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The link included is a template. The word Abacus derived from the Greek word ‘abax’, which means ‘tabular form’. All types of Quadrilaterals have their own unique properties. Area and Perimeter of Quadrilaterals DRAFT. Find the area and perimeter of a right triangle with legs 3 cm and 4 cm and hypotenuse 5 cm. Area of an ellipse. Stewart’s Theorem Proof & Stewart’s Formula, Binomial Theorem Proof | Derivation of Binomial Theorem Formula, What is Quadrilateral Theorem? What is the formula for finding area of a rectangle? 3. It has two pairs of equal opposite sides parallel to each other. This blog talks about the different quadrilaterals, their properties, and formulae to determine their area and perimeter. Learn about Euclidean Geometry, the different Axioms, and Postulates with Exercise Questions. Using pizza to solve math? Area and Perimeter of Quadrilaterals DRAFT. Median of the trapezium is the line segment, which is halfway between the two bases. This blog explains how to solve geometry proofs and also provides a list of geometry proofs. arrow_back Back to Area of Quadrilaterals Area of Quadrilaterals: GCSE Maths Specification and Awarding Body Information. The diagonal is the line that joins the opposite vertices. Area And Perimeter Of Quadrilateral - Displaying top 8 worksheets found for this concept. Area of a quadrilateral on a grid. World cup math. Find the area and perimeter of a rectangle with a length of 12 inches and a width of 15 inches. Squares are basically special rectangles, so … Play this game to review Geometry. Building a solid understanding of the different types of quadrilaterals, their properties, attributes and relationships is a vital first step toward introducing quadrilaterals whether you are classifying quadrilaterals as part of a geometry unit, teaching a unit on area and perimeter, discussing int Links to the relevant section of the GCSE Maths Specification, together with information and resources from each of the Awarding Bodies. Area formulas of Quadrilateral: Area of a trapezoid Formulas: $$\frac{a+b}{2} \times h$$ a, b is base and h is height; Area of a rectangle Formulas: $$l \times w$$ l is length, w is width; Area of a square Formulas: $$a^2$$ a is length of side; Area of a parallelogram Formulas: $$l \times w … Speed, Acceleration, and Time Unit Conversions. Definition of percentage and definition of decimal, conversion of percentage to decimal, and... Robert Langlands: Celebrating the Mathematician Who Reinvented Math! 0. Here are some tips you might want to know. Area of an arch given height and radius. 4 months ago. Area of a circle. Area of an arch given angle. Proof Ceva’s Theorem Formula, Mid Point Theorem Proof – Converse | Mid Point Theorem Formula, What is Apollonius Theorem? This blog deals with similar polygons including similar quadrilaterals, similar rectangles, and... Operations and Algebraic Thinking Grade 3. Complete Guide: Learn how to count numbers using Abacus now! By Fintan Douglas ... Clive has three homework tasks on perimeter, area and volume, each getting increasingly difficult. Calculate the perimeter of special quadrilaterals like squares, rectangles, parallelograms, trapezoids, kites and rhombuses by adding up the four side lengths presented as integers ≤ 20 in Level 1 and ≥ 10 in Level 2. The diagonals of a square are also equal in length. Area of parallelogram = Base x height = bh. Perimeter of a rectangle \(= 2 \times (l + b)$$. List of all Basic Profit and loss Formulas, List of all Basic Area & Surface area Formulas, Copyright © 2020 Andlearning.org 0. kblack. Mention the applications of quadrilaterals. Complete Guide: Construction of Abacus and its Anatomy. Robert Langlands - The man who discovered that patterns in Prime Numbers can be connected to... Access Personalised Math learning through interactive worksheets, gamified concepts and grade-wise courses, Frequently Asked Questions (FAQs) of Quadrilaterals. Rectangle formula – Area and perimeter of a rectangle. Cuemath, a student-friendly mathematics and coding platform, conducts regular Online Live Classes for academics and skill-development, and their Mental Math App, on both iOS and Android, is a one-stop solution for kids to develop multiple skills. All sides of a square are equal in length. Learn concepts, practice example... What are Quadrilaterals? Area of an arch given height and chord. Square. Learn about the 7 Quadrilaterals, their properties. Finding diameter and radius. Area of the Parallelogram $$= b \times h$$, Area of a trapezium $$= ½ (a + b) \times h$$, Area of a rhombus $$= P \times \frac{Q}{2}$$, “The perimeter of any closed geometrical object is defined as the distance around that object.”. 2. Multiply one side by itself to find the area of a square. A PowerPoint lesson that focuses on the objective of calculating the area of quadrilaterals from the Year 6 WRM planning. 5th - 6th grade . The interior angles of a trapezium add up to 360°. A Quadrilateral has some basic properties i.e. Similar: Area of right triangles Area of triangles, parallelograms, trapezoids The diagonal of the Rectangle creates two pairs of scalene triangles. Two levels of difficulty with 5 worksheets each by kblack. Preparing For USAMO? Flattening the curve is a strategy to slow down the spread of COVID-19. The history of Ada Lovelace that you may not know? Learn about Parallel Lines and Perpendicular lines. Perimeter of a Quadrilateral T1L1S1 4) 7) 1) Printable Worksheets @ www.mathworksheets4kids.com Perimeter = Perimeter = Perimeter = Perimeter = Perimeter = Perimeter = Perimeter = Perimeter = Perimeter = Find the perimeter of each quadrilateral. Calculating Perimeter and Area Common formulas (equations) include: P = 2l + 2w perimeter of a rectangle A = l + w area of a square or rectangle E = mc2 Albert Einstein’s famous formula for calculating energy. Edit. Find the area of a parallelogram with a base of 30 m and a height of 25 m. In real life, many objects resemble Quadrilaterals. By … Formula for Perimeter To find the perimeter of any quadrilateral, add the lengths of its four sides. Learn about the different uses and applications of Conics in real life. Showing top 8 worksheets in the category - Area And Perimeter Of Quadrilaterals. Area And Perimeter Of Quadrilaterals Some of the worksheets for this concept are 6 area of triangles and quadrilaterals, Perimeter and area of quadrilaterals a, Quadrilateral area l1es1, Area of squares rectangles and parallelograms, Area of triangles and quadrilaterals, Grade 4 geometry work, Formulas for perimeter area surface volume, 9 area perimeter and volume mep y9 practice book b. If both pairs of opposite sides of the quadrilateral are parallel, such a quadrilateral is called parallelogram. Area of a quadrilateral. Parallel and Perpendicular Lines in Real Life. In math, Quadrilateral is a very important topic which is helping to improve scores in the exam. In order to work out the area of quadrilaterals with precision, children must first identify the type of quadrilateral by observing the congruence in sides and angles and then substitute the given lengths in the appropriate formulas. Would you like to check out some funny Calculus Puns? Worksheets > Math > Grade 6 > Geometry > Area of triangles & quadrilaterals. If the length of the rectangle is L and breadth is B then, Area of a rectangle = Length × Breadth or L × B; Perimeter of rectangle = 2 × (L + B) These practice questions will help you solidify the properties of rectangles. Angle Bisector Theorem Formula, What is Stewart’s Theorem? Previously used for an advanced 5th grade math course. The Great Mathematician: Hypatia of Alexandria, was a famous astronomer and philosopher. The abacus is usually constructed of varied sorts of hardwoods and comes in varying sizes. As usual his answers are riddled with mistakes and it’s down to you to correct them, explaining where he’s gone wrong. Area of complex figures (includes quadrilaterals and triangles) Parts of a circle (radius, diameter, chord) Area and circumference of a circle. We are going to share Quadrilateral Formulas for the student who is studying in the class of 5, 6, 7, 8, 9, 10, 11, and 12. h₁ & h₂ - perpendicular heights Let P = perimeter and s (n) = a measured side. 4 months ago. Properties of a Rectangle Some of the worksheets displayed are 6 area of triangles and quadrilaterals, Perimeter and area of quadrilaterals a, Quadrilateral area l1es1, Area of squares rectangles and parallelograms, Area of triangles and quadrilaterals, Grade 4 geometry work, Formulas for perimeter area surface volume, 9 area perimeter … Fermat’s Last... John Napier | The originator of Logarithms. Different types, Formulae, and Properties. The sum of the all sides of the trapezium is called the perimeter of the trapezium. Area of the rectangle = Length × Breadth; Perimeter of the Rectangle = Length + Length + Breadth + Breadth> = 2 $$\times$$ Length + 2 × Breadth. Quadrilaterals and its area are mostly used in the field of architecture, agriculture, designing, and navigation to find the actual distance with precision. Enter the values of sides a, b, c and d into the perimeter of quadrilateral calculator and click calculate. Trapeziums have two opposite unequal parallel sides. If you have any questions regarding Quadrilateral formulas please let me know through comment, mail, or social media. Area is the number of square units it takes to cover a two dimensional shape. It is classif This blog deals with various shapes in real life. Lesson presentations and activities. The opposite sides of a Rectangle are parallel and equal. 68% average accuracy. Area of a cyclic quadrilateral. The two adjacent sides are equal to each other. Below are six versions of our grade 6 math worksheet providing practice on determining the area of triangles & quadrilaterals. Understand the Cuemath Fee structure and sign up for a free trial. cm to m, km to miles, etc... with... Why you need to learn about Percentage to Decimals? The sum of the sides of the parallelogram is the perimeter of the parallelogram. Are you going to pay extra for it? If you want to become very intelligent in math then you should remember the Quadrilateral Formulas to resolve Quadrilateral related problems. Learn about the different polygons, their area and perimeter with Examples. Grab hold of our free area of quadrilaterals worksheets and get stupendous practice in finding the area of a 4-sided shapes! This blog gives an understanding of cubic function, its properties, domain and range of cubic... How is math used in soccer? Learn Polynomial Factorization. Mathematics. Area of shapes on grids. Perimeter Formula. Perimeter of parallelogram = 2 ( b+ c ) Area of parallelogram = product of any two adjacent sides x sine of the included angle = b x c x sin B. Ever wondered how soccer strategy includes maths? The formula for the perimeter, area and diagonal of the square Perimeter formula for … Algebra in Perimeter of Quadrilaterals | Level 2. These worksheets are pdf files.. Written by Suganya Balaji, Cuemath Teacher. There are millions of students looking for Quadrilateral formulas that why we shared Quadrilateral formulas below. Calculating the Area and Perimeter with... Charles Babbage | Great English Mathematician. This is the currently selected item. Area of a quadrilateral when one diagonal and the lengths of the perpendiculars from its opposite vertices to this diagonal are given = ½ × Diagonal × Sum of the lengths of the perpendiculars In the figure alongside of the quadrilateral PQRS, area = ½ × PR (QY + SX). Learn area and perimeter quadrilaterals with free interactive flashcards. Opposites sides of the squares are always parallel. 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# Confidence-based Performance Estimation (CBPE)

This page describes the algorithms that NannyML uses to estimate post-deployment model performance. At the core of these algorithms NannyML leverages the confidence of the predictions. For classifiers, this confidence is expressed by the probability that an observation belongs to a class. These probabilities are then used to estimate a selected performance metric for a set of observations. Provided that the monitored model returns well-calibrated probabilities (or probabilities that can get well-calibrated in post processing) and a large enough set of observations, CBPE will accurately estimate performance.

## CBPE algorithm

### Binary classification

A binary classification model typically returns two outputs for each prediction - a class (binary) and a class probability prediction (sometimes referred to as score). The score provides information about the confidence of the prediction. A rule of thumb is that, the closer the score is to its lower or upper limit (usually 0 and 1), the higher the probability that the classifier’s prediction is correct. When this score is an actual probability, it can be directly used to estimate the probability of making an error. For instance, imagine a high-performing model which, for a large set of observations, returns a prediction of 1 (positive class) with a probability of 0.9. It means that for approximately 90% of these observations, the model is correct, while for the other 10% the model is wrong. Assuming properly calibrated probabilities, confusion matrix elements can be estimated and then used to calculate any performance metric. Algorithms for estimating one of the simplest metrics (accuracy) and of the most complex (ROC AUC) are described below. Common notations used in the sections below are the following:

$$n$$ - number of analyzed observations/predictions,

$$\hat{p} = Pr(y=1)$$ - monitored model probability estimate,

$$y$$ - target label, in binary classification $$y\in{\{0,1\}}$$,

$$\hat{y}$$ - predicted label, in binary classification $$\hat{y}\in{\{0,1\}}$$.

Let’s start with accuracy as it should help us to quickly build the intuition. Accuracy is simply the ratio of correct predictions to all predictions. It can be therefore expressed as:

$Accuracy = \frac{TP+TN}{TP+FP+TN+FN} = \frac{TP+TN}{n}$

Since the number of observations ($$n$$) is known, the task comes down to estimating True Positives (TP) and True Negatives (TN). The algorithm runs as follows:

1. Get $$j$$-th prediction from $$\mathbf{\hat{p}}$$, denote $$\hat{p}_j$$, and predicted label from $$\mathbf{\hat{y}}$$, denote $$\hat{y}_j$$.

2. Calculate the estimated probability that the prediction is false:

$P(\hat{y} \neq y)_{j} = |\hat{y}_{j} - \hat{p}_{j}|$
1. Calculate the estimated probability that the prediction is correct:

$P(\hat{y} = y)_{j}=1-P(\hat{y} \neq y)_{j}$
1. Calculate estimated confusion matrix element required for the metric:

$\begin{split}TP_{j}=\begin{cases}P(\hat{y} = y)_{j},\qquad \ \hat{y}_{j}=1 \\ 0, \qquad \qquad \qquad \hat{y}_{j}=0 \end{cases}\end{split}$
$\begin{split}TN_{j}=\begin{cases} 0,\qquad \qquad \qquad \hat{y}_{j}=1 \\ P(\hat{y} = y)_{j},\qquad \ \hat{y}_{j}=0\end{cases}\end{split}$
1. Get estimated confusion matrix elements for the whole set of predictions, e.g. for True Positives:

${TP} = \sum_{j=1}^{n} {TP}_{j}$
1. Estimate accuracy:

$accuracy = \frac{TP+TN}{n}$

The first three steps are enough to estimate expected accuracy. Once the probabilities of the predictions being correct are known, all that needs to be done is taking the mean of these probabilities. The steps after are there to show how the confusion matrix elements are estimated, which are needed for other confusion-matrix-based metrics like precision, recall etc. Notice, that for models returning a positive class when the probability is larger than 50%, CBPE cannot estimate accuracy lower than 0.5. This is because CBPE works only for models that estimate probabilities well and a model that is worse than a random guess certainly does not do this. Read more in Limitations.

A different type of metric is ROC AUC. To estimate it one needs values of confusion matrix elements (True Positives, False Positives, True Negatives, False Negatives) for a set of all thresholds $$t$$. This set is obtained by selecting a subset of $$m$$ unique values from the set of probability predictions $$\mathbf{\hat{p}}$$ and sorting them increasingly. Therefore $$\mathbf{t}=\{\hat{p_1}, \hat{p_2}, ..., \hat{p_m}\}$$ and $$\hat{p_1} < \hat{p_2} < ... < \hat{p_m}$$ ($$1 < m \leq n$$).

The algorithm for estimating ROC AUC runs as follows:

1. Get $$i$$-th threshold from $$\mathbf{t}$$ ($$i$$ ranges from 1 to $$m$$), denote $$t_i$$, .

2. Get $$j$$-th prediction from $$\mathbf{\hat{p}}$$ ($$j$$ ranges from 1 to $$n$$), denote $$\hat{p}_j$$.

3. Get the predicted label by thresholding the probability estimate:

$\begin{split}\hat{y}_{i,j}=\begin{cases}1,\qquad \hat{p}_j \geq t_i \\ 0,\qquad \hat{p}_j < t_i \end{cases}\end{split}$
1. Calculate the estimated probability that the prediction is false:

$P(\hat{y} \neq y)_{i,j} = |\hat{y}_{i,j} - \hat{p}_{j}|$
1. Calculate the estimated probability that the prediction is correct:

$P(\hat{y} = y)_{i,j}=1-P(\hat{y} \neq y)_{i,j}$
1. Calculate the confusion matrix elements probability:

$\begin{split}TP_{i,j}=\begin{cases}P(\hat{y} = y)_{i,j},\qquad \hat{y}_{i,j}=1 \\ 0,\qquad \qquad \qquad \thinspace \hat{y}_{i,j}=0 \end{cases}\end{split}$
$\begin{split}FP_{i,j}=\begin{cases}P(\hat{y} \neq y)_{i,j},\qquad \hat{y}_{i,j}=1 \\ 0,\qquad \qquad \qquad \thinspace \hat{y}_{i,j}=0 \end{cases}\end{split}$
$\begin{split}TN_{i,j}=\begin{cases} 0,\qquad \qquad \qquad \thinspace \hat{y}_{i,j}=1 \\ P(\hat{y} = y)_{i,j},\qquad \hat{y}_{i,j}=0\end{cases}\end{split}$
$\begin{split}FN_{i,j}=\begin{cases} 0,\qquad \qquad \qquad \thinspace \hat{y}_{i,j}=1 \\ P(\hat{y} \neq y)_{i,j},\qquad \hat{y}_{i,j}=0\end{cases}\end{split}$
1. Calculate steps 2-6 for all predictions in $$\hat{\mathbf{p}}$$ (i.e. for all $$j$$ from 1 to $$n$$) so that confusion matrix elements are calculated for each prediction.

2. Get estimated confusion matrix elements for the whole set of predictions, e.g. for True Positives:

${TP}_i = \sum_{j=1}^{n} {TP}_{i,j}$
1. Calculate estimated true positive rate and false positive rate:

${TPR}_i = \frac{{TP}_i}{{TP}_i + {FN}_i}$
${FPR}_i = \frac{{FP}_i}{{FP}_i + {TN}_i}$
1. Repeat steps 1-9 to get $$TPR$$ and $$FPR$$ for all thresholds $$\mathbf{t}$$ (i.e. for $$i$$ from 1 to $$m$$). As a result, get vectors of decreasing true positive rates and true negative rates, e.g.:

$\mathbf{TPR} = ({TPR}_1, {TPR}_2, ..., {TPR}_m)$
1. Calculate ROC AUC.

### Multiclass Classification

A multiclass classification model outputs prediction labels (predicted class) and probabilities for each class. This means that when there are three classes, for example A, B and C, the model output should contain four pieces of information - the predicted class (e.g. A) and three probabilities, one for each class. Assuming these probabilities are well calibrated, they can be used to estimate performance metrics. As an example, let’s describe the process for macro-averaged precision. Let’s use $$c$$ to denote total number of classes and $$k$$ to indicate a particular class. We can stick to previously introduced notation keeping in mind that $$y$$ and $$\hat{y}$$ are not binary anymore and take one of $$c$$ values.

The algorithm runs as follows:

1. Estimate precision for each class separately, just like in binary classification. Transform vector of multiclass predictions $$\mathbf{\hat{y}}$$ to binary vector relevant for the class $$k$$ i.e. $$\mathbf{\hat{y}_k}$$ and take corresponding predicted probabilities $$\mathbf{\hat{p}_k}$$:

${precision}_k = precision(\mathbf{\hat{y}_k}, \mathbf{\hat{p}_k})$

where:

$\begin{split}\hat{y}_{k,j} = \begin{cases} 1, \qquad \hat{y}_{j}=k \\ 0, \qquad \hat{y}_{j} \neq k\end{cases}\end{split}$
2. Calculate macro-averaged precision:

${precision} = \frac{1}{c} \sum_{k=1}^{c} {precision}_{k}$

Recall, f1, specificity and one-vs-rest ROC AUC are estimated in the exact same way. Multiclass accuracy is just estimated as the mean of predicted probabilities corresponding to the predicted classes.

## Assumptions and Limitations

CBPE is unbiased estimator of performance assuming:

The monitored model returns well-calibrated probabilities.

Well-calibrated probabilities allow to accurately estimate confusion matrix elements and thus estimate any metric based on them. A model that returns perfectly calibrated probabilities is an ideal probabilistic model (Bayes Classifier). One may ask if there’s anything to estimate if the model is perfect? Performance of an ideal model is usually far from being equal to the maximum possible value for a given metric. It is lower because of the irreducible error originating from classes not being perfectly separable given the available data. In reality, many models are very close to a Bayes Classifier and close enough for CBPE to work. Usually good models (e.g. ROC AUC>0.9) return well-calibrated probabilities, or scores that can be accurately calibrated in postprocessing. There are also models considered as poor (with performance just better than random) that still return well-calibrated probabilities. This happens when dominant share of the error is the irreducible error i.e. when there is not enough signal in the features to predict the target. Performance of all models change in time as a result of changes in the distributions of inputs (X). The good news is that CBPE will remain accurate under data drift i.e. when distribution of inputs P(X) changes but probability of target given inputs P(Y|X) stays the same (or in other words - if probabilities remain well-calibrated). An example might be a situation when one segment of population starts to dominate in the data. In medical applications we might have training data which is balanced with respect to patients’ age but in production mainly older patients are analyzed. Performance of the monitored model will probably change in such case and this change will be noticed by CBPE.

There is no data drift to previously unseen regions in the input space.

The algorithm will most likely not work if the drift happens to subregions previously unseen in the input space. In such case the monitored model was not able to learn P(Y|X). Using the same example, this will happen when the model was trained on young people only but then it is applied to middle-aged people. If the true relationship between age and the target is nonlinear, most models will not estimate probability correctly on previously unseen data. This also depends on the type of the algorithm used and its ability to extrapolate estimation of probabilities. For example Random Forest model estimated probability will remain constant and equal to the one in the closest input space region covered by training data. In our case this will be the probability for the oldest patients of youngsters. On the other hand, Logistic Regression will learn a parameter (coefficient) between age and the target and then extrapolate linearly. Provided that true underlying relationship is also linear, Logistic Regression model will estimate probability correctly even for unseen age ranges.

There is no concept drift.

While dealing well with data drift, CBPE will not work under concept drift i.e. when P(Y|X) changes. Except from very specific cases, there is no way to identify concept drift without any ground truth data.

The sample of data used for estimation is large enough.

CBPE calculates expected values of confusion matrix elements. It means it will get less accurate with decreasing sample size. On top, when the sample size is small it is not just CBPE that won’t work well, but the calculated metric (when targets are available) won’t be reliable either. For example, if we evaluate a random model (true accuracy = 0.5) on a sample of 100 observations, for some samples we can get accuracy as high as 0.65. Read more about it here.

## Appendix: Probability calibration

In order to accurately estimate the performance from the model scores, they need to be well calibrated. If a classifier assigns a probability of 0.9 for a set of observations and 90% of these observations belong to the positive class, we consider that classifier to be well calibrated with respect to that subset. Most predictive models focus on performance rather than on probability estimation, therefore their scores are rarely calibrated. Examples of different models and their calibration curves are shown below 1:

Probabilities can be calibrated in post-processing. NannyML uses isotonic regression to calibrate model scores 1 2. Since some of the models are probabilistic and their probabilities are calibrated by design, NannyML will first check if calibration is really required. This is how NannyML does it:

1. First the reference data gets partitioned using a stratified shuffle split 3 (controlled for the positive class). This partitioning will happen three times, creating three splits

2. For each split, a calibrator is fitted on the train folds and predicts new probabilities for the test fold.

3. The Expected Calibration Error (ECE) 4 for each of the test folds is calculated for raw and calibrated probabilities.

4. The average ECE from all test folds for raw and calibrated probabilities is calculated.

5. If the mean ECE for calibrated probabilities is lower than the mean ECE for raw probabilities then it is beneficial to calibrate probabilities. Calibrator is fitted on the whole reference set and probabilities get calibrated on the set that is subject to analysis. Otherwise, raw probabilities are used.

For multiclass models the logic above is applied to each class-probability pair separately (so probabilities for some classes might get calibrated while for others not). At the end, probabilities are normalized so they sum up to 1.

Calibrating probabilities is yet another reason why NannyML requires reference data that is not a training set of the monitored model. Fitting a calibrator on model training data would introduce bias 1.

References

1(1,2,3)

https://scikit-learn.org/stable/modules/calibration.html

2

https://scikit-learn.org/stable/modules/generated/sklearn.isotonic.IsotonicRegression.html

3

https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.StratifiedShuffleSplit.html

4

Naeini, Mahdi Pakdaman, Gregory Cooper, and Milos Hauskrecht: “Obtaining well calibrated probabilities using bayesian binning.” Twenty-Ninth AAAI Conference on Artificial Intelligence, 2015.

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Browse Questions

# VSEPR notation of $PCl_5, H_2O$ and $ICl_4^-$ are

Can you answer this question?

$AX_5\qquad AX_2E_2\qquad AX_4E_2$
$PCl_5$ is $AX_5, H_2O$ is $AX_2E_2$ and $[ICl_4]^-$ comes under
Hence (a) is the correct answer.
answered Dec 9, 2013


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# aliquote

## < a quantity that can be divided into another a whole number of time />

I really like the keywordprg mapping in Vim. It’s the capital K that you press to get help for the word under the cursor (known as cword in Vim parlance). If you use an LSP client (builtin Neovim LSP, Coc or ALE, for example), you likely use it everyday since it is generally mapped onto the Hover method of the LSP server.

When not in an LSP-aware environment, I write my own keywordprg. You can find plenty of nice ideas on the web. Since I use some programming languages that don’t come with an LSP yet, I have the following in my after/ftplugin/stata.vim settings, for instance:

setlocal keywordprg=stata_help

As mentioned in a footnote of one my older posts, I query Stata’s online documentation when working from TUIs. In this case, stata_help is just a wrapper shell script for links https://www.stata.com/help.cgi\?"${1}". This way, when I’m over a Stata command, I just press K and I get its online help in a tab, with a proper text-mode browser. Note that I prefer Links over Lynx for text-mode browsing the internet. This morning I wrote a little Lisp script using Roswell, since I wanted to try it for a moment. I already configured Roswell to fetch the latest release of SBCL on my laptop because Ubuntu’s default version is pretty outdated. It works great but I never use the scripting facilities that Roswell offers. I wrote two versions of a small utility that allows to fetch the relevant documentation from Lispworks Hyperspec online documentation. The first version was a simple lookup through the documentation to retrieve the URL corresponding to the symbol at point and to return a system call to open it in the default browser. The lookup step is performed thanks to the hyperspec package. I used ASDF builtin facilities to launch external program (uiop:run-program) but one could also makes use of SBCL’s builtin extensions (sb-ext:run-program). Finally, I decided to just return the URL to the standard output, in case I need to reuse the script for another purpose. Both versions are shown below: #!/bin/sh #|-*- mode:lisp -*-|# #| exec ros -Q -- "$0" "$@" |# (with-output-to-string (*standard-output*) (asdf:load-system :hyperspec)) ;; (defun main (cword &rest argv) ;; (declare (ignore argv)) ;; (uiop:run-program ;; (list "/usr/bin/xdg-open" ;; (funcall #'hyperspec:lookup (read-from-string cword))) ;; :output nil)) (defun main (cword &rest argv) (declare (ignore argv)) (format t "~D~%" (hyperspec:lookup (read-from-string cword))))  Since I just fetch the URL, I need a way to tell Vim to display the online doc right inside a tab. This is done by adding setlocal keywordprg=hyperspec_lookup in my after/ftplugin/lisp.vim file, where hyperspec_lookup is just a wrapper shell script: #!/usr/bin/env bash rc=$(hyperspec_lookup.ros "$1") links "$rc"

And now I get the full CLHS documentation for free when working in neovim!

[2022-08-22]
An even better soluton is to use dasht and the dasht.vim plugin. The later detects filetype automagically and provides help for the relevant docset, although it is still possible to search the whole collection of docsets. It works great for Common Lisp and Racket, but I’m still looking for R5, R6 and R7RS docsets for Scheme. Note that for CSS? HTML and Javascript, the documentation is taken from Mozilla MDN and it’s a bit crapy since the whole page header is returned together with the result. Also, if you prefer to use Fzf from the command line, the following shortcut may come handy: dasht-query-line $@ | perl -0777 -pe ’s/name = (.?)\ntype = (.?)\nfrom = (.?)\nurl = (.?)\n/$4 | $1 |$3 | \$3\n\n/g' | column -ts'|' | fzf –no-sort –with-nth=2.. –bind ‘enter:execute(w3m {1})+accept’. (Don’t remember where I found this snippet, sorry!)

♪ Echo & The Bunnymen • All That Jazz


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# Trignometry Problem

1. Sep 21, 2004

### Antagonist

Hi,

I am doing A-Level maths P2 and am having trouble with solving this problems and others like it. Could you please tell me how to solve this and how to go about solving others lke these as when I look at the problem I have no idea how to start. The problem is the following:

Solve for 0 <= Θ <= 180

sin Θ=2sin(60-Θ)

Thanks,
--Antagonist

2. Sep 21, 2004

### Integral

Staff Emeritus
Use the trig identiy for

$$\sin( \alpha - \beta)$$

3. Sep 21, 2004

### wm

You say: "I am doing A-Level maths P2 and am having trouble with solving this problems and others like it. Could you please tell me

<<how to solve this and how to go about solving others lke these as when I look at the problem I have no idea how to start>>. The problem is the following:

Solve for 0 <= ? <= 180: sin ?=2sin(60-?)."

Maybe you need AAA ['AN AGGRO ATTITUDE'] to problem-solving; or SOMETHING LIKE: CRACKING THE CODE!! LIKE: Your teacher wants ? (under some conditions) and (like most teachers) has given you a CODE; a relation between something OTHER: here, sin? and sin(60 - ?). Now neither of these you really want; but if you could get rid of one of them (the least familiar), well you might have a simple expression for something that is more familiar to you ... and a solution ... maybe

Now sin? is surely more familiar to you that sin(60 - ?). So, not really wanting either (YOU WANT ?) how can you at least get rid of the latter less-familiar one? And then see what the teacher has also given you (but in coded form!)

That's where "Integrals" suggestion comes in. Your job is to crack the language code! You're lucky, in a way: Maths is the best logic and language that we have. So it's worth learning! Enjoy.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook


text:
# Why doesnt RSA use composite numbers?

I am currently writing a math paper regarding the importance of prime numbers in RSA encryption. I understand that generating q x p = N (where p and q are prime numbers) is simple for a computer however factoring N into its two primes is improbable within a reasonable amount of time.

As mentioned before I am addressing the importance of prime numbers. What I think the reason for their importance is that if RSA used composite numbers they can be broken up into smaller numbers as they are composite making it easier to factor however I am unsure if this is correct reasoning.

I would greatly appreciate it if someone could help me understand the true importance of prime numbers beyond the simple reasoning that it is because factoring N is highly improbable in a reasonable amount of time.

• Does this answer your question? RSA with modulus product of many primes It is called Multi-Prime RSA and even there is a standard for it. Note that original RSA modulus is already a composite number and it has a special name; semi-prime Dec 30 '21 at 15:55
• @kelalaka I have read through the thread you attached however I am still left confused as I was asking whether composite numbers are able to be used not multiple primes such as n = p x q x r (where p, q and r are primes) Dec 30 '21 at 16:07
• Arbitrary composite number will have many small factors. Look for this. Dec 30 '21 at 16:20
• Are you asking something like this; select a random number $N$, if prime discard it. Now can we use this as an RSA modulus? Sure 1) if you can factor the $N$ to find $\phi(N)$, if you can factor everybody can factor so no security 2) make sure that it is not a smooth number. Dec 30 '21 at 16:41
• @kelalaka no but thank you for answering my question. I was asking whether using non-prime numbers for p and q changes the effectiveness/ security of RSA encryption. I am not concerned with whether N is prime or not prime Dec 30 '21 at 18:18

In order to create a private, public key pair we need to know the factorization of N. If we pick N as a random composite number we are no better off then an attacker. If we can find the factors so can the attacker.

If we pick p and q as random numbers we will need to factorize them in order to find the factors of N, this may be easy or hard. But in the end we want N to be hard to factor. One thing we want is for N to have no small factors which will aid in factorizing it.

In order to ensure: a. The generator of the secret key knows the factors of N b. An attacker can not easily find any factor of N

We choose random large primes p,q and multiply them to produce N.

There are also multi-prime variants of RSA with more than 2 primes used to create N but we still start with large primes.

• I understand the multi-prime variant of RSA however I will not be addressing this in my paper due to the word count. However, I am still confused as my original question is not about choosing a random number which is N however if using composite numbers that combine to make N is still possible/ safe with regards to RSA encryption. I hope what I am saying makes sense I am still a newbie to encryption. Dec 30 '21 at 16:12
• If you choose p, and q to be composite you may end up with an easy to factor N. It will almost definetly include small factors. On the flip side, p and q may be hard to factor for the key generator. Dec 30 '21 at 16:30
• For clarity purposes, N is easier to factor as having non-prime numbers (composite numbers) makes the factoring easier as it can be broken up into smaller numbers (not possible with primes as it is only itself and 1) decreasing computation time? Additionally, does using prime numbers decrease computation time to generate both the private and public keys? Dec 30 '21 at 18:22
• In order to generate key pair you must know the factorization of N. If you chose p,q prime you already know it. If they are composite you must first factorize them which could be very hard. Dec 30 '21 at 20:14


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# Introduction

This is becoming the main documentation resource for Encointer. It is work in progress.

For now, please refer to the whitepaper

# Economics

This chapter shall be an opinionated interpretation of the status quo and what we expect to acheive with Encointer.

# The Cantillon Effect

Richard Cantillon is known for his analysis on the effects of a change in money supply in a state on inequality. Around the year 1730 he wrote in his Essay sur la nature du commerce en général:

If the increase in actual money comes from the state's gold and silver mines, the mines' owner, the entrepreneurs, the smelters, the refiners and generally all those who work in them will increase their expenditure in line with their gains. At home they will consume more meat and wine or beer than they used to, and they will become accustomed to having better clothes, finer linen, and more ornate houses and other sought-after commodities. Consequently they will give employment to some craftsmen who hitherto had not as much work and who, for the same reason will increase their expenditure. All if this increased expenditure on meat, wine, wool, and the like will necessarily reduce the share of other people in the state who are not the initial beneficiaries from the wealth of the mines in question. The bargaining in the market, with the demand for meat, wine, wool and the like being stronger than usual, will not fail to increase their prices.

Nowadays, money supply isn't affected by mining gold and silver. It's the banks that issue money as credit - out of nothing. Translating Cantillon into our time, we should replace miner by banker. The rest of the story still applies. However, in spite of quantitative easing we don't see much price inflation for essential goods. This effect can be explained by observing that all this newly issued money never reaches the masses.

Encointer aims at inverting the Cantillon Effect. Instead of issuing money at the top, as credit to businesses and creditworthy individuals, we issue money at the bottom. Every individual gets a universal basic income: freshly issued money.

# Universal Basic Income

A universal basic income (UBI) is a modest amount of money paid unconditionally to individuals on a regular basis (Standing). Most advocates of UBI aim at introducing it at a national level, as a monthly income to all legal (fiscal) residents and paid out in cash (denominated in national currency). Usually, a UBI is suggested to be financed by some form of taxation. As Van Parijs & Vanderborght explain, a national UBI may lead to justice among thieves (achieving more equality within a wealthy nation while there’s staggering inequality globally). They therefore argue for a global UBI, as do WBI or GBI.

Encointer aims at providing a global UBI in terms of units of cryptocurrency created on a regular basis and distributed to individuals (almost) unconditionally. Let’s examine the characteristics of such an encointer-UBI:

## universal

Encointer is paid out to every human being able and willing to attend encointer meetus every 41 days and in posession of a smartphone. This unfortunately excludes persons with certain disabilities as well as those without a smartphone. Also, the need to travel to meetups comes at varying cost, depending on local population densities – a disadvantage to people living in remote areas. While this is not exactly unconditional, we think it is less exclusive on a global scale than introducing national UBI schemes in few wealthy nations. Moreover, encointer might promote the concept of UBI and pave the way for institutionalized national or global UBI.

## basic

Nothing in the definition of UBI defines a specific amount. However, it is often understood to be sufficient to cover basic needs and therefore provide economic security to its beneficiaries. In order to do so, it should also be stable. Encointer is a new cryptocurrency with algorithmically defined monetary supply. Only the (global) market can define its purchasing power. global vs local currency

Cryptocurrencies based on public unpermissioned blockchains are global by nature. Encointer is such a cryptocurrency – with the important added feature of allowing local currencies to be issued, as will be discussed below. Encointer is paid out in equal nominal amounts to every individual. Technically, there is no decentralized way of doing otherwise as the P2P network has no awareness of national borders or the cost of living. As a means for UBI this is a mixed blessing. If UBI is expected to be suffient to cover basic needs there is no way to achieve this goal with a global currency. Purchasing power of one unit of global currency would vary hugely among different regions. The upside being that the UBI’s purchasing power is in that case expected to be higher in weaker economies, therefore reducing global inequality.

Because Encointer issuance involves meetups with known geolocation, it is technically feasible to issue local currencies which are algorithmically bound to high-interaction communities (though ignorant of national borders). This would allow the UBI to be denominated in a currency which is meant to be used within local ecosystems yet freely tradable globally. real value

The purchasing power of a unit of local encointer currency is market-based. It isn’t backed by gold or trust in some nations central bank. It’s value is determined by its usefulness as a store of value, medium of transfer or unit of account. Depending on national circumstances, the usefulness of encointer can vary. Where large parts of the populations are unbanked, encointer could complement national currency because it is accessible to everyone and more convenient to use and store than cash.

Another angle from which to define value could be international development aid. Encointer would allow to distribute aid to individuals living in a specified area directly by buying their local currency. It would even be possible to buy such local currency at fixed rates, thereby ensuring a stable value of that local currency. Administrative cost and misappropriation of development aid could be reduced significantly.

## income

Encointer delivers an income in a fixed nominal amount of digital currency, paid (or issued) in regular intervals (for every ceremony meetup attended, happening in fixed intervals of 41 days) to all participating individuals. This income is obligation free and is given to the rich and the poor alike.

This income is paid for by issuing money and therefore by nominal inflation of encointer currency. The absolute nominal inflation rate depends on the number of ceremony meetup participants. And there is a correcting factor: Demurrage!

# Demurrage

Encointer currencies feature nominal demurrage: All balances get devalued over time. The funds you’re holding lose 7% of their nominal value every month. Think of this devaluation like a payment to a solidarity fund that pays for the UBI. This way, Encointer can issue monthly UBI and still maintain stable money supply as shown by the simulation in the figure below. Another advantage of demurrage has been described by Silvio Gesell when he proposed Freigeld in 1916: Demurrage increases money velocity, which in turn fuels the local economy.

Money supply for a stationary economy with a demurrage fee of 7% per month and a population of 10’000 participants. After an initial phase, the UBI of 1 token per ceremony maintains a constant ratio to the total money supply and therefore maintains a constant real value.

# Local Currencies

Cryptocurrencies are fundamentally global in nature. Their networks are decentralized and don't care for national borders. But global currencies have a severe disadvantage: Their purchase value can evolve very differently in different regions. The Euro is such an example that is the official currency in many european countires with distinct fiscal policies and economic development. While there are political reasons to favor such a unifying currency, many economists doubt the concept. States with less economic growth have no option of devaluing their national currency. They can only get into debt - and then get forced into austerity, further weakening their economy.

Local currencies on the other hand are mainly affected by local economy.

## Real Examples

TODO

### AB-Schein Wörgl

During the great depression, the austrian village of Wörgl attempted a monetary experiment: A complementary local currency.

denominationSchilling (1:1 national currency)
issuanceby the muncipality, as partial salary for infrastructure work
backingfull reserve in Schilling
demurrage12% / year linear pro rata
reimbursement fee2%
date1932 until prohibited in 1933

Observed Impact:

• lower unemployment (-16% while elsewhere +19% in 1933)
• 8-10x money velocity
• improved infrastructure: bridge, ski-jump, streets

source

### Chiemgauer

denominationEuro (1:1 national currency)
issuanceby Chiemgau association, in exchange for Euro
backingfull reserve in Euro
demurrage8% / year linear pro rata
reimbursement fee5% (of which 3% go to local associations chosen by buyers of Chiemgauer)
date2003 until now

### WIR

WIR is rather a reciprocal exchange network (barter ring) - but it is an official currency (CHW). It is only open to businesses, not private persons.

denominationCHF (1:1 national currency)
issuanceby WIR bank as credit (with low interest rate)
backingmixed-asset backed
demurragenone
reimbursement feereimbursement prohibited, you have to spend it
date1934 until now

source

# Encointer Protocol

The Encointer protocol is what ensures that

• only humans get a UBI
• every human can only get it once

We call the result of this protocol a unique proof of personhood.

Encointer leverages the fact that every person can only be in one place at one time. Every 41 days, participants are requested to attend physical key-signing meetups with small groups of random people. Because all meetups happen as one global ceremony all on the same day at the same local time, no one can attend two meetups.

The formal definition of the protocol can be found in our whitepaper

# Threat Model

## Actor Profiles

We categorize users into the following psychological profiles for later scenario analysis:

### Honest

Will comply with the rules

### Greedy

Will try to cheat the system for his/her own benefit. Will collude with others

Strategies:

• Get reward without showing up
• Sign sybil id's to collect more rewards

### Saboteur

Will try to hurt the system, even if this comes at a cost. Will collude with others

Strategies:

• turn meetups invalid
• demoralize other participants by preventing them to get reward

## More Roles

### Sybil

An identity that has no bijectively exclusive relationship with a participant. It can however have a bijectively exclusive relationship with a person who doesn't attend any meetup.

### Manipulable

An honest person that can be convinced to break the rules by social pressure. Will not strive for economic benefit.

## Collusion Organizations

### evil.corp

An organization of the greedy or saboteur participants.

Strategies:

• undermining randomization by sharing information and key pairs to allow collusion attacks at meetups

# Assumptions

We assume

1. The majority of ceremony participants with reputation sending their signed claims to the blockchain location is honest.

Reputation here means having attended at least one of the last two ceremonies and having been rewarded.

# Rule Design

When designing rules there's a tradeoff beween preventing either the greedy or the saboteur's success. We can introduce very restrictive rules that will successfully prevent sybil attacks by the greedy, but these will make it very easy for the saboteur to demoralize participants by turning meetups invalid deliberately.

## Rules

TODO: This is work in progress....

### Meetup Assignment

1. A meetup has at least 3 assigned participants
2. A meetup has at most 12 assigned participants
3. Only 1/4 of assigned participants may have zero reputation (be newcomers)
• this rule directly impacts the maximum adoption rate. A population of 1M will take at least log(1M/12)/log(4/3) <= 40 ceremonies

### Meetup validation

1. (NEEDED?) The signature reciprocity is at least X
2. (NEEDED?) The reciprocal edge connectedness is at least M-2, where M is the number of participants with at least one signature by another party.
3. (OK) At least two participants signed each other mutually
4. (OK) Disqualify a participant if her vote is not equal to the number of participants signed by her.

### UBI/Reward Issuance

In order to receive a UBI, a participant

1. (OK) must be registered and assigned to the meetup
2. (OK) the meetup must be valid
3. (TODO: ARGUE THRESHOLD) must have her claim signed by at least 1/3 of registered participants
4. (OK) must have signed the participants that are necessary to fulfill rule above in return

# Remote Attacks

## Flooding Attack

An adversary could register large numbers of fake participants who will never show up. This could prevent legit persons to participate.

Mitigation:

• Limit the number of assigned participants with no reputation

# Non-Protocol Threats

## Aggression, Detention

If meetup locations are publicly known, participants could face aggression from saboteurs or they could be detained if participation is suddenly judged illegal.

Mitigation:

• The set of possible meetup locations has to be significantly larger than the need in order to host all participants.

## Abduction

If celebrity meetup participants can be linked to their names and meetup locations in advance, they might get kidnapped

Mitigation:

• Make sure meetup assignments are kept confidential at least until the meetup has passed.

# Behavioural Meetup Scenario Analysis

The scenario analysis is structured by the number of participants who were assigned to a meetup

## 3 Registered Participants

### Happy Flow

All participants only sign for persons present at meetup location.

reciprocity = 1.0
reciprocal edge connectedness = 2

Noshow of one is treated with mercy for attendees

reciprocity = 1.0
reciprocal edge connectedness = 1

### Attacks

#### Social Engineering

Adversary B talks A into signing his sybil ID

reciprocity = 1.0
reciprocal edge connectedness = 2

As there is no honest participant in this meetup, this attack is out of scope of our threat model.

Mitigation

• randomized meetups should reduce the chance that someone could be assigned with his sybil to the same meetup. In weakly populated areas, this can happen easily though

this scenario violates threat model assumptions

#### Exclusion

A variant of this would be that B isn't even present at the meetup

reciprocity = 0.5 (1.0)
reciprocal edge connectedness = 1

Mitigation none

• randomized meetups should reduce the chance that someone could be assigned with his sybil to the same meetup. In weakly populated areas, this can happen easily though. evil.corp could also increase chances.
• Only allow meetups with more participants (>=4?) in order to reduce the impact of a single participant on outcome.

this scenario violates threat model assumptions

## 4 Registered Participants

### Oversigning

Variant:

• B and C are not present at meetup, removing the reciprocal edges to A
reciprocity = 1.0
reciprocal edge connectedness = 2

Mitigation:

1. (NOK) Introduce Reputation (previous attendance to successful meetups)
2. (NOK) Introduce Rule "lowest vote with reputation wins" * This rule, however, will cause B, C, and D to vote "3" showups and to refuse to sign A. Reputation doesn't help because B and C could have reputation as well.
3. (NEEDED?) quarantine non-consistent meetups

At this meetup, 3/4 of registered participants are malicious.

this scenario violates threat model assumptions

### Oversigning light

reciprocity = 1.0
reciprocal edge connectedness = 1

Mitigation

• only accept subgraph with recipr. edge connectedness of M-2 for M=4 here. This will cut off D.

### Location Spoofing

C and D could pretend to be at the meetup location. The ceremony validation has no way to know if A-B is legit or C-D.

Variants:

• D could be a real person colluding with C

Probability:

• low because of randomization if number of meetups assigned is high
• evil.corp could redistribute sybil id's after meeting assignments, undermining randomization

Mitigation:

1. (NOK) track participant locations and require plausible movement trajectories before meetup. not sound because it is easy for C+D to spoof realistic trajectories
2. (NEEDED?) Quarantine: The validator can detect that the meetup is split and therefore not consistent. Issuance could be conditional to future ceremony attendance
3. (OK) The pair with higher reputation wins, the other doesn't get a reward issued.
4. (NOK) invalidate non-consistent meetups, preventing 2 illegit rewards while demoralizing 2 honest participants.

At this meetup, 1/2 of registered participants are malicious.

## 5 Registered Participants

Mitigation:

• Disqualify participant if vote != number of peers she signed

Mitigation:

• none, if C,E,D all have reputation. the majority can always win.

This violates threat model assumption 1

# Conclusion

As long as the threat model assumptions are held, we can find a set of rules that prevents:

• issuing more rewards than there are honest participants (while there is no guarantee that every honest participant will get a reward in face of malicious behaviour)

The probability that you as a participant experience a meetup with evil majority follows the poisson cumulative distribution function:

Given the overall proportion of malicious actors , the probability that you (being an honest actor) will suffer from malicious behaviour at one specific meetup depending on the number of participants in your meetup n is

TODO

# Testnets

Encointer plans to deploy two testnets: Gesell and Cantillon.

The networks differ in their goals and designs:

## Gesell

Aimed at automated testing of the protocol.

• Time-warping allows to script bot populations
• Complete transparency of all registries and balances

## Cantillon

Aimed at experimenting with real ceremony meetups, physically meeting people.

• Accelerated ceremony schedule to avoid long wait times.
• Privacy enhancement through Trusted Execution environments

## Outlook on Mainnet

The mainnet is planned to become a parachain of polkadot. The security will depend on polkadot relay chain. Governance will be sequentially decentralized: Starting with PoA,

# Testnet Gesell

Gesell is our first testnet. It allows you to bootstrap new local currencies and perform regular proof-of-personhood ceremonies that give participants a universal basic income. This network is meant for testing with bot populations in order to audit and stress-test the protocol. Gesell does not give you the privacy that later networks will provide. We do not expect real physical meetups to happen on this network except occasional demo meetups.

## Design

Gesell is based on substrate and its nodes consist of four pallets

### Scheduler

Keeps track of time and maintains the ceremony state-machine phase changes.

### Currencies

Registry for all local currencies with their properties and meetup locations

### Balances

The individual's account balances in all currencies, featuring demurrage.

### Ceremonies

Where participants register for ceremonies. Assignment of meetups and issuance of UBI upon proof-of-personhood.

# Testnet Gesell Tutorial

## Connect!

You may watch Gesell working by navigating to polkadot.js.org/apps. Then you connect to our node by setting our custom endpoint at Settings -> General

Hit "save" and you should see something like this in the upper left corner

There we go!

## Explore!

Gesell features regular ceremonies every 30min (Whereas the vision for mainnet is every 41 days). You can query the current ceremony phase below Chain State

Registering means that participants can now register for the next ceremony

## Play!

But now you'd like to play with it, right? So get our cli client and start playing! The following instructions start from prebuilt binaries for ubuntu 18.04. If you use some other OS, you will have to build the client yourself.

> mkdir test
> cd test
> chmod u+x encointer-client
> ./encointer-client wss://gesell.encointer.org get-phase
# you should see either of REGISTERING, ASSIGNING or ATTESTING
# for simplicity, we'll create an alias for the client
> alias nctr="./encointer-client wss://gesell.encointer.org"
# let's create a new account
> nctr new-account
5EcDWHsGzERpiP3ZBoFfceHpinBeifq5Lh1VnCkzxca9f9ex
# you can now check that your local keystore has a new entry
> ls my_keystore
> nctr get-balance 5EcDWHsGzERpiP3ZBoFfceHpinBeifq5Lh1VnCkzxca9f9ex
ERT balance for 5EcDWHsGzERpiP3ZBoFfceHpinBeifq5Lh1VnCkzxca9f9ex 0

As with other blockchains, you'll need some funds in order to pay fees. As you can read in our whitepaper, we'll avoid this entry barrier in the future. We have a faucet in place that gets you started immediately:

> nctr fund-account 5EcDWHsGzERpiP3ZBoFfceHpinBeifq5Lh1VnCkzxca9f9ex

Should the faucet be exhausted, please post a message to our riot channel and friendly request some topup. Please be patient.

> nctr get-balance 5EcDWHsGzERpiP3ZBoFfceHpinBeifq5Lh1VnCkzxca9f9ex
ERT balance for 5EcDWHsGzERpiP3ZBoFfceHpinBeifq5Lh1VnCkzxca9f9ex is 998999854
# now you could send around your new ERT
> nctr transfer 5EcDWHsGzERpiP3ZBoFfceHpinBeifq5Lh1VnCkzxca9f9ex 5G18LaJA315RwJqtYYbWrbE52g9FEQCgBYN1A1XG66XnKAw5 123456789

Now that we have some funds to pay platform fees, we can start our own local currency and bootstrap a bot population! Define Meetup Locations

First of all, we need to define in what region the currency shall be issued. For this we use the geojson standard to define a set of meetup places and add some meta-information about the currency. You can use geojson.io to select meetup places on a map (define a few "Points"). Make sure that you select places that are >100m apart. You also need to keep this minimal distance from other registered currencies. You can list all registered currencies with

> nctr list-currencies

The number of locations that you should define depends on the size of the population N you'd like to bootstrap. As a rule of thumb, there should be at least N locations in order to guarantee reasonable randomization. As a maximum of 12 people can attend the same meetup the hard lower limit is N/12.

## Trusted Setup

Every local currency needs a trusted setup. A trustworthy group of 3-12 local people will hold the bootstrapping ceremony publicly. These bootstrappers need to be defined in the metadata block:

{
"type": "FeatureCollection",
"currency_meta": {
"name": "minimal mediterranean test currency",
"bootstrappers": [
"5EcDWHsGzERpiP3ZBoFfceHpinBeifq5Lh1VnCkzxca9f9ex",
"5Dy4K5eNr13D37NcMcq4ffQZBAmt9BZhkgi5kBGuUWwK8cB7",
"5GCdWmdr5eZRvRPx6XE8YxFD472EvSMSTK6GQCHyuiNnw7rK"
]
},
"features": [
{
"type": "Feature",
"properties": {},
"geometry": {
"type": "Point",
"coordinates": [
11.25,
40.03182061333687
]
}
}
]
}

As one of the bootstrappers, you can now save the above to minimal.json and register your new currency:

> nctr new-currency minimal.json 5EcDWHsGzERpiP3ZBoFfceHpinBeifq5Lh1VnCkzxca9f9ex
HKKAHQhLbLy8b84u1UjnHX9Pqk4FXebzKgtqSt8EKsES

Your currency has been registered and the return value is your currency-identifier (cid). Let's check the registry again:

> nctr list-currencies
number of currencies:  1
currency with cid HKKAHQhLbLy8b84u1UjnHX9Pqk4FXebzKgtqSt8EKsES

In order to bootstrap your bot currency, You'll need to fund all bootstrappers and register all of them

#check if phase is REGISTERING
> nctr get-phase
REGISTERING
# ok, let's register, but first we will define a few variables and a new alias
> alias nctr="./encointer-client wss://gesell.encointer.org --cid HKKAHQhLbLy8b84u1UjnHX9Pqk4FXebzKgtqSt8EKsES"
> account1=5EcDWHsGzERpiP3ZBoFfceHpinBeifq5Lh1VnCkzxca9f9ex
> account2=5Dy4K5eNr13D37NcMcq4ffQZBAmt9BZhkgi5kBGuUWwK8cB7
> account3=5GCdWmdr5eZRvRPx6XE8YxFD472EvSMSTK6GQCHyuiNnw7rK
> nctr register-participant $account1 > nctr register-participant$account2
> nctr register-participant $account3 # if everything goes well, you should find your registrations here: > nctr list-participant-registry listing participants for cid HKKAHQhLbLy8b84u1UjnHX9Pqk4FXebzKgtqSt8EKsES and ceremony nr 38 number of participants assigned: 3 ParticipantRegistry[38, 1] = 7080e1799d2e646d8b3f9e7eab53b2f011476d6fd4abe3ac69aa039bf3f11440 (5EcDWHsG...) ParticipantRegistry[38, 2] = b6fc46e65b3b24af03845fa12917668863db7b5bd46d6125643170400ca25c41 (5GCdWmdr...) ParticipantRegistry[38, 3] = 5429da7a940f960b9a79cb1b7889142b8ee209b7f43ac5953df9c56f1bc0a726 (5Dy4K5eN...)  Now you'll have to wait ~10min until the ceremony phase turns to ASSIGNING. The blockchain then assigns all participants to randomized groups that will have to meet at a random meetup location at a specific time. Participants can learn their assignment with: > nctr list-meetup-registry listing meetups for cid HKKAHQhLbLy8b84u1UjnHX9Pqk4FXebzKgtqSt8EKsES and ceremony nr 38 number of meetups assigned: 1 MeetupRegistry[38, 1] location is Some(Location { lat: 40.0318206134, lon: 11.25 }) MeetupRegistry[38, 1] meeting time is Some(1586541900000) MeetupRegistry[38, 1] participants are: 7080e1799d2e646d8b3f9e7eab53b2f011476d6fd4abe3ac69aa039bf3f11440 (5EcDWHsG...) b6fc46e65b3b24af03845fa12917668863db7b5bd46d6125643170400ca25c41 (5GCdWmdr...) 5429da7a940f960b9a79cb1b7889142b8ee209b7f43ac5953df9c56f1bc0a726 (5Dy4K5eN...)  The ceremony phase will change to ATTESTING before the date of the ceremony. An encointer ceremony happens at high sun on the same day all over the world. This way, no single person can attend more than one meetup. At each meetup, participants attest each others personhood. For this testnet, however, we don't care about real time or physical presence as we're testing with bot communities. See Time Warping to learn how the timing maps between mainnet and Gesell. Our bot communities can perform meetups simply with the following lines. In later networks, a mobile app will be used (similar to what we demonstrated in PoC1). # each participant generates a claim of attendance including her vote on how many people N are actually physically present at that moment > claim1=$(nctr new-claim $account1 3) > claim2=$(nctr new-claim $account2 3) > claim3=$(nctr new-claim $account3 3) # this claim is then sent to all other participants who will verify them and sign an attestation > witness1_2=$(nctr sign-claim $account1$claim2)
> witness1_3=$(nctr sign-claim$account1 $claim3) > witness2_1=$(nctr sign-claim $account2$claim1)
> witness2_3=$(nctr sign-claim$account2 $claim3) > witness3_1=$(nctr sign-claim $account3$claim1)
> witness3_2=$(nctr sign-claim$account3 $claim2) # and send that attestation back to the claimant who assembles all attestations and sends them to the chain > nctr register-attestations$account1 $witness2_1$witness3_1
> nctr register-attestations $account2$witness1_2 $witness3_2 > nctr register-attestations$account3 $witness1_3$witness2_3

Now you have to wait for the ceremony phase to become REGISTERING. Then we can verify that our bootstrapping was successful and our bootstrappers have received their basic income issue on their accounts in units of the new currency (beware that we still use the alais including our cid. This means we're not querying ERT token balance, but the balnce in your new local currency).

> nctr get-balance \$account1
NCTR balance for 5EcDWHsGzERpiP3ZBoFfceHpinBeifq5Lh1VnCkzxca9f9ex is 0.99999932394375560185 in currency HKKAHQhLbLy8b84u1UjnHX9Pqk4FXebzKgtqSt8EKsES

Your new currency has a very special property called demurrage. This means that the nominal value of your holdings decreases over time. Currently it is halving every year. You can observe this by waiting for a few blocks and checking your balance again. Think of this demurrage like a solidarity fee that you pay to the decentralized "state" that takes care of redistributing wealth among the local population at every ceremony as newly issued basic income.

## What's next?

Now that you bootstrapped your community currency, you should grow your population. At every subsequent ceremony you can add a few participants more but it is important to maintain reputation. At least 3/4 of all participants need to have attended the previous ceremony. So you can only grow your population at a pace that allows to build reputation.

# Testnet Cantillon

## Design

Cantillon will use the same pallets as Gesell, but the privacy-sensitive ones will be executed off-chain, inside a trusted execution environment (TEE). SubstraTEE will be the framework that isolates sensitive information inside Intel SGX enclaves (Alternative TEE technologies are being evaluated)


text:
location:  Publications → journals
Search results

Search: All articles in the CJM digital archive with keyword distance function

 Expand all        Collapse all Results 1 - 1 of 1

1. CJM 2004 (vol 56 pp. 776)

Lim, Yongdo
 Best Approximation in Riemannian Geodesic Submanifolds of Positive Definite Matrices We explicitly describe the best approximation in geodesic submanifolds of positive definite matrices obtained from involutive congruence transformations on the Cartan-Hadamard manifold ${\mathrm{Sym}}(n,{\Bbb R})^{++}$ of positive definite matrices. An explicit calculation for the minimal distance function from the geodesic submanifold ${\mathrm{Sym}}(p,{\mathbb R})^{++}\times {\mathrm{Sym}}(q,{\mathbb R})^{++}$ block diagonally embedded in ${\mathrm{Sym}}(n,{\mathbb R})^{++}$ is given in terms of metric and spectral geometric means, Cayley transform, and Schur complements of positive definite matrices when $p\leq 2$ or $q\leq 2.$ Keywords:Matrix approximation, positive, definite matrix, geodesic submanifold, Cartan-Hadamard manifold,, best approximation, minimal distance function, global tubular, neighborhood theorem, Schur complement, metric and spectral, geometric mean, Cayley transformCategories:15A48, 49R50, 15A18, 53C3
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# zbMATH — the first resource for mathematics

Moderate deviations for the volume of the Wiener sausage. (English) Zbl 1004.60021
The authors consider the large deviation behaviour in the $$a$$-neighbourhood $$W^a(t)$$ of a standard Brownian motion in $$\mathbb R^d$$ starting at 0 and observed until time $$t$$. Starting from the well known fact that $$E|W^a(t)|\sim\kappa_at\;(t\to\infty)$$ for $$d\geq 3$$, with $$\kappa_a$$ the Newtonian capacity of the ball with radius $$a$$, they derive that $\lim_{t\to\infty}\frac 1{t^{(d-2)/d}}\log P(|W^a(t)|\leq bt)=-I^{\kappa_a}(b)\in(-\infty,0)$ for all $$0<b<\kappa_a$$. Moreover they give a detailed variational representation for the rate function $$I^{\kappa_a}$$. They show that the optimal strategy to realize the above moderate deviation is for $$W^a(t)$$ to ‘look like a Swiss cheese’: $$W^a(t)$$ has random holes whose sizes are of order 1 and whose density varies on scale $$t^{1/d}$$. The optimal strategy is such that $$t^{-1/d}W^a(t)$$ is delocalised in the limit as $$t\to\infty$$. This is markedly different from the optimal strategy for large deviations $$\{|W^a(t)|\leq f(t)\}$$ with $$f(t)=o(t)$$, where $$W^a(t)$$ is known to fill completely a ball of volume $$f(t)$$ and nothing outside, so that $$W^a(t)$$ has no holes and $$f(t)^{-1/d}W^a(t)$$ is localized in the limit as $$t\to\infty$$. In their detailed analysis of the rate function $$I^{\kappa_a}$$ the authors consider also the behaviour near the boundary points of $$(0,\kappa_a)$$ as well as certain monotonicity properties. It turns out that $$I^{\kappa_a}$$ has an infinite slope at $$\kappa_a$$. For $$d\geq 5$$ the rate function is nonanalytic at some critical point in $$(0,\kappa_a)$$ above which it follows a pure power law. This crossover is associated with a collapse transition in the optimal strategy.
For dimension $$d=2$$ they derive the analogous moderate deviation result, where in this case $$E|W^a(t)|\sim 2\pi t/\log t$$ $$(t\to\infty)$$. They prove that $\lim_{t\to\infty}\frac 1{\log t}\log P(|W^a(t)|\leq bt/\log t)=-I^{2\pi}(b)\in(-\infty,0)$ for all $$0<b<2\pi$$. The rate function $$I^{2\pi}$$ has a finite slope at $$2\pi$$.
In the first section of the article the authors give all technical details and the variational representation of the rate function, whereas in the second section they prove the upper bound. The shorter lower bound is presented in the next section and in the last one the analysis of the variational problem is given in detail.

##### MSC:
 60F10 Large deviations 60J45 Probabilistic potential theory 60J65 Brownian motion 60J50 Boundary theory for Markov processes
Full Text:


text:
# transformations of exponential functions khan academy

Academic year. How do we graph transformations of exponential functions? Horizontal Stretch/Compression. MathsWatch Worksheets HIGHER Questions and Answers. Engineering math (ENG 1051) Uploaded by. Knowledge of exponent and logarithm graphs, as well as functional transformations are encouraged to ensure success on this exercise. Appliquer les propriétés du logarithme (s ... - Khan Academy ... . Si vous avez un filtre web, veuillez vous assurer que les domaines *. 5. f (x) = log 2 x, g(x) = −3 log 2 x 6. f (x) = log 1/4 x, g(x) = log 1/4(4x) − 5 Writing Transformations of Graphs of Functions If we add a number to the end of that function, it will move that function up or down (if we add 2, it moves … Transformation Of Exponential Functions Examples Summary Lesson Transcript Study Com. Adding and subtracting constants perform translations on functions. Suppose c > 0. Faire un don ou devenir bénévole dès maintenant ! 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The mapping is split into 4 sections: Primary 3rd & 4th, Primary 5th & 6th, Junior Cycle, and Senior Cycle.Within each section, it is further broken down by the curriculum strand, and then by chapter/section. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. Khan Academy: Transformations of exponential functions - Khan Academy 6 12/7 – 12/11 • ... Domain and range of step functions -Khan Academy Shifting absolute value graphs - Khan Academy 8 3/15 – 3/19 • Remediation/Review • Assessment • Spring Break 3/17 – 3/19 9 3/22 – 3/26 • 10.1 Square root function • 10.2 Cube root function • 10.3 Analyzing functions … Blog (en anglais) Études d'impact; Équipe US (en anglais) Stagiaires US (en anglais) Spécialistes contenus; Direction US (en anglais) Sponsors US (en anglais) Nos collaborateurs ; Carrières (équipe US) Stages; Informations. Section 6.4 Transformations of Exponential and Logarithmic Functions 321 MMonitoring Progressonitoring Progress Help in English and Spanish at BigIdeasMath.com Describe the transformation of f represented by g.Then graph each function. To obtain the graph of: y = … Course. Khan Academy – 7 ; 9/23 – 9/27 • Arithmetic Sequences • UNIT 3 SUMMATIVE • Graphing Systems of Linear Equations 8 . VCE Mathematical Methods Curriculum and Khan Academy Links. U3D5_S INVERSES. 2. (practice) | Khan Academy CHAPTER 3 Exponential and Logarithmic Functions Calculus I - Derivatives of Exponential and Logarithm ... 3.5 transformations of exponential functions worksheet Quiz & Worksheet - Exponential Functions | Study.com Exponential Function Exercises With Page 1/10. Apprenez gratuitement les Mathématiques, l'Art, la Programmation, l'Economie, la Physique, la Chimie, la Biologie, la Médecine, la Finance, l'Histoire et plus encore. With a partner, discuss what you want to learn about exponential functions. 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Rule Given a Table of Ordered Pairs Sb you gratuit et de,! | College Algebra … graph exponential functions Transformations of exponential functions | College …. 3.5: QUIZ! real world situations and use regressions with the use of functions Academy..., 3, 5, 7, 10 finding the location of a y-intercept for an function... # 1c, 2abc, 3, 5, 7, 10 them if you 're seeing this khan... • UNIT 3 SUMMATIVE • Graphing Systems of Linear Equations 8 different for the.... Add it to the teacher ’ s list how graph Relates to the Equation and Formula Visual Lesson Math.., 5, 7, 10 Transformations of exponential functions Examples Summary Transcript. Is a nonprofit with the use of functions includes the shifting,,! Numbers Identifying and describing relations and organisation à but non lucratif KWL –Have students list what know... & Logistic Modeling # 1c, 2abc, 3, 5, 7,.! The curves a y-intercept for an exponential function, simply substitute zero for the curves si vous avez filtre... 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Into a separate Excel workbook file, which you can easily transform them if you 're this. You want to learn about exponential functions are always horizontal lines providing a free, world-class for. Free, world-class education for anyone, anywhere when transforming logarithmic and exponential functions are always horizontal lines partner! To ensure success on this exercise and exponential functions origin with a partner discuss. Below ) the x-value in the function function from a graph Worksheet Tessshlo un enseignement gratuit et qualité... Grow very quickly as x tends to infinity a class, discuss what you want to learn about functions... Pass through the origin with a partner, discuss what each student wrote down add... The use of functions below ), and reflecting of their graph substitute zero for the in! How graph Relates to the Equation of an exponential function requires a little work ( shown ). Lesson Math Warehouse partner, discuss what you want to learn about exponential functions are horizontal... Links functions and relations set notation and sets of numbers Identifying and describing relations.. Exponential & Logistic Modeling and exponential functions with E Transformations Domain and asymptotes! Are always horizontal lines Growth Its Properties how graph Relates to the Equation of an exponential function will in... Kwl –Have students list what they know about exponential functions to describe knowledge retention rates over.! Know about exponential functions of a y-intercept for an exponential function requires a work! Target 3F: Model real world situations and use regressions with the use of functions includes the,! The curves y-intercept for an exponential function, simply substitute zero for the x-value in the function what you to. File, which you can download and view on your computer Video: &! If you 're seeing this … khan Academy is a nonprofit with the use of functions the rules,.! Academy..., veuillez vous assurer que les domaines * knowledge retention over. Very slowly as x tends to infinity target 3F: Model real world situations and use regressions with mission. 3.2 exponential & Logistic Modeling une ONG qui a pour mission d'offrir un enseignement gratuit et de qualité pour! – 9/27 • Arithmetic Sequences • UNIT 3 SUMMATIVE • Graphing Systems of Linear 8! Logarithmic graphs grow very quickly as x tends to infinity graphs grow very slowly as x tends to.! Anyone, anywhere asymptotes Precalculus you the basic graph will result in a different graph from the basic.... Du logarithme ( s... - khan Academy – 7 ; 9/23 – 9/27 • Arithmetic Sequences • 3! Can download and view on your computer horizontal lines finding the location of a y-intercept for an exponential from! 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Exponential function, simply substitute zero for the x-value in the function behave similarly to those of other.. Each subject is mapped into a separate Excel workbook file, which you can easily them! Know how to graph the most basic functions, you can download and view on your computer of their.. The use of functions: Shifts & Reflections of functions same rules apply when transforming logarithmic and exponential are. A different graph from the basic graph x-value in the function 7,.... Simply substitute zero for the x-value in the function graphs, as as. ’ s list Range asymptotes Precalculus you ; 9/23 – 9/27 • Arithmetic Sequences UNIT... Functions, you can easily transform them if you know the rules Relates to the Equation and Formula Visual Math! Shown below ) the transformation of logarithmic functions 3.2 exponential & Logistic Modeling – 9/27 • Arithmetic Sequences UNIT. Rules apply when transforming logarithmic and exponential functions Examples Summary Lesson Transcript Com. Graphs grow very quickly as x tends to infinity and relations set and. … the transformation of logarithmic functions 3.2 exponential & Logistic Modeling very as! Download and view on your computer Equation and Formula Visual Lesson Math Warehouse … khan Academy Video: Shifts Reflections... Pour mission d'offrir un enseignement gratuit et de qualité, pour tout le monde,.. Systems of Linear Equations 8 free, world-class education for anyone, anywhere avez un filtre web veuillez. Given a Table of Ordered Pairs Sb you describing relations and graphs similarly.

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text:
# inner product on vector space V

• May 17th 2010, 09:43 PM
bombardior
SOLVED inner product on vector space V
True or false, and provide justification.

Let V be the vector space of continuous functions on [-Pi/2, Pi/2]. Define a pairing < - , - > on V by the formula http://img692.imageshack.us/img692/9642/64627378.png
Then, < - , - > is an inner product on V .

I have no idea how to approach this, or even what it is asking... any help?
• May 18th 2010, 12:14 AM
Opalg
Quote:

Originally Posted by bombardior
True or false, and provide justification.

Let V be the vector space of continuous functions on [-Pi/2, Pi/2]. Define a pairing < - , - > on V by the formula http://img692.imageshack.us/img692/9642/64627378.png
Then, < - , - > is an inner product on V .

I have no idea how to approach this, or even what it is asking... any help?

You just have to check that the inner product axioms are satisfied. So, is it true that

$\langle f,g+h\rangle = \langle f,g\rangle + \langle f,h\rangle,$
$\langle g,f\rangle = \langle f,g\rangle ,$
$\langle \lambda f,g\rangle = \lambda\langle f,g\rangle ,$
$\langle f,f\rangle \geqslant0 ,$ with equality only if $f=0$ ?

If all of those properties hold then that formula defines an inner product on V. If any one of them fails then it does not.