltrami operator. One defines it, just as the Laplacian, as the divergence of the gradient. To be able to find a formula for this operator, one will need to first write the divergence and the gradient on a manifold.

If $g$ denotes the (pseudo)-metric tensor on the manifold, one finds that the volume form in local coordinates is given by

${\mathrm {vol}}_{n}:={\sqrt {|g|}}\;dx^{1}\wedge \ldots \wedge dx^{n}$

where the $dx^{i}$ are the 1-forms forming the dual basis to the basis vectors

$\partial _{i}:={\frac {\partial }{\partial x^{i}}}$

for the local coordinate system, and $\wedge$ is the wedge product. Here $|g|:=|\det g|$ is the absolute value of the determinant of the metric tensor. The divergence of a vector field X on the manifold can then be defined as

${\mathcal {L}}_{X}{\mathrm {vol}}_{n}=({\mbox{div}}X)\;{\mathrm {vol}}_{n}$

where ${\mathcal {L}}_{X}$ is the Lie derivative along the vector field X. In local coordinates, one obtains

${\mbox{div}}X={\frac {1}{{\sqrt {|g|}}}}\partial _{i}{\sqrt {|g|}}X^{i}$

Here (and below) we use the Einstein notation, so the above is actually a sum in i.

The gradient of a scalar function f may be defined through the inner product $\langle \cdot ,\cdot \rangle$ on the manifold, as

$\langle {\mbox{grad}}f(x),v_{x}\rangle =df(x)(v_{x})$

for all vectors $v_{x}$ anchored at point x in the tangent bundle $T_{x}M$ of the manifold at point x. Here, df is the exterior derivative of the function f; it is a 1-form taking argument $v_{x}$. In local coordinates, one has

$\left({\mbox{grad}}f\right)^{i}=\partial ^{i}f=g^{{ij}}\partial _{j}f$

Combining these, the formula for the Laplace-Beltrami operator applied to a scalar function f is, in local coordinates

$\Delta f={\mbox{div grad}}\;f={\frac {1}{{\sqrt {|g|}}}}\partial _{i}{\sqrt {|g|}}\partial ^{i}f$.

Here, $g^{{ij}}$ are the components of the inverse of the metric tensor $g$, so that $g^{{ij}}g_{{jk}}=\delta _{k}^{i}$ with $\delta _{k}^{i}$ the Kronecker delta.

Note that the above definition is, by construction, valid only for scalar functions $f:M\rightarrow {\mathbb {R}}$. One may want to extend the Laplacian even further, to differential forms; for this, one must turn to the Laplace-deRham operator, defined in the next section.

One may show that the Laplace-Beltrami operator reduces to the ordinary Laplacian in Euclidean space by noting that it can be re-written using the chain rule as

$\Delta f=\partial _{i}\partial ^{i}f+(\partial ^{i}f)\partial _{i}\ln {\sqrt {|g|}}.$

When $|g|=1$, such as in the case of Euclidean space, one then easily obtains

$\Delta f=\partial _{i}\partial ^{i}f$

which is the ordinary Laplacian. Using the Minkowski metric with signature (+++-), one regains the D'Alembertian given previously. Note also that by using the metric tensor for spherical and cylindrical coordinates, one can similarly regain the expressions for the Laplacian in spherical and cylindrical coordinates. The Laplace-Beltrami operator is handy not just in curved space, but also in ordinary flat space endowed with a non-linear coordinate system.

Note that the exterior derivative d and -div are adjoint:

$\int _{M}df(X)\;{\mathrm {vol}}_{n}=-\int _{M}f{\mbox{div}}X\;{\mathrm {vol}}_{n}$     (proof)

where the last equality is an application of Stokes theorem. Note also, the Laplace-Beltrami operator is symmetric:

$\int _{M}f\Delta h\;{\mathrm {vol}}_{n}=\int _{M}\langle {\mbox{grad}}f,{\mbox{grad}}h\rangle \;{\mathrm {vol}}_{n}=\int _{M}h\Delta f\;{\mathrm {vol}}_{n}$

for functions f and h.

## Laplace-de Rham operator

In the general case of differential geometry, one defines the Laplace-de Rham operator as the generalization of the Laplacian. It is a differential operator on the exterior algebra of a differentiable manifold. On a Riemannian manifold it is an elliptic operator, while on a pseudo-Riemannian manifold it is hyperbolic. The Laplace-de Rham operator is defined by

$\Delta ={\mathrm {d}}\delta +\delta {\mathrm {d}}=({\mathrm {d}}+\delta )^{2},\;$

where d is the exterior derivative or differential and δ is the codifferential. When acting on scalar functions, the codifferential may be defined as δ = −∗d∗, where ∗ is the Hodge star; more generally, the codifferential may include a sign that depends on the order of the k-form being acted on.

One may prove that the Laplace-de Rahm operator is equivalent to the previous definition of the Laplace-Beltrami operator when acting on a scalar function f; see the Laplace operator article proofs for details. Notice that the Laplace-de Rham operator is actually minus the Laplace-Beltrami operator; this minus sign follows from the conventional definition of the properties of the codifferential. Unfortunately, Δ is used to denote both; which can sometimes be a source of confusion.

### Properties

Given scalar functions f and h, and a real number a, the Laplace-de Rham operator has the following properties:

1. $\Delta (af+h)=a\Delta f+\Delta h\!$
2. $\Delta (fh)=f\Delta h+2\partial _{i}f\partial ^{i}h+h\Delta f$    (proof)


text:
# How to calculate the integral $\int_0^\infty {\rm d}k\, k^{d-1} \frac{1}{\exp(\beta(E_k+\mu))+1}$?

How to calculate the integral $\int_0^\infty {\rm d}k\, k^{d-1} \frac{1}{\exp(\beta(E_k+\mu))+1}$? Here $E_k=\sqrt{a*k^2-b^2}$, and you can think $a, b, d, \mu$ is Real constant.

I don't now how to calculate it, and I use Wolfram Mathematica also can't get any useful information.

• What's $\beta$ ? – Nosrati Jul 30 '18 at 11:09
• Also a real constant. – J.W Kang Jul 30 '18 at 13:15


text:
# The Riemann Hypothesis in One Picture

I wrote this article for machine learning and analytic professionals in general. Actually, I describe a new visual, simple, intuitive method for supervised classification. It involves synthetic data and explainable AI. But at the same time, I describe in layman’s terms the Riemann Hypothesis (RH). Also, I offer a new perspective on the subject for those who attempt to solve the most famous unsolved mathematical problem of all times. I included the Python code to generate the videos, producing some of the most beautiful orbits.

## Introduction

On YouTube, you can find many videos about RH, including mines. Most are produced by mathematicians. Typically, they don’t do a great job at explaining the topic to a large audience. Foremost, I am a machine learning scientist. So my perspective is different. While I try to come up with machine learning techniques that are math-free and model-free (this is also the case here), my datasets require good math knowledge to produce. Also, I spend a lot of time developing ML algorithms to gain insights on advanced math problems.

This article summarizes my most recent progress in this direction. Hopefully, it will entice the reader to further explore RH, its mathematical beauty, and potential applications to ML. It is a continuation in a series of articles: you can find some of the previous ones on Data Science Central, here and here.

## The Riemann Hypothesis in a Nutshell

Possibly the simplest way to introduce RH, yet with enough math to fully grasp the problem and start your own original research, is to start with the Dirichlet eta function η(z) in the complex plane. Here z = σ + it is a complex number. But you don’t need to know anything about complex numbers: z is simply a vector (σ, t). The horizontal axis is the real one, and the vertical axis is the imaginary one. In other words, σ is the real part of z, and t the imaginary one. Also, t represents the time, when plotting an orbit of η(z) for a fixed value of σ.

The η function accepts complex arguments z and returns complex values η(z). The real and imaginary parts of η(z) are respectively:

\begin{align}
\eta_X(z) & = \sum_{k=1}^\infty (-1)^{k+1} \frac{\cos(t\log\sigma)}{k^\sigma}\\
\eta_Y(z)& =  \sum_{k=1}^\infty (-1)^{k+1} \frac{\sin(t\log\sigma)}{k^\sigma}\\
\end{align}

The reason to work with η(z) rather than its sister — the Riemann zeta function ζ(z) — is that the above series converges if σ > 0. To the contrary, the series for ζ(z), where -1 is replaced by +1, converges only for σ > 1. Yet all the interesting action takes place when 0.5 ≤ σ < 1. We also have

\eta(z) = (1-2^{1-z})\prod_{p}\frac{1}{1-p^{-z}} = (1-2^{1-z})\zeta(z),

where the product is overall prime numbers. Again, the product converges only if σ > 1. Thus the η function is used to extend the definition of ζ to σ > 0. The two functions η and ζ have the same roots if 0 < σ < 1. The Riemann Hypothesis states that all these roots lie on the line σ = 0.5, called the critical line. The band 0 < σ < 1 (in the complex plane) is called the critical strip.

## Visualizing the Orbits

Figure 1 visually explains RH. It is the last frame of a Python video, viewable on YouTube, here. The left black dot on the X-axis is the origin; the right one is (1, 0). There is a circular area around the origin that the blue orbit never hits or crosses. Same with the yellow orbit, though the corresponding area is larger and further to the right: the center of the empty zone is not the origin in this case. On the contrary, the red orbit has no such area; indeed the origin is an attraction point.

An empty zone inside an orbit is called a repulsion basin in dynamical systems. Let’s use the word “hole” instead. Since the origin is inside the hole of the blue orbit, η(z) has no root if σ = 0.75. The same is true for any value of σ strictly between 0.5 and 1. This is equivalent to RH! Note that the orbits in Figure 1 are displayed only for 0 < t < T, with T = 1,000. The more you increase T, the more the hole shrinks. In the end, when you display the entire orbit (when T is infinite), the hole shrinks to either a single point (the origin) or an empty step. Whether it is a single point or an empty set, nobody knows. RH states that the hole becomes a single point, not an empty set.

The implications are enormous. There is a one million dollar award to solve this problem, offered by the Clay Institute. Finally, any tiny modification to η(z) results in losing the hole entirely. There is very little leeway here. Other functions with the same behavior exist, but they are not common.

## Visual Supervised Classification

To produce the orbits, I used evenly spaced values of t. If you look at the video, the orbits move at varying velocities depending on t, resulting in uneven point densities. You can correct that, using uneven sampling. Either way, you end up with a set of points in two dimensions. Now you can perform supervised classification: assigning a color to an arbitrary location in the 2D space.

The dataset is a challenging one. This is due to massive cluster overlapping, bounded and unbounded clusters (the yellow one is bounded, the other ones are not), and holes in the blue and yellow clusters. You can use the dataset to benchmark different classification algorithms. For some locations, you can tell that the label is either red or yellow with some probabilities, but not blue. It is similar to saying you don’t know with certainty what disease the patient has, but you can rule out cancer. Bayesian classifiers seem particularly appropriate in this context.

My classification algorithm requires first to map the dataset into an image bitmap. Then you apply convolution filters — an image processing technique — to perform the classification of the entire window (or at least, a large portion of it). You can do it in GPU. It generalizes to more than two dimensions, using tensors. The result is pictured in Figure 2. The full description, including Python code for classification and producing the videos, is available here and here. The Python code also produces the data sets. A video, showing the classification in progress, is available here.

The core of the methodology uses blending colors and transparency levels, to perform the classification. In the end, the classifier is a neural network in disguise: the pixels are the neurons, and the weights in the convolution filter are the parameters of the neural network. If you filter the entire image multiple times, each full iteration corresponds to a layer in a deep neural network. The whole procedure allows you to classify a new point very fast, but it uses a lot of memory.


text:
# Trigonometric equations $\tan\theta-\sec\theta=\sqrt3$

For the following problem(s) I cannot get any answer(s). I would appreciate your help very much.

$$\tan { \theta -\sec { \theta } =\sqrt { 3 } }$$

TI get 30 degrees as the reference angle. What am I doing wrong because the answer is 210 degrees.

Link for my work since the post is not showing up.

Thanks for the help.

• Be sure that your answer makes sense with the quadrant where the angle is placed. – Ángel Mario Gallegos Aug 23 '15 at 21:19
• Posting a picture instead of writing the problem is discouraged and likely to be downvoted, can you make your post self-contained? – Alessandro Codenotti Aug 23 '15 at 21:24
• @MarioG I was thinking that, but usually I find the answer by solving it. Since it equals root3/3 shouldn't the answer be 30 degrees? – Asker123 Aug 23 '15 at 21:29
• The function tangent is not one to one, you are right with $\tan x=\frac{\sqrt{3}}{3}$, but there are two angles not coterminals satisfaying the equation, namely: $30^{\circ}$ and $210^{\circ}$. – Ángel Mario Gallegos Aug 23 '15 at 21:41
• @MarioG Yes but 30 does not work for some reason. – Asker123 Aug 23 '15 at 21:43

$$\tan { \theta -\sec { \theta } =\sqrt { 3 } } \\ \frac { \sin { \theta } }{ \cos { \theta } } -\frac { 1 }{ \cos { \theta } } =\sqrt { 3 } \\ \sin { \theta -\sqrt { 3 } \cos { \theta =1 } } \\$$ divide both side to $2$ $$\frac { 1 }{ 2 } \sin { \theta -\frac { \sqrt { 3 } }{ 2 } } \cos { \theta } =\frac { 1 }{ 2 } \\ \sin { \frac { \pi }{ 6 } \sin { \theta } -\cos { \frac { \pi }{ 6 } \cos { \theta =\frac { 1 }{ 2\\ } } } } \\ \cos { \left( \frac { \pi }{ 6 } +\theta \right) =-\frac { 1 }{ 2 } } \\ \frac { \pi }{ 6 } +\theta =\pm \arccos { \left( -\frac { 1 }{ 2 } \right)+2n\pi =\pm \left( \pi -\frac { \pi }{ 3 } \right) } +2n\pi \\ \theta =\pm \frac { 2\pi }{ 3 } -\frac { \pi }{ 6 } +2n\pi,n\in\Bbb Z\$$

• I don't quite understand the last part. Any help would be appreciated. – Asker123 Aug 27 '15 at 1:44

$$\tan x-\sec x=\sqrt3\iff\tan x+\sec x=-\dfrac1{\sqrt3}$$

Adding we get $\tan x=\dfrac1{\sqrt3}\implies x=n\pi+\dfrac\pi6\ \ \ \ (1)$

Subtracting we get $\sec x=-\dfrac2{\sqrt3}\iff\cos x=-\dfrac{\sqrt3}2=\cos\left(\pi-\dfrac\pi6\right)$

$\implies x=2m\pi\pm\left(\pi-\dfrac\pi6\right)$

i.e, $=(2m+1)\pi-\dfrac\pi6\ \ \ \ (2)$ or $=(2m-1)\pi+\dfrac\pi6\ \ \ \ (3)$

$(1),(2),(3)\implies x=(2r-1)\pi+\dfrac\pi6$

HINT:

Using Weierstrass substitution $$\dfrac{2t}{1-t^2}-\dfrac{1+t^2}{1-t^2}=\sqrt3$$ where $t=\tan\dfrac\theta2$

Rearrange to form a Quadratic equation in $t$

Hint:

the solutions of $\tan x= \dfrac{\sqrt{3}}{3}$ are $x=\dfrac{\pi}{6}+k\pi$ (or in degrees: $x=30°+k 180°$).

Since you have squared to find the final equation, we must test the solutions in the starting equation.

For $x= \dfrac{\pi}{6}$ we find : $$\dfrac{\sqrt{3}}{3}-2\dfrac{\sqrt{3}}{3}=-\dfrac{\sqrt{3}}{3} \ne \sqrt{3}$$ so it is an improper solution.

For $x= \dfrac{\pi}{6}+\pi$ we find : $$\dfrac{\sqrt{3}}{3}+2\dfrac{\sqrt{3}}{3}= \sqrt{3}$$ so this is the principal solution.

• I got that answer and noticed I did something wrong. However I can't seem to find it. – Asker123 Aug 23 '15 at 21:36
• I have corrected my answer. I hope that now it is usefull. – Emilio Novati Aug 24 '15 at 9:47


text:
# How to auto indent latex code with Kile?

Is there a way for Kile to automatically correct the indentation of the latex code of an entire document?

If yes, what is combination of keys (shortcut) or the menus that I should use?

I made a search in Google but I did not find the answer. Thanks in advance!

• ctrl+a to select all text, then TAB to indent. Is this what you mean? – Nico Boni Jun 25 '13 at 16:52
• No, if do I that the entire document gets +2 (or +4) extra spaces. What I want is an automatic way to correct indentation in my latex code. Like the one available in Eclipse (per example) that corrects you Java's indentation when you press CTRL+I. – Flame_Phoenix Jun 25 '13 at 17:03
• I don't know about Kile, but you could try latexindent. – Torbjørn T. Jun 25 '13 at 17:07
• I do not want to indent Java. For that I actually use the listigns package. All I want, is to know if there is a way to auto indent my latex code. As for @Papiro, is my question not clear? – Flame_Phoenix Jun 25 '13 at 17:13
• I see now... what you're looking for is under Tools -> indentation mode. There you'll find a selection of programming languages indentation styles. Unfortunately there is indentation style for LaTeX. So if you want to have this feature you have to write your own style. To do that you should check the "Configuring With Document Variables" part in kate manual (Kile uses the kate part for the text editor). After you have your style, the command to apply the indentation is Tools -> align – Nico Boni Jun 25 '13 at 17:22

I was looking for the same thing, and could not find it. Below is a Kate script I've written to manage indentation for {} \begin and \end, handling escape characters.

The script is submitted in the Master-branch in Kate's repository. I won't update any changes here. If it checks out, they plan to include it in the next release. If you want to try it out, save what is underneath into a file called latex.js. On my system the indentation scripts are in folder: /usr/share/kde4/apps/katepart/script. After you restart Kile, you get a "Latex" indentation option in your menu. Turn that on, and all newly typed text is properly indented, for existing documents you can use "Align" from the menu. Kile's multiple line inserts (e.g. "Bulleted list") are not processed by the indenter, but you can configure the indentation for that in Kile. Multi-line user tags are not properly aligned when inserted, but you can re-align those lines or the entire doc (I have Align under alt-A as a shortcut).

Let me know if you encounter problems.

/** kate-script
* name: Latex
* author: Jeroen Vuurens <jbpvuurens at gmail.com>
* revision: 1
* kate-version: 3.4
* type: indentation
*
* Simple indentation for Latex. This script indents sections within
* \begin{ and \end{ parts, as well as within { and }. Parts after
* an \ escape character are ignored for proper handling of
* \{ \} and \%. In other cases every { is regarded as an extra
* indent, every } as a de-indent, and everything after % is comment.
*/

// specifies the characters which should trigger indent, beside the default '\n'
var triggerCharacters = "{}";
var lineStartsClose = /^(\s*\}|\s*\\end\{)/;

function indent(line, indentWidth, character) {
// not necessary to indent the first line
if (line == 0)
return -2;

var c = document.line(line); // current line

// Search backwards for first non-space, non-comment line.
var prev = line;
while (prev--) {
if (!document.line(prev).match(/^\s*\$|^%/)) {
var previousLine = document.line(prev); // previous non-space line
var prevIndent = document.firstVirtualColumn(prev);
var end = document.lineLength(prev);

var delta = 0;    // count normal openers/closers

// Walk over openers and closers in the remainder of the previous line.
if (previousLine.match(lineStartsClose))
delta++;
var escaped = false;
for (var i = 0; i < end; i++) {
var char = previousLine.charAt(i);
if (char == "\\") { // escaped affects detection of rules
escaped = true;
continue;
}
if (escaped) {
if (char == "b" && end > i + 5 && previousLine.substr(i, 6) == "begin{" ) {
delta++;
} else if (char == "e" && end > i + 3 && previousLine.substr(i, 4) == "end{" ) {
delta--;
}
} else {
if (char == "%") { // ignore rest of line as comment
break;
} if (char == "{") {
delta++;
} else if (char == "}") {
delta--;
}
}
escaped = false;
}

// now count the number of closers in the beginning of the current line.
if (c.match(lineStartsClose))
delta --;
return Math.max(0, prevIndent + delta * indentWidth);
}
}
return 0;
}

// kate: space-indent on; indent-width 2; replace-tabs on;

• Hey, could you post your script as part of the answer? It would be pretty sweet. – Flame_Phoenix Nov 8 '13 at 18:36
• By the way, there are no options for personal messages at this site. – Torbjørn T. Nov 8 '13 at 19:00
• Thanks, it is in the message now. Hope it works for you. – Jeroen Vuurens Nov 9 '13 at 13:08
• I have this by default in Kile now which is fantastic. Thanks for your work on this. I'm just wondering if there is anyway to make it play nicely with the 'bracket' notation which many tree packages use. (forest is one example but it is not the only one.) Or just to make Kile not touch the indentation in forest or other tree environments? It keeps 'realigning' everything which makes it impossible to keep track of the tree and means I have to turn the indentation feature off :(. – cfr Jun 28 '14 at 21:39
• Could you please post an example of code that is incorrectly indented? – Jeroen Vuurens Jun 29 '14 at 14:38

Kile text editor is inherited from the KDE general purpose editor (Kate), which provides an an option to set indentation according to some programming language conventions in:

Tools -> indentation mode

After the mode is set, Tools -> align is used to indent selected code.

Unfortunately there is no indentation style for LaTeX, so you can

1. write your own style (I have no idea how hard this is);

2. ask Kile/Kate devs to provide a LaTeX style (good luck with that);

3. as suggested by Torbjørn T. you can switch to a editor-agnostic solution using a package like latexindent.


text:
## Monday, January 20, 2020 ... //

### Kubera, Czech constitution's man #2, abruptly dies

I do think that the cigarettes "helped" the sudden cardiovascular event to come

The chairman of the Senate, the upper chamber of the Czech Parliament, Mr Jaroslav Kubera abruptly died today (of a heart attack, unconfirmed reports say; ambulance was transferring him to a cardiovascular center), at age of 72. He belonged to the tolerable wing (or at least to the joint connecting the wing with the chest) of ODS, the Klaus-founded party that I supported up to Spring 2019.

Source: Profimedia.cz. Sorry, I couldn't find a picture without a cigarette, such moments were rare

He's been a true veteran of (nationwide and North Bohemian regional) politics. He was chosen as the chairman of the Senate in 2018 and, as promised, he became the uniter and the social glue that dramatically improved the relationships between the main constitutional representatives of Czechia and the parties, too.

## Friday, January 17, 2020 ... //

### Critic of science: universities should protect physics students from Arkani-Hamed's ideas on QFTs

...the ultimate safe spaces...

Mark Goodsell is a young (but habilitated) HEP professor at LPTHE, Paris. He has a not very well-known blog, Real Self Energy, and wrote something about the critics of HEP yesterday:

How to make progress in High Energy Physics
His article starts with an LHCb CERN press release about some... 1-sigma... flavor violation seen by the experiment that is sort of compatible with some other flavor violation excesses at LHCb. That's great and it might indeed be a small step towards making a clear picture of a new, flavor-violating (electron-muon-asymmetric) phenomenon or a new decaying particle.

But even if that will be the case, I am afraid that I will always consider a 1-sigma step as something that is right to ignore – and I would see it in this way even if the flavor-violating new physics is discovered and I reinterpret the history with hindsight.

## Thursday, January 16, 2020 ... //

### The culture of chronic complainers

The decay of the Western society is mostly powered by the postmodern Left. All of us know the typical words associated with this growing, degenerated portion of the society – verbs that must be repeated more often than Allah is repeated by the Muslims. They're words like

discriminate, privilege, oppression, victim, microaggression, offended, diversity, outrage, cancel, racism, Islamophobia, sexism, misogyny, homophobia, transphobia, pedophilophobia
and many others. Clearly, some of these are associated with radicals who still represent at most 15% of the Western nations. But there is one "more civilian" verb that used to be rather normal but whose role in the society has transformed to dangerous proportions and it's the verb
to complain.
Each of us may sometimes complain, there may be good reasons for it but complaints may also be unjustified. My main point is that our societies have transformed to the worshipers of complainers.

## Wednesday, January 15, 2020 ... //

### Craig Wright claims to have received $10 billion ...it's more likely that he is Satoshi... The prices of cryptocurrencies have increased by something of order 10% in a recent day or two. The total capitalization is$238 billion at this moment, the BTC Bitcoin is 66.4% of it i.e. $158 billion. It's followed by Ethereum at$18 billion, Ripple at $10 billion and... BSV (Bitcoin Satoshi Vision) championed and engineered by Craig Wright has become the 4th cryptocurrency by capitalization, over$6 billion right now (since Christmas, its price has quadrupled).
The fifth is the old Bitcoin Cash (it jumped above BSV some hours after this text was written, it's a fierce contest), the sixth is Tether USD, and the seventh is the Litecoin.

The main reason is that Craig Wright, the Australian self-admitted father of the Bitcoin, has submitted the documents claiming that he has received the keys needed to unlock his BTC 1.1 million (well, plus over a million of all other forks of the Bitcoin). Only he can be sure whether he may unlock the coins but a sufficient market was persuaded by the validity of the claim.

## Monday, January 13, 2020 ... //

### Cosmologists neglecting the motion of the Solar System are crackpots

For a year or two, all of us were aware of discrepancies in the measurement of Hubble's constant.

Several updated, comparably plausible methods yield values of $H_0$ that differ by as much as 10%. I think that without the elimination of some of these determinations, we are forced to admit that very many cosmological parameters, perhaps including the age of the Universe, are only known with the precision of 10% or so and the "high-precision cosmology" started in the late 1990s was an illusion, at least at this moment it should be treated as one.

It is possible that the resolution to these strange results will be mundane – some error in some of the methods. It may be very deep, connected with some of the deepest facts about string theory that we still don't understand – some deep insights that will completely change our views about the landscape, swampland, and the cosmological constant in string theory. There exist various strategies by which the people try to wrestle with this new Hubble confusion.

### Jonathan Kerr, a new featured anti-quantum warrior

Dark energy an error? Phys.org reviewed a one-month-old Korean preprint claiming to have made measurements and showing that type IA supernovae's light intensity is correlated with their population age, after all. Such an "astrophysical" drift of the "standard candles" may mimic the "cosmological" behavior attributed to dark energy and dark energy as extracted from the supernovae may therefore be spurious. Of course it's plausible (and would be far-reaching if true), we may hear from others soon... Well, Rubin+Heitlauf have already claimed that the Koreans err in their treatment of distributions and even neglect the motion in the Solar System. Colin et al. (who wrote a similar paper to the Koreans in August 2018) disagree and they even criticize the corrections from the Solar System motion as "arbitrary corrections". Sorry, this is silly. Failing to recognize Galileo's "And yet it moves" is a pretty serious and unquestionable mistake. Galileo isn't an "arbitrary correction". ;-)
We haven't discussed the "mainstream" media's hype about a perfectly deluded critic of quantum mechanics for a few weeks.

Well, Max told us that there is no hiatus. The Telegraph's Sarah Knapton (also reprinted at MSN) chose the title
New theory of quantum mechanics shows matter is not in the eye of the observer
We're promised that a 19-page-long paper (PDF) will soon appear in a "well-respected peer-reviewed journal". By a complete accident, a popular book by the author, Jonathan Kerr, just appeared in the bookstores (click at the icon in the corner) and the Telegraph readers are encouraged to buy it.

## Saturday, January 11, 2020 ... //

### Bitcoin halvening optimistic arguments, an example of wishful thinking

A great portion of the activists' arguments that are completely irrational may be classified as symptoms of a wishful thinking. Czech ex-president Klaus who has spent years by fights against the wishful thinking would also add the term in German where he has used it often, Wunschdenken. In general, these people often conflate two things:

1. What is true or what is likely to happen
2. What would be good for me or for my favorite product or my social system or my political movement
Arguments defending socialism are often of this type because they implicitly assume that people behave in ways that would make socialism work. They just ignore the fact that according to observations or logical arguments, people actually behave very differently.

The mandatory belief that $P\neq NP$ in computer science is arguably another example of a wishful thinking. The actual argument that drives those people towards the fanatical $P\neq NP$ faith is that $P$ couldn't possibly be $NP$ because if $P$ were equal to $NP$, computers could someday replace the thinkers and left-wing intellectuals (who are looking for the path for a traveling salesman when they're not destroying Trump cereals, the job of theirs that they actually care about) would become unemployed.

It mustn't happen that they become useless, the reasoning goes, and therefore $P\neq NP$. However, this argument is totally irrational. It may just happen that $P = NP$ and the exponent and prefactor may even be low and some people's work could really become cheap etc. It could be bad for some people but it doesn't mean that it's untrue or impossible. After all, computers and robots are replacing many of these occupations right now, almost completely independently of someone's belief in $P$ vs $NP$.

### Truth on Ukrainian Boeing, arsonists slowly unmasks itself

Hours after an Ukrainian Boeing 737 crashed near Tehran, I wrote:

I don't know about you but I would think that the Ukrainian aircraft near Tehran - 180 casualties - was taken down as a part of the revenge against the U.S. and "its allies". [...]
Well, it took a day before before the U.S. and Canadian intelligence services (and any sources in the West) joined me.

For another day, Iran denied that the Boeing was downed by any missiles. Finally, on Saturday morning, Iran admitted that the Iranians shot down the airplane, indeed. It was a mistake, we hear. Well, maybe, we don't know and we will probably never know for sure (because any such intentional downing may be claimed to be a mistake and vice versa, any mistaken downing may be claimed as an achievement by a warrior) but it's almost certainly a "mistake" related to the ongoing U.S.-Iranian tension. It's just extremely unlikely that the same country of Iran would see such two major events at almost the same time if they were unrelated to each other.

I hope that this tragedy will help to calm down the situation. 147 Iranians died along with 12 Afghani, 11 Ukrainians, and 6 Westerners. However, many Iranians had some dual citizenship, too. Some ancestry matters to most of us, however, so most of the fatalities were Persian in this sense.

## Thursday, January 09, 2020 ... //

### Dollar: 500th birthday

LHC: ATLAS likelihoods offer theoretical physicists a new way to access the open HEPdata: see CERN, ATLAS
Today, we celebrate the 500th anniversary of the birth of the dollar. Well, it was pronounced and spelled "tolar" back in 1520 but the "dollar" is clearly a result of the evolution of that word. And yes, the dollar was born in a Czech town where 3,500 people live right now, Jáchymov.

The same town is also the source of uraninite that has allowed Marie Sklodowska to discover radium and therefore radioactivity. In 1898, she along with a French assistant and the first major sex toy Pierre Curie discovered radioactivity in that ore; in 1910, she isolated radium (along with polonium) inside these rocks.

If you click at the dirty coin above, you may buy a tolar from 1550 or so – minted a few decades after the 1520 beginning – for as little as \$500.

The BBC published a fun story, Welcome To Jáchymov, the Czech Town That Invented the Dollar. Cutely enough, we learn that no one in the town accepts the dollars today – only crowns, euros, and perhaps roubles seem to be OK – and they haven't seen an American for 3 years. This town which is really the "Mother of All Federal Reserves" should be a tourist magnet for the Yankees on steroids but it isn't.

## Wednesday, January 08, 2020 ... //

### Donald Knuth clarifies why $P=NP$ seems likely

Neutrino physics: IceCube has ruled out an astrophysical explanation of the strange ANITA events, see arXiv, by placing an upper limit on the flux from the would-be sources, thus strengthening the odds that they have observed a stau (supersymmetric partner of the tau lepton $\tilde \tau_R$)
Old men who have been amazing contributors to STEM fields evolve in various ways. When I randomly saw the 599th followup of the Weak Gravity Conjecture – the first hep-th paper posted in 2006 (hep-th/0601001: I didn't have to be particularly fast to get this nice number), it turned out to be a paper titled "Musings..." by Mikhail Shifman who got an even better number arXiv:2001.00101 but it only appeared on a historical archive dedicated to crackpots, senile men, and the public.

Shifman has been great and he's still extremely active but I think that he has lost the ability to follow and evaluate the new ideas from the truly best physicists who are around right now. In many respects, the paper seems as shallow as the whining by many childish fake scientists who just repeat "physics or string theory must be wrong because I don't understand why they're correct, so it must be bad science or no science" and all this amazing garbage often heard from the failers-to-think who pretend to be thinkers.

Thanks to Willie Soon for the video

When I listen to Donald Knuth, it's a totally different experience: even though he sometimes stutters (and if you are annoyed by this superficial imperfection like I am, believe me that our reactions are mostly due to our compassion and intelligence, we just can't help ourselves), he is clearly the intellectual master in the room, despite the fact that the young host Lex Fridman isn't just a journalist. He is developing some AI and autonomous vehicles at MIT. But relatively to Knuth and his depth, Fridman sounds like just another journalist who is interviewing someone who is vastly smarter.

Between 58:02 and 1:10:05 in this 1:46:00 long interview, he addresses his reasons to think that $P=NP$ is more likely than $P\neq NP$ although many people would love to promote the latter to the only allowed faith. I have previously discussed Knuth and $P=NP$ in 2016.

### Fukushima: boars, pheasants, monkeys...

The Fukushima-ruining earthquake took place 8.9 years ago (TRF about Fukushima) and whole irrational nations that live tens of thousands of kilometers away have abused that event as an excuse to abandon the nuclear energy entirely.

Nations such as the so-called Germans will pretend that there are no nuclei sitting in the heart of each atom, no seeds where the characteristic energy changes are one million times higher than the energy associated with the atomic orbitals i.e. the state of the electrons. Given the fact that Germans suck this much in nuclear energy, you must forgive Werner Heisenberg that he wasn't capable of producing the damn bomb.

Meanwhile, like in Chernobyl, animals behave as if this weren't even a local catastrophe, let alone a global one:

Wildlife is doing just fine... (ZME)

Rewilding of Fukushima's human evacuation zone (Frontiers of Ecology and Env.)
James Beasley et al. from University of Georgia have installed lots of camera traps at 106 places in the region around the Japanese nuclear power plant.

## Tuesday, January 07, 2020 ... //

### Bushfires: 183 arrested

...including 24 arsonists: State of Fear?

The Australian bushfires look terrible and half a billion animals may have died (including 18 animals from the homo sapiens species).

The authenticity of this apparent photograph has been disputed, see the comments.

Some sources say that these are the worst Australian bushfires in the living memory. Jennifer Marohasy disagrees and argues that it has been hotter and fires have burnt larger areas, in January 1889 and Summer 1938-1939, respectively (yes, Australia has a summer when we have the winter).

## Monday, January 06, 2020 ... //

### A paper on highly damped quasinormal modes

According to InspireHEP.net, our quasinormal paper with Andy Neitzke joined our "famous" articles according to their terminology (250+ cits; more inclusive Google Scholar shows 302) because a two-year-old Indian thesis was finally scanned.

It was a fun calculation with a rather exciting pre-history and post-history – with lots of interesting technicalities but also some very general conceptual insights about the scientific method as a general approach to the truth. I described much of the context in A Quasinormal Story On Quasinormal Modes but let me add a few more comments about this specific paper.

## Sunday, January 05, 2020 ... //

### Will Trump turn Iraq into a full-blown enemy?

Exactly 50 years ago today, Max Born died. In 2020, it's common for pseudoscientific activists to question the fundamentally probabilistic meaning of quantum mechanics that brought him his Nobel Prize.
Donald Trump has decided to assassinate Iranian Gen. Qassem Soleimani, a widely respected general in Iran whom Trump blames for the death of many Americans and for his plans to murder many more. The U.S. military has fulfilled Trump's order flawlessly. Some extra powerful Iraqi folks were assassinated, too.

Iran vs U.S., perhaps a helpful 101 ten-minute-long video.

I am willing to believe that there is a good justification for the assassination of that Gentleman and even if his personal guilt were insufficient, I think that it may be a good idea for the U.S. to remind Iran who is stronger – before a hypothetical peaceful negotiation takes place. But I am not actually sure that the attack was a great idea. Also, I am not sure whether it was mainly decided as a Trump's idiosyncrasy, or by the deep state, or by the public opinion.

Even more curiously, I am not sure what I would do if I could make such decisions. Well, I didn't really know what to think about the 2003 Iraq War, either.


text:
# Tangents of circles problems

Solve problems related to tangents of circles.

### Problem

is tangent to circle O at point C.
What is the measure of angle, A, C, O?
degree


text:
#### Volume 14, issue 4 (2014)

 Recent Issues
Author Index
 The Journal About the Journal Editorial Board Subscriptions Editorial Interests Editorial Procedure Submission Guidelines Submission Page Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 To Appear Other MSP Journals
$L^{2}$–invariants of nonuniform lattices in semisimple Lie groups

### Holger Kammeyer

Algebraic & Geometric Topology 14 (2014) 2475–2509
##### Abstract
[an error occurred while processing this directive]

We compute ${L}^{2}$–invariants of certain nonuniform lattices in semisimple Lie groups by means of the Borel–Serre compactification of arithmetically defined locally symmetric spaces. The main results give new estimates for Novikov–Shubin numbers and vanishing ${L}^{2}$–torsion for lattices in groups with even deficiency. We discuss applications to Gromov’s zero-in-the-spectrum conjecture as well as to a proportionality conjecture for the ${L}^{2}$–torsion of measure-equivalent groups.

##### Keywords
$L^2$–invariants, lattices, Borel–Serre compactification
##### Mathematical Subject Classification 2010
Primary: 22E40
Secondary: 57Q10, 53C35


text:
When AdSense runs out of inspiration (i.e.: no targeted ads are available), it displays public service ads by default. You can choose to replace this with a custom ad of your own choosing. To do this, you have to put a HTML page somewhere and change the alternate ads settings for the appropriate ad unit:

Instead of the public service ads, I wanted to serve a banner ad to promote our beautiful family vacation home. I created this image a few years ago for an AdWords campaign started by my uncle because he wanted to reach more potential vacation goers.

The 728x79 banner image

I put put up a page with the image at http://www.bigsmoke.us/schuilplaats-banner-ad/. The HTML is very simple:

<html>
<body>
</body>
</html>

Although I put the alternate ad up over a year ago, I was prompted to blog about it because two months ago, for the first time, I suddenly saw the ad actually being serviced on my Dutch HardwoodWiki:


text:
Calculating the $\underset{n \rightarrow \infty}{\lim} \int_{0}^{\infty}f_n(t)dt$

Suppose you have $$f_n: \mathbb{R} \rightarrow \mathbb{R}$$ $$x \mapsto \frac{x^n e^{-x}}{n!}$$

I am asked to find the limit of this function and prove its uniform convergence.

For finding the limit(basically showing that it converges pointwise) I did this:

Using the stirling's formula, I found that $$f_n(x)\sim \frac{x^n e^{-x}}{n^n e^{}-x \sqrt{2 \pi n}} = \left(\frac{x}{n}\right)^n \frac{e^{-x}}{e^{-n}} \frac{1}{\sqrt{2 \pi n}}=\left (\frac{x}{n}\right)^n e^{n-x} \frac{1}{\sqrt{2 \pi n}} = \left(\frac{xe^{1- \frac{x}{n}}}{n}\right)^n \frac{1}{\sqrt{2 \pi n}}$$ Thus it converges to the null function.

For the uniform convergence, I derived the function and searched when it reached its maximum.

The derivative of $f_n(x)$ is $$f'_n(x)=\frac{1}{n!}\left(\frac{nx^{n-1}-x^n}{e^x}\right)$$ Thus is equals to zero whenever $x=n$. This allows me to state that the function $f_n$ reaches it's maximum whenever $x=n$, yet $f_n(n) \sim \frac{1}{\sqrt{2 \pi n}}$

Now I am asked to find $$\underset{n \rightarrow \infty}{\lim} \int_{0}^{\infty}f_n(t)dt$$, but thinking logically, I am most likely asked to integrated the limit function because I proved the uniform convergence. Yet I don't know exactly to what it converges. Can someone help me out?

• Every $f_n$ is a non-negative function with unit integral over $\mathbb{R}^+$. – Jack D'Aurizio Feb 22 '17 at 13:03

I think the goal of the exercise was to give an example of sequence of function which converge pointwisely and uniformly to zero, yet their intergrals are all equal to $1$.
You have $$\int_0^\infty x^{s-1}e^{-s}ds = \Gamma (s),$$ where $\Gamma$ is the Gamma-function. For natural $n$ you can find - by integration by parts - that $\Gamma(n+1)=n!$, hence for your problem $$\forall n\in \Bbb N \quad\int_0^{\infty}\frac{x^ne^{-x}}{n!}dx = 1.$$
Digression. We know that if $f_n\to f$ uniformly on a set $\Omega$, with $f_n$ and $f$ being in $L^1(\Omega)$ and $|\Omega| <\infty$, then $f_n\to f$ in $L^1(\Omega)$. In your exercise, however, we do not have $|\Omega|<\infty$, hence the convergence in $L^1$ is not guaranteed and we build an explicit counterexample.


text:
eulerian2 - Maple Help

combinat

 eulerian2
 second order Eulerian numbers

 Calling Sequence eulerian2(n, k)

Parameters

 n, k - non-negative integers

Description

 • The eulerian2(n, k) command counts the number of permutations ${\mathrm{pi}}_{1}{\mathrm{pi}}_{2}\mathrm{...}{\mathrm{pi}}_{2n}$ of the multi-set $\left[1,1,2,2,\mathrm{...},n,n\right]$ having two properties:
 1 All numbers between the two occurrences of $m$ are greater than $m$.
 2 There are k ascents, namely, k places where ${\mathrm{pi}}_{j}<{\mathrm{pi}}_{j+1}$.
 • This function can be computed via the recurrence

$\mathrm{eulerian2}\left(n,k\right)=\left(k+1\right)\mathrm{eulerian2}\left(n-1,k\right)+\left(2n-k-1\right)\mathrm{eulerian2}\left(n-1,k-1\right)$

 • Second-order Eulerian numbers are important because of their connection with Stirling numbers. For integers $m$ and $0\le n$ we have:

$\mathrm{Stirling2}\left(m,m-n\right)={\sum }_{k=0}^{n}\mathrm{eulerian2}\left(n,k\right)\left(\genfrac{}{}{0}{}{m+n-1-k}{2n}\right)$

 $\left|\mathrm{Stirling1}\left(m,m-n\right)\right|$ = ${\left(-1\right)}^{n}\mathrm{Stirling1}\left(m,m-n\right)$ = ${\sum }_{k=0}^{n}\mathrm{eulerian2}\left(n,k\right)\left(\genfrac{}{}{0}{}{m+k}{2n}\right)$

Examples

 > $\mathrm{with}\left(\mathrm{combinat}\right):$
 > $\mathrm{Matrix}\left(\left[\mathrm{seq}\left(\left[\mathrm{seq}\left(\mathrm{eulerian2}\left(n,k\right),k=0..5\right)\right],n=0..5\right)\right]\right)$
 $\left[\begin{array}{cccccc}{1}& {0}& {0}& {0}& {0}& {0}\\ {1}& {0}& {0}& {0}& {0}& {0}\\ {1}& {2}& {0}& {0}& {0}& {0}\\ {1}& {8}& {6}& {0}& {0}& {0}\\ {1}& {22}& {58}& {24}& {0}& {0}\\ {1}& {52}& {328}& {444}& {120}& {0}\end{array}\right]$ (1)

References

 R.L. Graham, D.E. Knuth, O. Patashnik, "Concrete Mathematics", Addison-Wesley, Reading, Mass., 1989.


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Highly Optimized Object-oriented Many-particle Dynamics -- Blue Edition
hoomd_script.pair Namespace Reference

Commands that create forces between pairs of particles. More...

## Classes

class  coeff
Defines pair coefficients. More...
class  nlist
Interface for controlling neighbor list parameters. More...
class  pair
Generic pair force. More...
class  lj
Lennard-Jones pair force. More...
class  gauss
Gaussian pair force. More...
class  slj
Shifted Lennard-Jones pair force. More...
class  yukawa
Yukawa pair force. More...
class  ewald
Ewald pair force. More...
class  cgcmm
CMM coarse-grain model pair force. More...
class  table
Tabulated pair force. More...
class  morse
Morse pair force. More...
class  dpd
NVT Integration via Dissipative Particle Dynamics pair force. More...
class  dpd_conservative
DPD Conservative pair force. More...
class  eam
EAM pair force. More...
class  dpdlj
NVT Integration via Dissipative Particle Dynamics pair force with a Lennard Jones conservative force. More...
class  force_shifted_lj
Force-shifted Lennard-Jones pair force. More...

## Detailed Description

Commands that create forces between pairs of particles.

Generally, pair forces are short range and are summed over all non-bonded particles within a certain cutoff radius of each particle. Any number of pair forces can be defined in a single simulation. The net force on each particle due to all types of pair forces is summed.

Pair forces require that parameters be set for each unique type pair. Coefficients are set through the aid of the coeff class. To set this coefficients, specify a pair force and save it in a variable

 my_force = pair.some_pair_force(arguments...)

Then the coefficients can be set using the saved variable.

 my_force.pair_coeff.set('A', 'A', epsilon=1.0, sigma=1.0)
my_force.pair_coeff.set('A', 'B', epsilon=1.0, sigma=2.0)
my_force.pair_coeff.set('B', 'B', epsilon=2.0, sigma=1.0)

This example set the parameters epsilon and sigma (which are used in pair.lj). Different pair forces require that different coefficients are set. Check the documentation of each to see the definition of the coefficients.