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# The GNU 3DLDF Animation Page

Author: Laurence D. Finston

This copyright notice applies to the text and source code of this web site, and the graphics that appear on it. The software described in this text has its own copyright notice and license, which can be found in the distribution itself.

Copyright (C) 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014 The Free Software Foundation

Permission is granted to copy, distribute, and/or modify this document under the terms of the GNU Free Documentation License, Version 1.3 or any later version published by the Free Software Foundation; with no Invariant Sections, with no Front-Cover Texts, and with no Back-Cover Texts. A copy of this license is included in the file COPYING.TXT

Last updated: February 21, 2007

 Top Animation Full and Limited Animation Cels Rotoscoping Effects Fade Blur The Birth of a Dodecahedron Rotating Sphere Titles and Text Effects Contact

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## Animation

Animation, with cartoons and puppets as well as computer animation, is my main interest. It's also one of the reasons I started writing GNU 3DLDF in the first place. Now that I've started to use it for making animations. I will be putting examples and explanations on this webpage.

Cinematic film is projected at a rate of 24 frames per second (fps). This translates to 1440 frames per minute. Video, on the other hand, generally runs at a faster rate. This is why artistic animation is measured in seconds or small numbers of minutes rather than hours.

In Germany, the United Kingdom, and possibly other European countries, video runs at 25 fps or 1500 frames per minute. In the US, I believe it runs at 30 fps per second. The ppmtompeg program from the Netpbm package creates an MPEG-1 video stream with a frame rate of 23.976, 24, 25, 29.97, 30, 50, 59.94, or 60 frames per second.

An animation sequence where the image changes with every frame is said to be animated on ones. Often, however, when the motion depicted isn't too fast, the images are displayed on two subsequent frames; this is called animating on twos. If you have a video player with single-frame advance, you can step through an animated film frame-by-frame, which can be very instructive. If you do so with a video containing full animation, such as Hollywood cartoon animation from the 1930s or 1940s, you are likely to see predominantly animation on twos interspersed with short sequences of animation on ones.

When nothing moves in a scene for more than 1/12 seconds (at 24 fps) or 2/25 seconds (at 25 fps), then, of course, the same image will appear on more than two subsequent frames. For example, for a title to appear for 5 seconds at 25 fps, there will have to be 125 frames containing that image.

The greater the number of frames per second, the smoother the animation can be. 24 or 25 frames per second is not really a lot. When I started watching videos with single-frame advance, I was surprised at how far apart the drawings were, especially during drastic action. One of the advantages of computer animation is that one is not limited to a single rate of advance.

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### Full and Limited Animation

During the 1920s and '30s, animation studios in the US, primarily in Hollywood and New York City (Fleischer Studios), made high-quality animated cartoons assembly-line fashion using lots of personnel. Many animation drawings were used, producing a convincing illusion of movement. This type of animation is called full animation.

Due to a number of factors, Hollywood-style cartoon animation began to decline around 1940. By around 1950, techniques of limited animation were well established in Hollywood animation. (By this time, Fleischer Studios had left New York for Florida. Soon thereafter, Max and Dave Fleischer lost control of the studio, which became Famous Studios. The name was apt---it became famous for making lousy cartoons.)

A typical limited animation technique is to have sets of mouths, eyes, noses, etc., which are placed on top of a head and photographed. In full animation, the whole head and all of its features would be redrawn. This allows the shape of the head to change depending on the expression, whereas in limited animation, the expressions will tend to look pasted-on.

There is no fixed borderline between full and limited animation. Nor is there anything wrong with the limited animation techniques in themselves. The reason why a lot of limited animation looks so bad is because the studios were trying to imitate the look of full animation while trying to make cartoons on the cheap.

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### Cels

In traditional cartoon animation, the animation drawings were transferred to cels, which were (nearly) transparent sheets of acetate. The name comes from celluloid, and was therefore a misnomer, since they were never made from this material. I doubt that anyone mourns the passing of the cel. They were probably not very much fun to work with. Only certain inks would stick to them, and since they were only nearly transparent, different shades of ink had to be used, depending on the position of a cel in the stack of cels being photographed. This took careful planning. In addition, only about four cels could be stacked before the combined effect became too dark. (Cels are still in use for some purposes, though. Acrylic paints do stick to them.)

Combining images using ImageMagick's composite program is analogous to stacking cels, but, theoretically, at least, there is no limit on the number of images that can be combined. Nor is there any need to use different colors depending on the layer.

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### Rotoscoping

Rotoscoping is another animation technique which can be simulated by using computer programs. The rotoscope (and rotograph) were tools for tracing outlines from live-action footage. There's nothing wrong with rotoscoping per se, but however you slice it, it's not really animation. I think it can be used creatively, but I find that I lose interest in cartoons where it's used too much, and too obviously as a way of cutting costs.

Incidentally, rotoscoping is not the worst debasement of the art of animation. I remember as a child watching the cartoons Space Angel and Clutch Cargo, which were notable for having virtually no movement, except for the mouths, which were real mouths from live-action footage---an effect of singular hideousness.

L. Nobre G., the author of the FEATPOST and ANEEMATE packages, has experimented with using the programs potrace, autotrace, and pstoedit to make MetaPost code from raster images. See his Vectorization page. This technique can be used to make vector images from artwork, which wouldn't be cheating.

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## Effects

### Text Fading In and Out

The effect of text or objects fading in or out can be achieved within the 3DLDF code. A loop is used to produce an image for each stage of the fade. The smoothest results are achieved by making an image for each frame, but a smaller number of images can be produced and copied. The text or object is drawn and/or filled using one or more color variables, whose values are reset in the loop. For example:

 verbatim_metapost "verbatimtex \font\large=cmbx12 scaled 5000 etex"; color c; color d; for i = 0 upto 30: j := i / 30; k := (30 - i) / 30; set c (j, j, j); set d (k, k, k); beginfig(i); label.rt("{\large Fade out}", origin shifted (0, 1.25)) with_text_color c; label.rt("{\large Fade in}", origin shifted (0, -1.25)) with_text_color d; endfig with_projection parallel_x_y; endfor; verbatim_metapost "bye;"; end;

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### Blurred Text

The effect of text going in or out of focus (blurring), on the other hand, can be achieved by using ImageMagick's mogrify program with the -blur option. For example:

3DLDF code:

 verbatim_metapost "verbatimtex \font\large=cmbx12 scaled 5000 etex"; beginfig(1); label("{\large Blur}", origin); endfig with_projection parallel_x_y; verbatim_metapost "bye;"; end;

Assume that the result of running 3dldf and MetaPost is the EPS file blur_1.1. The following Emacs-Lisp code performs the following actions:

1. Calls cnepspng to create the structured PostScript file blur_1_1.ps.
2. Copies the latter four times, creating the files blur_1_2.ps, blur_1_3.ps, blur_1_4.ps, and blur_1_5.ps.
3. Calls ImageMagick's mogrify program with the -blur option using the number of the file for both the radius and sigma arguments. Different values for these arguments will produce different effects.
4. Calls ImageMagick's display program in the background to display the images in order.
 (progn (let (i i-string (display-string "display blur_1.ps ")) (shell-command "cnepspng 3DLDFmp 1 1 1cm 1cm") (setq i 2) (while (<= i 5) (setq i-string (number-to-string i)) (shell-command (concat "cp blur_1.ps blur_" i-string ".ps")) (shell-command (concat "mogrify -blur " i-string "x" i-string " blur_" i-string ".ps")) (setq display-string (concat display-string " blur_" i-string ".ps ")) (setq i (1+ i)) ) ;; while (setq display-string (concat display-string "&")) (shell-command display-string) ) ;; let ) ;; progn

I like to use Emacs-Lisp for trivial tasks like this. Other people may prefer to write a shell script, or use some other method.

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## The Birth of a Dodecahedron

2005-05-09
MPEG movie: The Birth of a Dodecahedron.

MPEG animations like this one can be created by following these steps:

1. Run 3dldf to generate MetaPost code.
2. Run MetaPost to generate EPS (Encapsulated PostScript) files.
3. Run cnepspng to generate structured PostScript files from the EPS files. The source of cnepspng is available here: cnepspng.web. The reason for this step is that it's not possible to use EPS directly in the following step if the EPS files contain text typeset using TeX. I don't know whether it's possible if they have no text; I'll have to test this.
(Authors note : I've replaced cnepspng with conveps. The source code of the latter is available here: conveps.web.)
4. Convert the structured PostScript files to PBM files. PBM is a format defined and used by the Netpbm package. If the resulting movie should have frames which are duplicates of previous frames, the PBM files should be copied the appropriate number of times. Additionally, the images in PBM are coerced to the size 640x480 (width by height in pixels). The frame files must be numbered sequentially.
5. Call ppmtompeg to generate the movie.

The file generate.el contains Emacs-Lisp code for automating these steps, including the function (or defun, in LISP jargon) generate-file. I plan to use this code as the basis for an animation controller written in C using CWEB.

Thanks to L. Nobre G. for teaching me how to generate MPEG movies from the EPS files generated by MetaPost.

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## Rotating Sphere

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## Titles and Text Effects

2005-10-02.
The explanations that follow the animations were originally postings to a forum on an animation website. They require some editing, which I will do as I find time.

### Animations

MPEG movie: Scrolling Closing Titles 1
Copyright (C) 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014 The Free Software Foundation
Copyright (C) 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014 The Free Software Foundation
Source code:  scroll_1.ldf scroll_1.tex

This animation is already here, its title is Coming Soon 1.
MPEG movie: Coming Soon 1
Copyright (C) 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014 The Free Software Foundation
Copyright (C) 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014 The Free Software Foundation

Source code:  titles_2.ldf titles_2.tex

MPEG movie: Rotating Title 1
Copyright (C) 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014 The Free Software Foundation
Copyright (C) 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014 The Free Software Foundation

Source code:  titles_1.ldf titles_1.tex

### Part 1 Aug 16, 2005

TeX is a very powerful and flexible typesetting package. It is also Free Software. Therefore, it seems like a good choice for making titles and text effects for animations.

The short animations above demonstrate the use of TeX for text effects and titles.

While it is possible to use TeX by itself for these purposes in a limited way, I find it better to use it in combination with MetaPost. MetaPost can use TeX (or PostScript) for its labelling commands: label and dotlabel. It's much easier to position text in MetaPost than it is in TeX itself. It's also much easier to draw ruled boxes in MetaPost.

However, I generally use GNU 3DLDF instead of using MetaPost directly. It's more convenient for me, it gives me the chance to see whether I need to make any additions or changes to 3DLDF, and it makes it possible to combine titles with 3D objects.

This is how it works:
3DLDF writes MetaPost code, MetaPost calls TeX as a subprocess for the labels and writes PostScript code. If you're using PostScript fonts or no text at all, you can have MetaPost write structured PostScript (PS) right away. However, if you're using TeX fonts, you will have to have it write Encapsulated PostScript (EPS). This is what I'm describing here. In order to continue, you must convert EPS to PS. I use a utility called cnepspng for this purpose. (Authors note: I've replaced cnepspng with conveps, as described below.) It is included in the 3DLDF package. You then convert the PS files (containing the individual images) to PNG and then to PPM. Then you pack them into an MPEG animation using ppmtompeg, which is part of the NETPBM package.

In order for this to work, the size of the images must be either 320×240 or 640×480 pixels. I coerce them to this size after converting them from PS to PNG.

The original images (before coercion) must be of the same size, and they should also be aligned correctly. Otherwise, your animation will not look right. The easiest way to do this is to surround them with a frame. As far as MetaPost is concerned, the frame can be drawn in the background color, and it will still contribute to the final size of the image. However, cnepspng currently uses mogrify -crop 0x0 to cut off the margins created when converting from EPS to PS. So here, if the frame is in the background color, it will be ignored, and your image will almost certainly end up in the wrong size. Recently, I've just been keeping the black frame, but I may change cnepspng to use mogrify with the -shave option with specific values instead (it used to work this way). However, it would also be possible to use a color for the frame that's not used elsewhere in your image, and change it to the background color using mogrify with the -opaque and -pen options, after it's been resized. mogrify is part of the ImageMagick package.

It's also possible to use convert (ImageMagick) to make an animated GIF or MNG out of your images. However, I haven't found this to be very practical, because the files can get very large. The compression used for MPEGs is much better.

The 3DLDF code for the examples I've uploaded is here .

### Part 2 Aug 25, 2005

I've uploaded a new MPEG movie with a Speech Balloon Test. The bottleneck in this method is the conversion of Encapsulated PostScript (EPS) files to one of the Netpbm formats (PBM == Portable Bitmap, PGM == Portable Graymap, PPM == Portable Pixelmap, or PNM == Portable Anymap) so that they can be passed to ppmtompeg.

I've renamed the program cnepspng to conveps (included in GNU 3DLDF) and revised it a bit. It's primary purpose is no longer to convert EPS files to PNG, so I wanted to give it a more suitable name (convert EPS). I've added options for replacing colors and making them transparent. It was a bit tricky getting this to work, because ImageMagick's convert and mogrify programs perform pixel aliaising by default. This can increase the number of colors in an image. If this happens, it spoils the result if you want to make, for example, the blue regions in your image transparent, or change the orange regions to yellow.

Another problem is that I wasn't able to get convert or mogrify to resize the structured PostScript (PS) files. I was able to resize them by hand in display (also part of ImageMagick) and GIMP, but it's not practicable to do this for more than a couple of files. However, there's no reason to use the PS files for making animations, so I don't consider this a serious problem.

Speech Balloon Test 1 has 990 unique frames and 1050 frames in total. At 30 fps, this is only 35 seconds of animation. I think it took about 15 minutes to convert all of the EPS files to PNM. I plan to use POSIX threads to call convert and mogrify. There's always a certain amount of overhead involved in using threads, but I think it will increase the speed of conveps considerably.

### Part 3 Aug 26, 2005

conveps now uses threads, which increases its speed dramatically. I haven't yet tried using it with more than 51 images, though. It seems to work, but it may require some debugging. Currently, it will only work on systems supporting threads. I may add code for systems that don't support threads, but this doesn't have a high priority for me.

There's a lot of debugging output that I plan to put into conditionals. Since terminal output in one thread will cause other running threads to block if they try to write to the terminal, eliminating output will tend to increase speed.

I've also added the options --new-filename and --renumber, so that it's possible, for example, to generate the PNM files b_12.pnm to b_20.pnm from the EPS files a.0 to a.8.

It is now possible to remove the frame using the --fill and --opaque options, as long as it's in a color not otherwise used in the drawings. It's also possible to make colors transparent using the --transparent option. This will, of course, only work when converting to formats that support transparency.

I think it would be interesting to try to use GNU 3DLDF, MetaPost, and conveps for color separation. Multiple images could be generated where one had only the cyan areas, another the yellow, a third the magenta, and a fourth the black. One could also generate grayscale images and process them in GIMP using the Hue-Saturation-Value color model.

### Part 4 Aug 27, 2005

I used the threaded version of conveps to make the new version of the speech balloon test which I've uploaded to my website: http://wwwuser.gwdg.de/~lfinsto1. This animation has 991 unique images and 1050 frames. I have found that trying to do anything with this many images is difficult and time-consuming.

I ran into the unforeseen problem that using multiple threads for this many images caused so many temporary files to pile up that I ran out of disk space. I have now added code to limit the number of active threads at any given time. The default is 100, which seems to work on my system. It can be set to a different value using the command-line option --threads-limit.

Please note that conveps can still be called start and end values for any number of EPS files (subject to the limits of one's system): The threads limit simply limits the number of threads that can be active at one time. If the number of files exceeds the threads limit, one set of threads is created and run, then the main() function joins with them. Subsequently, a second set is created, main() joins with them, etc.

The number of active threads permitted by the system is likely to be large enough for most purposes. However, conveps calls system(), so it also creates heavy-weight processes (by means of fork()). It is quite possible that fork() could fail, because conveps has created too many processes. A threads limit value of 100 or less will probably solve this problem, too.

A frame in a color different from the background color is required in order to use mogrify --crop 0x0. However, this frame can be removed by using the --fill and --opaque options. In order to get rid of it without spoiling the rest of the image, the frame must be in a color not otherwise used in it, because these options will replace all pixels having the --opaque color.

The predefined color names in ImageMagick refer to different colors than the same names in dvips. It is therefore best to use explicit values for the arguments to the --opaque and --transparent options. For example: conveps --fill white --opaque rgb(255,0,0) 3DLDFmp 0 1 will create 3DLDFmp_0.pnm and 3DLDFmp_1.pnm from 3DLDFmp.0 and 3DLDFmp.1, replacing the red pixels with white ones. This will get rid of the frame, if the frame was drawn in red in GNU 3DLDF or MetaPost. The --fill option can use ImageMagick's names, because this is the new color that will appear in the converted and/or mogrified image or images.

I believe that it would be possible to draw to the edge of the image, i.e., to draw over the frame. However, this would require some extra care. It will be necessary to add a path corresponding to the outer edge of the frame and clip the picture to this path. I've added code to GNU 3DLDF for clipping pictures to paths, namely the clip_to command.

### Part 5 Aug 31, 2005

The basic idea behind the scrolling text examples is to make a picture containing the text, output it, and use a path as a mask to clip it. (picture and path are data types in GNU 3DLDF and MetaPost, which they are formatted in bold). Then I use a loop to shift the text picture slightly with each iteration.

The path must be closed, but needn't be rectangular. Nor does it have to be drawn or filled in order to be used for clipping.

The path used for clipping can be the outer frame, which is needed for aligning the images and ensuring that they're all the same size. This is the case in the example of vertically scrolling titles (Scrolling Closing Titles 2). However, it can also be some other path, as in the example of the horizontally scrolling text in Speech Balloon Test 1.

I thought it would be possible to shift the paths representing the frame or frames rather than the text picture, but this causes the images to go out of alignment. You can see this in Speech Balloon Test 1. I've uploaded a corrected version to my website (Speech Balloon Test 0, at http://wwwuser.gwdg.de/~lfinsto1).

Since the text effects, the frame, and the path used for clipping are all two-dimensional, it would have been possible to use MetaPost for the examples I've made so far. There are a few differences between MP and 3DLDF that would have to be accounted for. For example, pictures are not output in MP and the syntax of the label command (used for including the text) is slightly different.

It would, however, be possible to combine scrolling text with 3D constructions, animated or still, moving along with the text or remaining in one place behind or in front of it. I may try to make examples of this, if I get the chance.

TeX is designed for texts that are divided neatly into lines and pages, and not for really long, unbroken ones. It is therefore possible that using such texts will exceed some memory limit or other in 3DLDF, MetaPost, and/or TeX. In the examples I've done so far, the entire text has been in a single block, a vbox, or vertical box, in Scrolling Closing Titles 2 and an hbox, or horizontal box, in Speech Balloon Test 0.

A better way of doing this would be to divide the text into several vboxes and/or hboxes and only output the ones that are wholly or partially within the clipping path. However, in order to ensure that the texts appear and disappear at the right times, and that there is always the correct distance between them, it must be possible to determine their size.

MetaPost provides a way of measuring TeX text and this is documented in the manual. I have now added a way of doing the same thing in 3DLDF. This code:

numeric_vector nv; nv := measure_text ABCQabcq; show nv;
produces the following output:
size: 3 (0) : 1.762184 (1) : 0.244069 (2) : 0.068339
The text ABCQabcq is put into an hbox and measured. Boxes in TeX have width, height, and depth. \hbox{ABCQabcq} has width 1.762184cm, height 0.244069cm, and depth 0.068339cm.

The measurements of the text boxes can be used in the loop controlling the motion of the text picture to include or exclude text boxes according to their positions with respect to the clipping path. I haven't had a chance to try this out yet, though.

### Part 6 Sep 04, 2005

The MPEG movie MND Titles 0 doesn't contain any rotations or translations (shifting), but it is a realistic example that I plan to actually use, rather than just a test. I also did discover a couple of things while working on it.

It is possible to write in white on a black background using TeX (and MetaPost and 3DLDF), but I used the -negate argument to mogrify instead. I added a --negate argument to conveps in order to make this possible. I've also added one or two other options, and documented the options at the beginning of conveps.web.

When making the empty (black) image, --negate seemed not to work, unless I made some other mistake. I also had a problem with cropping, which I think may have to do with the way ImageMagick determines the background color. I use crop 0x0 to remove the part of the image in the background color outside of the frame. In an earlier version, the program measured the image and used explicit values to remove the unwanted edges. However, I could only measure in dimemsions of printer's points, and I determined that converting these to pixels was unreliable. I believe the problem is connected with the relationship between image size and resolution, but I haven't had time to look into this.

The order in which options are passed to mogrify and convert also affects the results. I had to make some adjustments, and it may be that I'll have to do so again.

At any rate, I was ultimately able to crop the image, and it did work to negate the pixels in the empty image with an additional, explicit call to mogrify (i.e., not via conveps).

This time, I built the movie up gradually by creating GOPs (GOP == Group of Pictures) and then calling ppmtompeg with the --combine-gops option. This allows more flexibility, because you can save the GOPs, rearrange them, insert new ones, etc., and then regenerate the movie. For example, if you make a GOP with 30 frames of the same image, and you decide you want to show it for two seconds instead of one, all you have to do is copy the GOP and call ppgmtompeg --combine-gops ... again. This is much faster than regenerating the whole movie. The GOPs are compact enough to save.

I did have a couple of problems with the entries in the parameter file (required by ppmtompeg) used for combining the GOPs. It didn't work to specify a different input directory or to list the names of the GOPs. However, I haven't yet read very far into the documentation for ppmtompeg or the MPEG format, so I may yet figure this out.

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text:
# Homework Help: Ferris Wheel & Ice Cream (circular and projectile motion?)

1. Oct 11, 2009

### flavoric3

1. The problem statement, all variables and given/known data
A Ferris wheel with radius R turns with a constant angular velocity $$\omega$$. A child rides the Ferris wheel with a fresh ice cream cone. When the child reaches an angular position $$\vartheta$$s [see diagram below], she is so distracted that she tips the cone and drops the nice big blob of ice cream (with sprinkles!) from the top of the cone. Since her arm is hanging over the side, the ice cream falls away. Upon discovering the loss of her ice cream, she begins to cry.

But luck is with this little girl. Just as the little girl reaches the point on the circle exactly opposite to the point where she lost the ice cream, the blob of ice-cream comes sailing right back into the ice cream cone. Now, it’s true that ice cream cone was totally destroyed by the impact. But the whole experience was so weird that the little girl became convinced that she was the luckiest little girl in the whole world.

a) Find the (numerical value) of the angle $$\vartheta$$s.
b) Find the centripetal acceleration of the little girl while she was on the Ferris wheel. Express your answer as a numeric multiple of g.
c) Find an expression for the relative speed between the ice cream cone and the ice cream blob as the blob hits the cone.

2. Relevant equations
I have no idea?

3. The attempt at a solution
I'm actually completely confused. I know this is a combination problem of circular and projectile motion, but I'm not sure how to combine them.

2. Oct 14, 2009

### gabbagabbahey

Hi Flavoric3, welcome to PF!

Would you mind posting the diagram so that we can visualize the problem properly?

format: plain


text:
constructing a choice set for the rational equivalence on the rational numbers

I must explicitly construct a choice set on $\Bbb Q$.

The rational equivalence relation is as follows "Two numbers in a set are rationally equivalent provided their difference is rational".

I don't think this is possible, since any two rational numbers have rational difference, and so they cannot satisfy the requirement that any two points in the choice set have irrational difference.

• You're right that any two rational numbers have rational difference, but I'm pretty sure by "two numbers" it means two real numbers. – Dan Simon Feb 29 '16 at 6:24
• Indeed that is the definition of the rational equivalence, but I am asked to construct it on $\Bbb Q$, the rationals. – Dr. John A Zoidberg Feb 29 '16 at 6:54
• Perhaps you're overthinking it: unlike on $\Bbb R$, it's really easy to specify a choice set on $\Bbb Q$ :) – BrianO Feb 29 '16 at 9:41

You're right that it's not possible to have two points in the choice set, since they would have to have irrational difference. But that doesn't mean the choice set can't exist: it just means it must have fewer than two points! Indeed, if $x\in\mathbb{Q}$ is any element, then the set $S=\{x\}$ is a choice set, since for each element $y\in\mathbb{Q}$, there exists a unique element of $S$ which is equivalent to $y$ (namely, $x$).


text:
Where am I supposed to go? Where was I supposed to know?get lost in questionsmore quotes

# circles: beautiful

DNA on 10th — street art, wayfinding and font

# visualization + design

The 2019 Pi Day art celebrates digits of $\pi$ with hundreds of languages and alphabets. If you're a kid at heart—rejoice—there's a special edition for you!

# The art of Pi ($\pi$), Phi ($\phi$) and $e$

2019 $\pi$ has hundreds of digits, hundreds of languages and a special kids' edition.
2018 $\pi$ day
2017 $\pi$ day
2016 $\pi$ approximation day
2016 $\pi$ day
2015 $\pi$ day
2014 $\pi$ approx day
2014 $\pi$ day
2013 $\pi$ day
Circular $\pi$ art

This section contains various art work based on $\pi$, $\phi$ and $e$ that I created over the years.

Some of the numerical art reveals interesting and unexpected observations. For example, the sequence 999999 in π at digit 762 called the Feynman Point. Or that if you calculate π to 13,099,586 digits you will find love.

$\pi$ day art and $\pi$ approximation day art is kept separate.

For some time I have been thinking about creating minimalist typographical art based on the digits of $\pi$. The $i$-ness $\pi$ project was one of my first forays into this kind of art.

### the $i$-ness of $\pi$

The $i$ness of $\pi$. (PNG, BUY ARTWORK)

In the $i$-ness of $\pi$ poster shown above, the average is mapped onto a color and the standard deviation onto size.

### the $i$-ness of $\phi$ and $e$

Compare the $i$-ness of $\pi$ to that of the other famous transcendental number, $e$, and the mysterious but attractive Golden Ratio, $phi$.

The 4ness of $e$. (PNG, BUY ARTWORK)
The 4ness of $phi$. (PNG, BUY ARTWORK)

### the 4-ness of $\pi$

These posters show the difference between each digit and 4,

The 4ness of $phi$. (PNG, BUY ARTWORK)

Spring and fall color themes of the posters are also available.

The 4ness of $\pi$ (spring theme). (PNG, BUY ARTWORK)
The 4ness of $\pi$ (fall theme). (PNG, BUY ARTWORK)

## curiously humorous variant

I assure you—$\pi$ has a lot of 4s. Why, in the first 19,528 digits there are 2,000 of them! That's a lot. Here they are.

If you stare at them long enough, they even appear to move. Amazing.

The 4ness of $\pi$. (PNG, BUY ARTWORK)
VIEW ALL

# Markov Chains

Tue 30-07-2019

You can look back there to explain things,
but the explanation disappears.
You'll never find it there.
Things are not explained by the past.
They're explained by what happens now.
—Alan Watts

A Markov chain is a probabilistic model that is used to model how a system changes over time as a series of transitions between states. Each transition is assigned a probability that defines the chance of the system changing from one state to another.

Nature Methods Points of Significance column: Markov Chains. (read)

Together with the states, these transitions probabilities define a stochastic model with the Markov property: transition probabilities only depend on the current state—the future is independent of the past if the present is known.

Once the transition probabilities are defined in matrix form, it is easy to predict the distribution of future states of the system. We cover concepts of aperiodicity, irreducibility, limiting and stationary distributions and absorption.

This column is the first part of a series and pairs particularly well with Alan Watts and Blond:ish.

Grewal, J., Krzywinski, M. & Altman, N. (2019) Points of significance: Markov Chains. Nature Methods 16:663–664.

# 1-bit zoomable gigapixel maps of Moon, Solar System and Sky

Mon 22-07-2019

Places to go and nobody to see.

Exquisitely detailed maps of places on the Moon, comets and asteroids in the Solar System and stars, deep-sky objects and exoplanets in the northern and southern sky. All maps are zoomable.

3.6 gigapixel map of the near side of the Moon, annotated with 6,733. (details)
100 megapixel and 10 gigapixel map of the Solar System on 20 July 2019, annotated with 758k asteroids, 1.3k comets and all planets and satellites. (details)
100 megapixle and 10 gigapixel map of the Northern Celestial Hemisphere, annotated with 44 million stars, 74,000 deep-sky objects and 3,000 exoplanets. (details)
100 megapixle and 10 gigapixel map of the Southern Celestial Hemisphere, annotated with 69 million stars, 88,000 deep-sky objects and 1000 exoplanets. (details)

# Quantile regression

Sat 01-06-2019
Quantile regression robustly estimates the typical and extreme values of a response.

Quantile regression explores the effect of one or more predictors on quantiles of the response. It can answer questions such as "What is the weight of 90% of individuals of a given height?"

Nature Methods Points of Significance column: Quantile regression. (read)

Unlike in traditional mean regression methods, no assumptions about the distribution of the response are required, which makes it practical, robust and amenable to skewed distributions.

Quantile regression is also very useful when extremes are interesting or when the response variance varies with the predictors.

Das, K., Krzywinski, M. & Altman, N. (2019) Points of significance: Quantile regression. Nature Methods 16:451–452.

Altman, N. & Krzywinski, M. (2015) Points of significance: Simple linear regression. Nature Methods 12:999–1000.

# Analyzing outliers: Robust methods to the rescue

Sat 30-03-2019
Robust regression generates more reliable estimates by detecting and downweighting outliers.

Outliers can degrade the fit of linear regression models when the estimation is performed using the ordinary least squares. The impact of outliers can be mitigated with methods that provide robust inference and greater reliability in the presence of anomalous values.

Nature Methods Points of Significance column: Analyzing outliers: Robust methods to the rescue. (read)

We discuss MM-estimation and show how it can be used to keep your fitting sane and reliable.

Greco, L., Luta, G., Krzywinski, M. & Altman, N. (2019) Points of significance: Analyzing outliers: Robust methods to the rescue. Nature Methods 16:275–276.

Altman, N. & Krzywinski, M. (2016) Points of significance: Analyzing outliers: Influential or nuisance. Nature Methods 13:281–282.

# Two-level factorial experiments

Fri 22-03-2019
To find which experimental factors have an effect, simultaneously examine the difference between the high and low levels of each.

Two-level factorial experiments, in which all combinations of multiple factor levels are used, efficiently estimate factor effects and detect interactions—desirable statistical qualities that can provide deep insight into a system.

They offer two benefits over the widely used one-factor-at-a-time (OFAT) experiments: efficiency and ability to detect interactions.

Nature Methods Points of Significance column: Two-level factorial experiments. (read)

Since the number of factor combinations can quickly increase, one approach is to model only some of the factorial effects using empirically-validated assumptions of effect sparsity and effect hierarchy. Effect sparsity tells us that in factorial experiments most of the factorial terms are likely to be unimportant. Effect hierarchy tells us that low-order terms (e.g. main effects) tend to be larger than higher-order terms (e.g. two-factor or three-factor interactions).

Smucker, B., Krzywinski, M. & Altman, N. (2019) Points of significance: Two-level factorial experiments Nature Methods 16:211–212.

Krzywinski, M. & Altman, N. (2014) Points of significance: Designing comparative experiments.. Nature Methods 11:597–598.

# Happy 2019 $\pi$ Day—Digits, internationally

Tue 12-03-2019

Celebrate $\pi$ Day (March 14th) and set out on an exploration explore accents unknown (to you)!

This year is purely typographical, with something for everyone. Hundreds of digits and hundreds of languages.

A special kids' edition merges math with color and fat fonts.

116 digits in 64 languages. (details)
223 digits in 102 languages. (details)

Check out art from previous years: 2013 $\pi$ Day and 2014 $\pi$ Day, 2015 $\pi$ Day, 2016 $\pi$ Day, 2017 $\pi$ Day and 2018 $\pi$ Day.


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# Simple Centripetal Force Question

1. Feb 23, 2006

### chrisdapos

Hello, I know that there are two possible formulas to solve for radius. You can use (mv^2)/r ,or, (m4pir^2)/T^2. Now, the question is asking when the radius is trippled, the Centripital force is....?

Using the first equation, I come out with 1/3. Using the second equation, I come out with 9.

That confuses me enough, but when I looked back on a quiz we had (sometimes I get solutions from quizs), I found that my teacher asked when radius is tripled, centripital acceleration is....? The answer was 3. Can anyone provide some insight into what I am doing wrong and what equation i should use to get my answer. Thank you in advance!!!

2. Feb 23, 2006

### Staff: Mentor

First off, there's another useful formula for centripetal force, which I show below. Realize that they are all equivalent; the only thing that changes are is variable of choice: linear speed, angular speed, period.

There's really not enough information given to give a sensible answer. It depends on what is being held constant. Can you give the exact question including any relevant context?

For example: If the problem stated something like "A car races on a circular track. If the speed stays the same, what happens to the centripetal force if the radius triples?" In that case, the relevant formula is the one containing v & r ($F_c = m v^2 /r$) and the answer is 1/3.

But what if it said "If the angular speed stays the same, what happens to the centripetal force if the radius triples?" In that case, the relevant formula is the one containing $\omega$ & r ($F_c = m \omega^2 r$) and the answer is that the force triples.

Last edited: Feb 23, 2006
3. Feb 23, 2006

### chrisdapos

The question reads exactly, if the radius were tripled, what would happen to the centripital force? The preceeding question is describe the relationship between Centripetal Force and: v, v^2, T and M. I dont think the preceeding question holds any context though. Thank you for your help!!!

4. Feb 23, 2006

### andrewchang

isn't $a_c = \frac{v^2}{r}$ and $F = \frac{mv^2}{r}$?

5. Feb 23, 2006

### Staff: Mentor

Of course. Oops! I'll fix my post. (Thanks.)


text:
Courses for Prospective Lexercise Therapists

#### Online Course 1: The Structure of Written English

This course includes units on phonology, orthography, morphology and syntax and semantics. Participants will learn the units of analysis and structures of written English. Mastery exercises are included for each unit. You can read the objectives for the course here

This course is equivalent to a semester-long, 3-credit-hour course, and is required to take Course 2. On average most trainees complete this course in 30-45 hrs. but there is a wide range. We suggest that you work through this course as quickly as you can but as slowly as you must to master the material it covers.

Upon registering, you will have 90 days (3 months) to complete the course. Within that time frame you will work through the course at your own pace. Registration is rolling and is open.

The required text book is Speech to Print: Language Essentials for Teachers, Ed. 3 (2020) by Louisa Cook Moats (ISBN-13: 9781681253305). You can buy the book from the publisher, Paul H. Brookes Publishing Co. or from book vendors like Amazon.com. (The associated Speech to Print workbook is not required.)

LearningAlly has an audiobook version of  Speech to Print.  It is not the current edition, but you may find it helpful nonetheless.  If you have a Specialist/Tutor account with LearningAlly, you can request 3 audiobooks for your bookshelf at no charge.

The cost of this course is $350. If you are planning to complete both Course 1 and Course 2 - please see our Course 1 and 2 Bundle. To get going create your account at this link and then make payment. Note: Course registrations are not refundable. #### Online Course 2: Multisensory, Structured Literacy Intervention Learn more about the course NOTE: Course 1 is a prerequisite to take this course. If you have successfully completed Course 1 or the Course 1 Test out, please email us at courses@lexercise.com to get started. Upon completion of this course you will be ready to practice using the multisensory, structured literacy approach with struggling readers and writers and qualified to enroll in Course 3 (Practicum), if you want. This course is equivalent to a semester-long, 3-credit-hour course. Upon registering, you will have 90 days (3 months) to complete the course and its final exam. On average most trainees complete this course in 30-45 hrs. but there is a wide range. We suggest that you work through the course as quickly as you can but as slowly as you must to master the concepts it presents. You can read the objectives for this course here The normal cost of this course is$350.

If you are planning to complete both Course 1 and Course 2 - please see the Course 1 and 2 Bundle.

To get going create your account at this link and then make payment.

The required  text book is:  Birsh, J. R., & Carreker, S. (Ed.) (2018). Multisensory teaching of basic language skills, (4th ed.).  (The associated workbook is NOT required.).  This book is available in several formats:

• LCCN 2018005328 (print)
• LCCN 2018010368 (ebook)

You can order the Birsh, et al. (2018) textbook from a variety of vendors, including:

For a list of vendors, including rental options see:  DirectTextbook.com

While the e-book version is less expensive,  you would want to be sure you will will comfortable reading and studying a text book in that format.

LearningAlly has an audiobook version of Multisensory Teaching of Basic Language Skills, 3rd Edition. If you have a Specialist/Tutor account with LearningAlly, you can request up to three free audiobooks for your bookshelf.  Learn more at LearningAlly at this link.

Note: Course registrations are not refundable.

Lexercise Courses 1 and 2 normally cost $350 a piece. So, if you already know that you would like to take both courses, just sign up for this "course" bundle to save$100 and get both courses for a total of $600. Please see the individual course descriptions for more details on what each one covers. To get going, create your account at this link and then make payment. Once you sign up for the bundle and make payment, you'll be automatically registered for Course 1 and you can get started right away. Once you complete Course 1, just send us an email (courses@lexercise.com) letting us know you're ready for Course 2. We will confirm your Course 1 completion and register you for Course 2 and will email you to let you know we've done so. Note: Course registrations are not refundable. #### Online Course 3: Practicum in Structured Literacy Teletherapy Learn more about the course Enrolling NOW! Course 3 is a 13-week clinical practicum course for professionals who have not had supervised, clinical experience in structured literacy working one-on-one with students. The International Dyslexia Association standards require that therapists have, in addition to coursework, a supervised clinical practicum in which they gain experience applying the knowledge and skills learned in coursework to clinical intervention. Educational professionals whose background is classroom teaching, for example, will need a practicum to qualify as a Lexercise therapist. Under the supervision of a Lexercise clinician and using the Lexercise teletherapy platform, the trainee will provide structured literacy therapy to 3 clients concurrently for 12 weeks (Lexercise will provide the clients). Prior to the 12 weeks of client sessions, 3-5 weeks are devoted to the prerequisite teletherapy technology training that is provided as part of the Course 3 course enrollment. Once the teletherapy technology training has been completed, the trainee will conduct tech checks and review client records (1 additional week) and the following 12 weeks are spent providing structured literacy teletherapy services. This course involves ~ 100 hours of supervised clinical experience (a minimum of 11.5 hours per week for approximately 100 supervised hours over the 13-weeks of client service in the course). Trainees will develop skills with teletherapy tools and with research-backed methodologies for structured literacy therapy. The regular cost of this course is$2,990 but we are offering a discounted price of $2,490 ($500 off) through the end of the month.

This course has been granted AccreditedPLUS status by the International Dyslexia Association as it prepares trainees for the Knowledge and Practice Examination for Effective Reading Instruction (KPEERI) exam. Course trainees are expected to take the KPEERI exam and are eligible for the Structured Literacy™ Dyslexia Specialist (SLDS) designation upon passing it. The cost of the KPEERI exam is $165 and there is an additional Certification Administration Fee of$150.00 for those wishing to have the SLDS designation. More information can be found in the CERI certification guidelines at this link

Note: Course registrations are not refundable.


text:
# Need help with Logarithm

1. Feb 23, 2005

### thomasrules

I don't know how to show that:

2/log underscore9 A-1/log underscore3 A = 3/log underscore3 A

2. Feb 23, 2005

### Jameson

$$\log_{9}(a-1) - \log_{3}(a) = 3 \log_{3}(a)$$

????

3. Feb 23, 2005

### thomasrules

NO.

2/((log under9)a)-((1/log under3)a)= 3/((log under3)a)

GOT IT?

4. Feb 23, 2005

### vincentchan

$$\frac{2}{log_9 A} - \frac{1}{log_3A} = \frac{3}{log_3A}$$

do you know the identity:
$$log_ax=\frac{log_bx}{log_ba}$$

this implies
log_9A= (1/2)log_3A

5. Feb 23, 2005

### thomasrules

yes

and so....

6. Feb 23, 2005

### Jameson

Ok. So you have $$\frac{2}{log_9 A} - \frac{1}{log_3A} = \frac{3}{log_3A}$$

If you get a common numerator of 6, you can rewrite this as

$$\frac{6}{3log_9 A} - \frac{6}{6log_3A} = \frac{6}{2log_3A}$$

From there you can multiply by $$\frac{1}{6}$$ and cancel out the top.

Can you solve it from there?

7. Feb 23, 2005

### vincentchan

see the white letter in my first post

8. Feb 23, 2005

### James R

Probably, you need the fact that

$$2\log_9 x = \log_3 x$$

which follows because:

If we put $$y = \log_9 x$$, then $$x = 9^y$$, and therefore

$$\log_3 x = \log_3 9^y = y\log_3 9 = 2y = 2\log_9 x$$

(I hope that's right.)

9. Feb 23, 2005

### thomasrules

nm holy ****.....how would I know to set y to that?

and so how does 2log_9x=log_3x?

Last edited: Feb 23, 2005
10. Feb 23, 2005

### thomasrules

damnit all of you gave me different ways but now I'm confused ....can someone really go easy step by step

I tried something else. DOn't know if its right but how do I prove:

log_9a=2log_3a

Last edited: Feb 23, 2005
11. Feb 23, 2005

### vincentchan

plug in $$log_9A=1/2 log_3A$$ in your left hand side of $$\frac{2}{log_9 A} - \frac{1}{log_3A} = \frac{3}{log_3A}$$

the prove had already provided by James R in #8 post, which part you don't understand?

12. Feb 23, 2005

### thomasrules

how you got 1/2log_3A

13. Feb 24, 2005

### vincentchan

see post number 8 by JamesR
or use the identity:
$$log_ax=\frac{log_bx}{log_ba}$$
this identity can be proved by the same method in post #8


text:
# “Verifiable information”: is this a known concept?

The following seems to me like a natural definition and I wonder whether it's been studied somewhere

Consider $\mathsf{X} \subset 2^{\lbrace 0, 1 \rbrace^*}$ a set of languages. Then $K \subset \lbrace 0, 1 \rbrace^\omega$ is called "$\mathsf{X}$-verifiable information" when there is $L \in \mathsf{X}$ s.t.

(i) Given $x \in L$, every prefix of $x$ is in $L$

(ii) Given $f \in K$, every prefix of $f$ is in $L$

(iii) Given $f \notin K$, the length $n$ prefix of $f$ is outside $L$ for $n >> 0$

For example $\lbrace f \rbrace$ is $\mathsf{R}$-verifiable information iff $f$ is computable. This can be seen by constructing an algorithm which runs the verification on all strings of length $n$ and collects the prefixes of length $m$ of those strings which passed the verification. For $n >> m$, the only prefix which remains is the correct one

However if $K$ is $\mathsf{R}$-verifiable information it doesn't mean every $f \in K$ is computable: for example consider $K = \lbrace 0, 1 \rbrace^\omega$

A non-trivial example of $\lbrace f \rbrace$ which is $\mathsf{P}$-verifiable is as follows. Consider $L \in \mathsf{NP} \cap \mathsf{coNP}$ and let $f$ be an encoding of $L$ together with the corresponding $\mathsf{NP}$ and $\mathsf{coNP}$ witnesses (i.e. for each $x \in \lbrace 0, 1 \rbrace^*$, $f$ encodes either an $\mathsf{NP}$-witness proving $x \in L$ or a $\mathsf{coNP}$-witness proving $x \notin L$)

• When you write "$\lbrace f \rbrace$ is $\mathsf{R}$-verifiable information iff $f$ is computable", I don't understand exactly what is $\lbrace \cdot \rbrace$ and what is $\mathsf{R}$. – a3nm Dec 29 '12 at 9:27
• @a3nm : {f} is the set with one element f. R is the set of recursive languages – Vanessa Dec 29 '12 at 11:37
• Your question seems to be a reformulation of an error correcting code problem (Golay code, Hamming code) but in terms of prefixes... Perhaps this may be a good start in the background literature for you? – Phil Jul 25 '13 at 4:21

$$K\subseteq\{0,1\}^\omega$$ is $$\mathsf{R}$$-verifiable if and only if $$K$$ is a $$\Pi^0_1$$ class (in Cantor space), a concept that has been studied extensively in . They are also called effectively closed sets.
A set $$K$$ is a $$\Pi^0_1$$ class iff it is the set of infinite paths through a recursive (computable) tree, and this is the version of the concept that you defined.


text:
# Into Math Grade 6 Module 9 Lesson 4 Answer Key Use One-Step Equations to Solve a Variety of Problems

We included HMH Into Math Grade 6 Answer Key PDF Module 9 Lesson 4 Use One-Step Equations to Solve a Variety of Problems to make students experts in learning maths.

## HMH Into Math Grade 6 Module 9 Lesson 4 Answer Key Use One-Step Equations to Solve a Variety of Problems

I Can write and graph equations to solve a variety of real-world situations involving addition, subtraction, multiplication, or division.

Step it Out

Question 1.
The sum of the measures of the two angles shown is 180°. What is the unknown angle measure?

A. In the diagram, the unknown angle measure is labeled x°. What is the measure of the given angle?
x° + 67° = 180°
x° = 180° – 67°
x° = 113°

B. Write an equation to represent the relationship in the diagram.
+ = 180
Answer: x° + 67° = 180°

C. Solve the equation using the Subtraction Property of Equality.

x° + 67° = 180°
x° = 180° – 67°
x° = 113°

D. The unknown angle measure is .
The unknown angle measure is 113°.

Question 2.
A store sells 3 cell phone cases for the price shown. Write and solve an equation to find how much money x the store charges for each case.

A. Write an equation to represent this situation.
x = $Answer: A store sells 3 cell phone cases for the price shown. The cost of 3 cell phones is$50.25
The equation would be
3x = $50.25 B. Solve the equation using the Division Property of Equality. What does x represent? Answer: 3x =$50.25
x = 50.25/3
x = $16.75 The cost of 1 cell phone is$16.75

Turn and Talk The sum of the measures of two angles is 90°. If the angles have the same measure, what is the measure of each angle? Explain.
The sum of the measures of two angles is 90°
x° + x° = 90°
2x° = 90
x° = 90/2
x° = 45°
Thus the measure of each angle is 45°.

Question 3.
Paul has his laptop open at a 105° angle. If he closes his laptop to a 19° angle or less, the laptop will go into sleep mode. How many degrees x does Paul need to close his laptop before it will go into sleep mode?

A. Write an equation you can use to solve for the unknown angle measure.
x + =
x + 19 = 105

B. Solve the equation using the Subtraction Property of Equality.

x + 19 = 105
x = 105 – 19
x = 86

C. The measure of the unknown angle is .
Answer: The measure of the unknown angle is 86 degrees.

Question 4.
The picture shows the flat and angled positions that an artist likes her tablet in when drawing. The flat viewing angle measures 180°. What is the measure of the unknown angle?

A. Write an equation you can use to find the second viewing angle.
+ x =
The flat viewing angle measures 180°.
42 + x = 180

B. Solve the equation.

42 + x = 180
x = 180 – 42
x = 138 degrees

C. The measure of the unknown angle is .
Answer: The measure of the unknown angle is 138.

Check Understanding

Question 1.
The perimeter of a square is 68 inches. Write and solve an equation to find the length of its sides.
Given,
The perimeter of a square is 68 inches.
We know that,
The perimeter of a square = 4s
68 = 4s
s = 68/4
s = 17 inches
Thus the length of its side is 17 inches.

Question 2.
Kamal makes $12.00 an hour at his job. Last week he earned$390. Write and solve an equation to determine how many hours Kamal worked last week.
Given,
Kamal makes $12.00 an hour at his job. Last week he earned$390.
x × 12 = 390
x = 390/12
x = 32.5
Thus Kamal worked 32.5 hours last week.

Question 3.
Model with Mathematics In a pack of pretzel sticks, one- quarter of the total number of pretzel sticks is 14. Write and solve an equation to find the total number of pretzel sticks in the pack x.

Given,
In a pack of pretzel sticks, one- quarter of the total number of pretzel sticks is 14.
1/4 × x = 14
x = 14 × 4
x = 56
Thus the total number of pretzel sticks in the pack x is 56.

Question 4.
The sum of Ryan’s age and Rene’s age is 35. If Ryan is 16 years old, how old is Rene?
A. Let x represent Rene’s age. Write and solve an equation for x.
Given,
The sum of Ryan’s age and Rene’s age is 35.
Ryan is 16 years old
x + 16 = 35

B. How old is Rene?
x + 16 = 35
x = 35 – 16
x = 19
Thus Rene’s age is 19 years.

Question 5.
The triangular-shaped walking path in the park shown has a perimeter of 990 feet.

A. Write an equation to find the length of the side of the path represented by x.
The triangular-shaped walking path in the park shown has a perimeter of 990 feet.
a = 280 ft
b = 300 ft
Perimeter is the sum of all sides.
280 + 300 + x = 990
x + 580 = 990
x = 990 – 580
x = 410

B. Solve the equation. How long is the third side of the path? Show your work.
280 + 300 + x = 990
x + 580 = 990
x = 990 – 580
x = 410
Thus the third side of the path is 410 ft.

Question 6.
A box is in the shape of a right rectangular prism. The area of one of the bases is shown. What is the height h of the box? Use the formula V = B × h, where V is the volume of the right rectangular prism, B is the area of the base, and h is the height.

Given,
A box is in the shape of a right rectangular prism. The area of one of the bases is shown.
Use the formula V = B × h,
where V is the volume of the right rectangular prism,
B is the area of the base, and h is the height.
V = 121 cubic inches
B = 22 sq. inches
121 = 22 × h
h = 121/22
h = 5.5 inches

Question 7.
The formula for the area A of a rectangle is A = l × w. The formula for the perimeter P of a rectangle is P = 2l + 2w. The area of the front of a rectangular window flower box is shown.

A. What is the length of the flower box?
The formula for the area A of a rectangle is A = l × w.
A = 10 1/2 sq. in
W = 2 1/4 in.
A = l × w.
10 1/2 = l × 2 1/4
21/2 ÷ 9/4 = l
l = 84/18 = 4 2/3 in.
Thus the length is 4 2/3 inches.

B. What is the perimeter of the front of the flower box?
The formula for the perimeter P of a rectangle is P = 2l + 2w.
P = 2(84/18 + 9/4)
P = 84/9 + 9/2
P = 13 5/6 inches
Thus the perimeter of the rectangle is 13 5/6 inches.

Question 8.
The sum of the measures of the two angles shown is 180°. Write and solve an equation to find the unknown angle measure.

The equation is ___________
The unknown angle measure is ____________
The sum of the measures of the two angles shown is 180°.
x° + 43° = 180°
x° = 180° – 43°
x° = 137°
Thus the unknown angle is 137°.

Question 9.
Open-Ended Write a word problem for the equation x – 6 = 20.
If 6 is subtracted from the unknown number x then the difference is 20.
x  – 6 = 20
x = 20 + 6
x = 26

Question 10.
Five pounds of cherries cost $14.95. Write and solve an equation to determine how much each pound of cherries costs. Answer: Given, Five pounds of cherries cost$14.95.
5x = 14.95
We need to write and solve an equation to determine how much each pound of cherries costs.
5x = 14.95
x = 14.95/5
x = 2.99
Thus the cost of each pound of cherries is $2.99 Question 11. Sophie buys milk and vegetables at the grocery store. She spends$3.29 on milk and has a total bill of $15.56. Write and solve an equation to determine how much Sophie spends on the vegetables. Answer: Given, Sophie buys milk and vegetables at the grocery store. She spends$3.29 on milk and has a total bill of $15.56. x + 3.29 = 15.56 x = 15.56 – 3.29 x = 12.27 Thus Sohpie spends$12.27 on the vegetables.

Question 12.
The area of a rectangle is 36 square inches. Its length is 9 inches. What is its width?
A. Write an equation to represent this situation. Let w represent the width.
Given,
The area of a rectangle is 36 square inches.
Its length is 9 inches.
width = x
Area of a rectangle = l × w
36 = 9 × x
x = 36/9
x = 4
Thus the width is 4 inches.

B. What is its width?
The width is 4 inches.

Lesson 9.4 More Practice/Homework

Question 1.
The two angles at the right have a combined measure of 90°. Write and solve an equation to find the measure of angle x. Show your work.

Given,
The two angles at the right have a combined measure of 90°.
The unknown angle is x degrees.
x° + 44° = 90°
x° = 90° – 44°
x° = 46°

Question 2.
Janelle weighed an unknown substance. It had a mass of 20.609 grams. She exposed the substance to a flame and carefully weighed the substance again. The substance then had a mass of 17.39 grams. Write and solve an equation to determine the amount of mass x the substance lost.

Given,
Janelle weighed an unknown substance. It had a mass of 20.609 grams.
She exposed the substance to a flame and carefully weighed the substance again.
The substance then had a mass of 17.39 grams.
The equation would be
x – 17.39 = 20.609
x = 20.609 + 17.39
x = 37.999 or 38 approx.

Question 3.
Model with Mathematics Rosario is working on an 8-foot-by- 8-foot floor covered with 64 white tiles. She replaces x white tiles with blue tiles. After she’s finished, there are 40 white tiles left. Write and solve an equation to find the number of blue floor tiles Rosario used.
Rosario used __________ blue tiles.
Rosario is working on an 8-foot-by- 8-foot floor covered with 64 white tiles.
She replaces x white tiles with blue tiles.
After she’s finished, there are 4.0 white tiles left.
The equation would be y = 64 – x
Now after she’s finished the work, there are 40 white tiles left.
y = 40
40 = 64 – x
x = 64 – 40
x = 24
Hence the number of blue tiles is 24.

Question 4.
Math on the Spot The distance between Professor Burger’s house and Chris’ house is 12 miles. Lila’s house is on the way from Professor Burger’s house to Chris’ house. The distance between Lila’s house and Chris’ house is 5 miles. Write and solve an equation to find the distance x between Professor Burger’s house and Lila’s house.
Given,
The distance between Professor Burger’s house and Chris’ house is 12 miles.
Lila’s house is on the way from Professor Burger’s house to Chris’ house.
The distance between Lila’s house and Chris’ house is 5 miles.
x + 5 = 12
x = 12 – 5
x = 7
Thus the distance between Professor Burger’s house and Lila’s house is 7 miles.

Question 5.
Model with Mathematics A store had a sale on baseball cards, so Percy bought several baseball cards to give as gifts. He gave a total of x baseball cards away to 5 friends. Each friend got 4 baseball cards. Write and solve an equation to figure out how many baseball cards Percy gave away.
Given,
A store had a sale on baseball cards, so Percy bought several baseball cards to give as gifts.
He gave a total of x baseball cards away to 5 friends. Each friend got 4 baseball cards.
x/5 = 4
x = 5 × 4
x = 20
Thus Percy gave away 20 baseball cards.

Test Prep

Question 6.
A swinging door opens to form a 90° angle. If the door is swung 36° closed, how many more degrees can the door close?
Given,
A swinging door opens to form a 90° angle.
If the door is swung 36° closed.
x + 36 = 90
x = 90 – 36
x = 54°
The door can close at 54 degrees.

Question 7.
The area of a rectangle is 120 square inches. Its length is 15 inches. Write an equation to find its width. What is its width?
Given,
The area of a rectangle is 120 square inches. Its length is 15 inches.
The equation to find width would be
x × 15 = 120
x = 120/15
x = 8
Thus the width is 8 inches.

Question 8.
Ginger withdrew $220 from her bank account. After her withdrawal, there was$345 left in her account. Write and solve an equation to find how much Ginger had in her account before the withdrawal.
Given,
Ginger withdrew $220 from her bank account. After her withdrawal, there was$345 left in her account.
x – 220 = 345
x = 345 + 220
x = 565
Therefore Ginger has \$565 in her account before the withdrawal.

Question 9.
The perimeter P of the triangle is equal to the sum of the lengths of the three sides. The perimeter is 194.2 centimeters. Find the value of b.

b = ____________
The perimeter P of the triangle is equal to the sum of the lengths of the three sides.
The perimeter is 194.2 centimeters.
63 + 58.5 + b = 194.2 cm
121.5 + b = 194.2 cm
b = 194.2 – 121.5
b = 72.7 cm
Thus the value of  b is 72.7 cm.

Question 10.
The sum of the measures of two angles is 90°. One angle has a measure of 32.8°. The measure of the other angle is represented by x. What is the value of x?
x = __________
Given,
The sum of the measures of two angles is 90°.
One angle has a measure of 32.8°.
The measure of the other angle is represented by x.
The equation would be
x + 32.8 = 90
x = 90 – 32.8
x = 57.2°
Thus the value of x is 57.2°

Spiral Review

Question 11.
Plot the following integers on the number line: -4, 6, -2, 5, -8.

The integer 0 is marked on the number line and positive integers on the right side from 0 and negative integers from the left side.
-4 is marked on the number line from the left side of 0.
6 is marked on the number line from the right side of 0.
-2 is marked on the number line from the left side of 0.
5 is marked on the number line from the right side of 0.
-8 is marked on the number line from the left side of 0.

Question 12.
A relay race covers a distance of 2$$\frac{1}{2}$$ miles. Each runner on the team will run $$\frac{1}{4}$$ mile. How many runners are needed for the team to cover the total distance of the race?
A relay race covers a distance of 2$$\frac{1}{2}$$ miles.
Each runner on the team will run $$\frac{1}{4}$$ mile.
$$\frac{1}{4}$$ x = 2$$\frac{1}{2}$$
$$\frac{1}{4}$$ x = $$\frac{5}{2}$$


text:
IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences
Preprint Series by Year

## Irregular Sampling of Band- Limited Functions on the Sphere and in More General Settings

A 2013 Preprint by K. Ivanov and P. Petrushev

• 2013:07
• An iterative algorithm for stable and accurate reconstruction of band-limited functions from irregular samples on the unit 2-d sphere and the general framework of Dirichlet spaces is developed. Geometric rate of convergence in the uniform norm is achieved. It is shown that a MATLAB realization of this algorithms can eff ectively recover high degree ($\geq$ 2000) spherical polynomials from their values at sufficiently dense scattered points on the sphere.

© Interdisciplinary Mathematics Institute | The University of South Carolina Board of Trustees | Webmaster


text:
# MTH633: Advanced Convex Analysis (Spring 2019)

Convex sets, convex hull, their properties, separation theorems, hyperplane, Best approximation theorem and its applications, Farkas and Gordan Theorems, Extreme points and Polyhedral. Convex functions, Basic Definitions, properties, various generalizations, differentiable convex functions, subgradient, characterization and applications in linear and nonlinear optimization, complementarity problems and its equivalent formulations.

• $\mathbb{R}$ and number sense
• $\mathbb{R}^n$ and subsets of $\mathbb{R}^n$
• Vector spaces including the concept of norm and inner product with examples.
• Euclidean space
• Concept of line with respect to vector in $\mathbb{R}$, $\mathbb{R}^2$ and in general $\mathbb{R}^n$.
• Affine set in $\mathbb{R}^n$
• Convex set in $\mathbb{R}^n$
• Half spaces
• Polyhedral
• Convex combination
• Convex hull
• Affince hull
• Cone and convex cone
• Affinely independent vectors
• Dimension of vector space, dimension of affine set and dimension of convex set.

Please click on View Online to see inside the PDF.

• Convex Analysis by R. Tyrrell Rockafellar.
• Convex Analysis By Jan van Tiel.
• Analysis: Convex Analysis and approximation theoryby R. V. Gamkrelidze, Sergeĭ Mikhaĭlovich Nikolskiĭ.
• Abstract convex Analysis by Ivan Singer.
• atiq/sp19-mth633


text:
<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
You are viewing an older version of this Concept. Go to the latest version.

# Stem-and-Leaf Plots

## Displaying and comparing actual data using place value.

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Practice Stem-and-Leaf Plots
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Stem-and-Leaf Plots

Have you ever seen a chimpanzee? Take a look at this dilemma.

A zoologist takes the weights of male and female chimpanzees at 1 year of age. She finds the following data, in pounds, and places it in order from smallest to largest.

Females: 14, 17, 19, 19, 20, 21, 23, 24

Males: 18, 22, 24, 25, 26, 28, 31, 32, 34

Make a double stem-and-leaf plot that represents this data so we can compare the males and the females in the same data display. Pay attention and you will know how to do this by the end of the Concept.

### Guidance

Measures of central tendency are an important method for interpreting a set of data. However, humans tend to be very visual. That is, many people understand things best when they can see them. For that reason, we have a variety of tools which allow us to see a set of data. These tools include plots and graphs. Each type of visual tool has advantages and the best type of plot or graph depends on the situation. Indeed, sometimes it is a matter of preference as many different graphs could be used to illustrate the same data.

Consider a stem and its leaves. The stem is a strong base from which the leaves sprout. This is the idea of a stem-and-leaf plot. They allow us to see groups of data and tendencies quickly while at the same time showing every single piece of data.

We organize a stem-and-leaf plot according to the largest base ten value and the smaller base ten values.

Take a look at this dilemma.

An accountant must consider the cost of healthcare for the employees at a company. The healthcare costs are based on age of the employees. She finds that the ages of the employees are as follows: 32, 19, 37, 22, 25, 46, 58, 35, 41, 45, 35, 27, 29, 42, 53, 70, 56, 34, 29, 30, 21, 24, 27, and 45.

This data is difficult to understand in an unorganized list. Measures of central tendency could be calculated but they would not help to determine healthcare costs. A stem-and-leaf plot will give her a better idea of numbers of employees per age group.

To create a stem-and-leaf plot, we first must put the data in order from smallest to largest:

19, 21, 22, 24, 25, 27, 27, 29, 29, 30, 32, 34, 35, 35, 37, 41, 42, 45, 45, 46, 53, 56, 58, 70.

Now, choose stem values. That means to choose values that would be the first digit(s) of appropriate groupings. In this case, because our youngest employee is 19 and the oldest is 70, we can use the tens place as our stem. We construct the stem vertically, then, as shown below. Then, we place each piece of data, the leaves, in the plot, next to its stem. We place the leaves in order, only separated by a column. The stem, the tens place, is not repeated.

The stem-and-leaf plot is complete.

Now, look at the plot. What trends can you see?

The bulk of the employees are in their 20’s and 30’s. By counting off, you can quickly locate the median. You may also notice the importance of lining up the numbers in columns so that you can quickly see how many data items there are per row.

If our situation had used numbers in the hundreds, then the hundreds would have become the largest stem. If it had been in the thousands, then the thousands would have been the largest stem. You get the idea!

If we had been given two sets of data, then we could have made a double stem-and-leaf plot!

Use this data set to answer the following questions.

#### Example A

Which stem would have the most leaves?

Solution: 20's

#### Example B

Would you use stems in the ones or tens?

Solution: Tens

#### Example C

Which stem would have the least leaves?

Solution: 40's

Now let's go back to the dilemma from the beginning of the Concept.

In this plot, the female data on the left begins with smallest data closest to the stem and increases as you go left. You can see from the stem-and-leaf plot that the tendency is for the males to weigh more than the females after a year. We can also see that there are more males in this group than females.

### Vocabulary

Stem-and-Leaf Plots
a visual display of data that takes the largest base ten of a value and separates it by large bases and smaller values in the data.
Double Stem-and-Leaf Plots
Stem-and-leaf plots that show two different sets of data on the same display by organizing according to stems and leaves of base ten values.

### Guided Practice

Here is one for you to try on your own.

Create a stem-and-leaf plot of the mass of geodes found at a volcanic site. Scientists measured 24 geodes in kilograms and got the following data: .8, .9, 1.1, 1.1, 1.2, 1.5, 1.5, 1.6, 1.7, 1.7, 1.7, 1.9, 2.0, 2.3, 5.3, 6.8, 7.5, 9.6, 10.5, 11.2, 12.0, 17.6, 23.9, 26.8.

Solution

Now we need to build a stem-and-leaf plot. We can begin by organizing the data.

The stem for this plot could be either the ones place or the tens place. If we use the ones place, it would require 24 rows. That’s too many to be useful. We should, then, use the tens place.

The stem-and-leaf plot is complete.

### Practice

Directions: Use each situation to answer the following questions.

Students spent the following total minutes on homework last Thursday evening: 45, 45, 40, 43, 36, 50, 60, 55, 55, 45, 60, 63, 90, 75, 80

1. Make a stem-and-leaf plot that represents the data.
2. Which stem has the greatest number of values?
3. Which stem has the least number of values?
4. What can you interpret from the plot?
5. Explain the intervals that you chose.
6. Why is it necessary to show intervals for which there was no data?

A hybrid car and a gasoline-only car filled up on the same days of the month. The drivers recorded the gasoline costs for the two cars.

Hybrid: $17,$24, $19,$21, $10,$12, $15,$20, $6,$16

Gasoline-Only: $34,$27, $15,$31, $29,$27, $24,$14, $35,$28

1. Create a double stem-and-leaf plot to represent this data.
2. Which stem has the greatest number of values for a hybrid?
3. Which stem has the greatest number of values for a gasoline-only car?
4. What can you conclude from your stem-and-leaf plot?

Kelly earned the following amounts of money babysitting: $30.00,$10.00, $15.00,$20.00, $18.00,$22.00, $35.00,$40.00 and \$58.00.

1. Make a stem-and-leaf plot that represents the data.
2. Which stem has the greatest number of values?
3. Which stem has the least number of values?
4. What can you interpret from the plot?
5. What was the median amount of money that she made?

### Vocabulary Language: English

bins

bins

Bins are groups of data plotted on the x-axis.
Continuous

Continuous

Continuity for a point exists when the left and right sided limits match the function evaluated at that point. For a function to be continuous, the function must be continuous at every single point in an unbroken domain.
Double Stem-and-Leaf Plots

Double Stem-and-Leaf Plots

Stem-and-leaf plots that show two different sets of data on the same display by organizing according to stems and leaves of base ten values.
Stem-and-leaf plot

Stem-and-leaf plot

A stem-and-leaf plot is a way of organizing data values from least to greatest using place value. Usually, the last digit of each data value becomes the "leaf" and the other digits become the "stem".
Truncate

Truncate

To truncate is to cut off a decimal number at a certain point without rounding.


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## Politics

Last week, I had to do one of those triple-takes at the TV screen. There was Dick Morris complaining to Sean Hannity about how the Democrats were going to cut back Medicare spending by $500 billion. I rubbed my eyes and thought, “Wait, aren’t the Democrats the party that tries to scare seniors by talking about cuts to Medicare–what’s going on here?” I’ve written previously about seniors and the health care debate, and specifically with the 2010 elections in mind. We know that seniors are the most skeptical age cohort when it comes to health care reform; that may be a generational effect, or it may just be that as the age cohort most dependent on government subsidization they are most risk-averse, or change-averse–even if only as a matter of reflex. But the specter of Republicans essentially running to the left of a Democratic President and Congress borders on the surreal. In a front page piece today, the Washington Post’s Lori Montgomery writes about this role reversal: After years of trying to cut Medicare spending, Republican lawmakers have emerged as champions of the program, accusing Democrats of trying to steal from the elderly to cover the cost of health reform. It’s a lonely battle. The hospital associations, AARP and other powerful interest groups that usually howl over Medicare cuts have also switched sides. Last week, they stood silent as the Senate Finance Committee debated a plan to slice more than$400 billion over the next decade from Medicare, the revered federal insurance program for people over 65, and Medicaid, which also serves many seniors…

Americans 65 and over have long been among those most critical of Obama’s reform plans, and a key factor is their concern about Medicare, according to an ABC News-Washington Post poll conducted this month. Fifty-six percent of seniors said they thought reform would weaken the Medicare program. With seniors likely to make up nearly 20 percent of the electorate in 2010, Republicans see Medicare as a potent campaign issue. In the Finance Committee, GOP senators moved repeatedly to strip the spending cuts from the bill.

Obama and other Democrats have assured seniors that the cuts will skim off a small margin of waste and inefficiency without affecting services. They say the cuts will actually strengthen a program that is rapidly outgrowing its primary source of funding — the payroll tax — and threatens to exhaust the surplus taxes accumulated in the Medicare trust fund by 2017. Cutting payments to providers, they argue, can help stabilize Medicare finances.

Is this smart strategy for the GOP?

In the short term, the answer has to be “yes.” Seniors tend to have less of a drop-off effect between presidential and midterm cycles. Senior citizens are also whiter than younger generations, which in part both explains why they supported John McCain at higher rates than any other age cohort in 2008, and why they are the best possible voting block for the GOP to begin any recovery.

But I have to ask: Are there not risks to this strategy? Specifically, does it not further cement the GOP’s image as an aged, out-of-touch coalition? Also, how is the GOP defense of cuts to Medicare not creating at least some dissonance with the very protesters who turned out for town halls and the recent march on Washington complaining about a too-big government getting bigger? (I suppose I’m presuming that people complaining about big government are, in fact, able to identify such contradictions; surely, some are not.)

Then again, maybe the risks are low and the upside for self-described small government Republicans far too tempting to pass up. In a recent poll analysis, ABC News’ Gary Langer confirmed the level of apprehension–downright fear, you might say–among the 65-plus set:

*56% of seniors think “reform would weaken the Medicare program,” compared to 37% of those under 65 who do.

*Opposition to reform generally is 61% among seniors, just 45% for everyone else. For the public option specifically, 59% of seniors oppose it, while just 39% of those under 65 do.

*62% of seniors say “reform will do more harm than good,” compared to 41% for those under 65.

*60% of seniors say reform will mean “too much government involvement” health care, with just 43% of those under 65 agreeing.

Then, Langer’s key graph: “We’ve further sussed this out with a regression analysis testing the predictive strength of views about the impacts of reform, and basic demographic variables, on opinions about reform overall. Result: Among seniors, the single strongest independent predictor of opposition to reform overall, and to a public option in particular, is the sense it’ll weaken Medicare.” (emphasis added)

And there you have it. For seniors, opposition to reform is related partially to fears about big government or deficits, but secondarily to worries about government tinkering with Medicare. Republican politicians and operatives can read these poll numbers too, of course–which goes a long way toward explaining why the GOP has taken to scare-mongering senior citizens about Medicare with a relish that would make even many Democratic consultants blush.

Filed under , ,

### Why The SNP Is Poised To Win In ScotlandApr 9, 2015

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text:
# PLI¶

class PLI(*args)

PLI base class.

Notes

The Perturbation Law Indices are based upon the modification of the probability density function (pdf) of the random inputs, when the quantity of interest is a failure probability. An input is considered influential if the input pdf modification leads to a broad change in the failure probability. These sensitivity indices can be computed using the sole set of simulations that has already been used to estimate the failure probability, thus limiting the number of calls to the numerical model. In this implementation, the sample must come from a Monte Carlo simulation.

The input perturbation is defined to obtain the perturbed density function as the closest to the original one, in the sense of the Kullback-Leibler divergence. The implemented perturbation includes a mean shift and a variance shift, accessible through the derived class. The current implementation only allows to modifiy Normal and Uniform density functions.

In order to compare equivalently the indices when the input distributions are not the same, it is possible to plot the indices with respect to the Hellinger distance.

These indices have been developed by Paul Lemaitre:
• Paul Lemaître, Ekatarina Sergienko, Aurélie Arnaud, Nicolas Bousquet, Fabrice Gamboa, et al.. Density modification based reliability sensitivity analysis. 2012.

• Paul Lemaitre. Analyse de sensibilité en fiabilité des structures. Mécanique des structures [physics.class-ph]. Université de Bordeaux, 2014. Français.

Methods

 computeConfidenceInterval(self[, …]) Accessor to the confidence interval of the indices. drawIndices(self[, confidenceLevel, label, …]) Draw all indices drawMarginal1DPDF(self, marginal, idelta[, …]) Draw the probability density function of a margin. getDeltaSample(self) Accessor to applied delta values. Accessor to the Gauss Kronrod algorithm used to compute integrals getIndices(self) Accessor to the Pertubation Law Indices. getOriginalDelta(self, marginal) Accessor to the original delta value Accessor to the perturbed probability of failure run(self) Run the analysis: - get the failure sample - evaluate the probabilities with the perturbed distributions - define the estimator distributions setGaussKronrod(self, algo) Accessor to the Gauss Kronrod algorithm used to compute integrals
computeConfidenceInterval(self, confidenceLevel=0.95)

Accessor to the confidence interval of the indices.

Parameters
confidenceLevel0 < float < 1

The wanted confidence level to compute the interval.

Returns
cilist of 2d sequence of float

A list of arrays for each marginal containing the lower and upper bound of the confidence interval for each delta values.

drawIndices(self, confidenceLevel=0.95, label=None, hellinger=False, name=None)

Draw all indices

Parameters
confidenceLevel0 < float < 1 or None

The wanted confidence level to compute the interval. If set to ‘None’ only the indices are plotted.

labellist of string

The labels of each parameters.

hellingerbool

If True, the indices are plotted with respect to the hellinger distance between the original PDF and the perturbed PDF.

Returns
figmatplotlib.figure

Matplotlib figure object.

axmatplotlib.axes

Matplotlib axes object.

drawMarginal1DPDF(self, marginal, idelta, showOriginal=True, label=None, xMin=None, xMax=None, pointNumber=None, name=None)

Draw the probability density function of a margin.

Parameters
marginalint

The index of the margin of interest.

ideltaint

The index in the delta array.

showOriginalbool

Display on the same figure the original pdf or not.

x_minfloat

The starting value that is used for meshing the x-axis. Defaults uses the quantile associated to the probability level 0.05.

x_maxfloat, $$x_{max} > x_{min}$$

The ending value that is used for meshing the x-axis. Defaults uses the quantile associated to the probability level 0.95.

n_pointsint

The number of points that is used for meshing the x-axis. Defaults uses DistributionImplementation-DefaultPointNumber from the openturns.ResourceMap.

Returns
figmatplotlib.figure

Matplotlib figure object.

axmatplotlib.axes

Matplotlib axes object.

getDeltaSample(self)

Accessor to applied delta values.

Returns
deltaSample2d sequence of float

The delta values.

getGaussKronrod(self)

Accessor to the Gauss Kronrod algorithm used to compute integrals

getIndices(self)

Accessor to the Pertubation Law Indices.

Returns
pli2d sequence of float

The indices for all marginals and all given delta values.

getOriginalDelta(self, marginal)

Accessor to the original delta value

Parameters
marginalint

The indice of the perturbed marginal.

getPerturbedProbabilityEstimate(self)

Accessor to the perturbed probability of failure

Returns
pfdeltafloat

The probability of failure computed with the perturbed density function.

run(self)

Run the analysis: - get the failure sample - evaluate the probabilities with the perturbed distributions - define the estimator distributions

setGaussKronrod(self, algo)

Accessor to the Gauss Kronrod algorithm used to compute integrals

Parameters
algoopenturns.GaussKronrod

The algorithm


text:
What is a short command for bold face and emph at the same time in a table cell?

I need a short command to replace \textbf{\emph{...}}. Especially, in entering tables in the text editor, this would help me to keep the structure of table uniform and easy to edit.

Thanks.

It would be more normal to use \textit rather than \emph in a table cell, as it isn't normally free text that requires emphasis,

You can make commands as short as you like, also the table cell automatically scopes the font change so you can use the declaration form rather than the form that takes an argument.

After

\newcommand\z{\bfseries\itshape}

You can use

.... &\z this is bold italic & this is not bold italic & ...\\

Why not define it yourself:

\newcommand{\bfem}[1]{\textbf{\emph{#1}}}

After that you can use it just like the predefined commands \textbf and \emph.

See also the Comprehensive list of tools that simplify the generation of LaTeX tables to make life even simpler.

• Thanks. Usually, I generate the Latex tables directly from the simulator. However, there are a few tables that I have to type in. – imriss Jul 3 '13 at 14:14


text:
# Event-/Input system with SFML: Cannot move diagonally in 2D

I am a beginner in anything with game development. I written a small prototype in which i can move a square around with the arrow keys. For that i use SFML.

At the moment i experiment around with my Event System: First, to keep things simple, i was polling for the arrow keys using sf::Keyboard::isKeyPressed(), which works fine for this small kind of "game"

// in handleUserInput():
if(Keyboard::isKeyPressed(Keyboard::Left))
{
player_.moveLeft();
}

// in player the player class:
void moveLeft()
{
velocity.x = -x_speed; // sf::Vector2f
}

// in my player-class update() method:
void update()
{
// Out of bounds check and so on...
shape.move(velocity);
velocity.x = 0;
velocity.y = 0;
}

With this i was able to move horizontally, vertically and diagonally.

Then i moved to create my "real" EventSystem based on callbacks. It wraps around sf::Window::pollEvent(). E.g. i register a callback method for the event type sf::Event::EventType::KeyPressed. So i changed my code to first register for the movement keys

event_system_.registerCallback(sf::Event::KeyPressed, [&] (const sf::Event& event)
{
switch(event.key.code)
{
case sf::Keyboard::Left:
log->info() << "Moving Left";
player_.moveLeft();
break;
case sf::Keyboard::Right:
log->info() << "Moving Right";
player_.moveRight();
break;
case sf::Keyboard::Up:
log->info() << "Moving Up";
player_.moveUp();
break;
case sf::Keyboard::Down:
log->info() << "Moving Down";
player_.moveDown();
break;
case sf::Keyboard::Escape:
window_.close();
break;
}
});

The problem i encountered was, that i couldn't move diagonally anymore. After adding the loggin parts i found out, that when i keep two arrow keys pressed the only event that gets fired over and over again was the key pressed latest (e.g. i try to press Left & Down and pressed the Down-Key slightly later the Down-Event would be captured over and over again and the Left-Event only once).

After that i changed my code not to reset the velocity in my player's update-method and also registered for sf::Event::KeyReleased so that it would reset the x/y-part of the velocity when the corresponding key was released.

event_system_.registerCallback(sf::Event::KeyReleased, [&] (const sf::Event& event)
{
switch(event.key.code)
{
case sf::Keyboard::Left:
case sf::Keyboard::Right:
log->info() << "Stopped moving horizontally";
player_.velocity.x = 0;
break;
case sf::Keyboard::Up:
case sf::Keyboard::Down:
log->info() << "Stopped moving vertically";
player_.velocity.y = 0;
break;
}
});

But somehow this does not seem right to me (But it wouldn't seem right to me to poll for every single possible input manually - So i think events is the things to take). Could anyone give me a hint what i am doing wrong and how to do it better?

Kind Regards

• Some people (like me) like to have a state for each key. A variable named, for example, key_right that we put to true when it is pressed and false when it is released. We then look up that state on update to move accordingly. – Alexandre Desbiens Jun 15 '15 at 20:25
• @AlexandreDesbiens How do you look up the state would be the question: Do you poll, or use callbacks? – Incubbus Jun 16 '15 at 10:44
• You use both the onKeyPress and onKeyRelease callbacks to change the state of the key, but afterwards, you poll this state. – Alexandre Desbiens Jun 16 '15 at 12:47

I would personally use the keyboard class that allows you to query the state of keys instead of waiting for an event.

The documentation is here

One of the reasons I prefer this method is that you can check the status of the key from almost anywhere in the code, and you don't have to store the state of the keys yourself.

f::Keyboard can retrieve the state of a key at any time (you don't need to store and update a boolean on your side in order to know if a key is pressed or released), and you always get the real state of the keyboard, even if keys are pressed or released when your window is out of focus and no event is triggered.

The other obvious advantage is that you can check the state of multiple keys at the same time, hence making it easy to detect key combinations :

if(sf::Keyboard::isKeyPressed(sf::Keyboard::Left) && sf::Keyboard::isKeyPressed(sf::Keyboard::Down))player_.moveDownLeft();

• Could you elaborate why you prefer to poll? – Incubbus Jun 16 '15 at 12:42
• Edited the answer – Lectem Jun 16 '15 at 13:01


text:
# Wine Study Shows Price Influences Perception

4 replies to this topic

### #1 C1ay

C1ay

¿42?

• 6,487 posts

Posted 17 January 2008 - 08:45 PM

A rose by any other name might smell as sweet, but slap on a hefty price tag, and our opinion of it might go through the roof. At least that's the case with the taste of wine, say scientists from the California Institute of Technology and Stanford University.

"left"http://hypography.com/gallery/files/9/9/8/Wine_thumb.jpg[/img]Antonio Rangel, an associate professor of economics at Caltech, and his colleagues found that changes in the stated price of a sampled wine influenced not only how good volunteers thought it tasted, but the activity of a brain region that is involved in our experience of pleasure. In other words, "prices, by themselves, affect activity in an area of the brain that is thought to encode the experienced pleasantness of an experience," Rangel says.

Rangel and his colleagues had 20 volunteers taste five wine samples which, they were told, were identified by their different retail prices: $5,$10, $35,$45, and $90 per bottle. While the subjects tasted and evaluated the wines, their brains were scanned using functional magnetic resonance imaging, or fMRI. The subjects consistently reported that they liked the taste of the$90 bottle better than the $5 one, and the$45 bottle better than the $35 one. Scans of their brains supported their subjective reports; a region of the brain called the medial orbitofrontal cortex, or mOFC, showed higher activity when the subjects drank the wines they said were more pleasurable. There was a catch to the experiment, however. Although the subjects had been told that they would taste five different, variously priced wines, they actually had sampled only three. Wines 1 and 2 were used twice, but labeled with two different prices. For example, wine 2 was presented as the$90 wine (its actual retail price) and also as the $10 wine. When the subjects were told the wine cost$90 a bottle, they loved it; at $10 a bottle, not so much. In a follow-up experiment, the subjects again tasted all five wine samples, but without any price information; this time, they rated the cheapest wine as their most preferred. Previous marketing studies have shown that it is possible to change people's reports of how good an experience is by changing their beliefs about the experience. For example, says Rangel, moviegoers will report liking a movie more when they hear beforehand how good it is. "Our study goes beyond that to show that the neural encoding of the quality of an experience is actually modulated by a variable such as price, which most people believe is correlated with experienced pleasantness," he says. The experiment doesn't reveal whether the subjects truly experienced more pleasure from the wines that they thought were more expensive. "The area of their brain that is thought to encode for the pleasantness of the experience was more active when they drank wine they believed had higher prices. Strictly speaking, that is the only hard finding of the paper," he says. However, he adds, "it is hard to believe that this is not affecting their actual experience somehow, but we don't have hard evidence for that." The results, while puzzling, actually make intuitive sense, Rangel says: "The brain encodes pleasure because it is useful for learning which activities to repeat and which ones to avoid, and good decision making requires good measures of the quality of an experience." But the brain is also a noisy environment, and "thus, as a way of improving its measurements, it makes sense to add up other sources of information about the experience. In particular, if you are very sure cognitively that an experience is good (perhaps because of previous experiences), it makes sense to incorporate that into your current measurements of pleasure." Most people believe, quite correctly, that price and the quality of a wine are correlated, so it is therefore natural for the brain to factor price into an evaluation of a wine's taste. Could the findings be used by marketers to mess even more with consumers' heads? "Not directly," Rangel says. "But it certainly points out a channel through which prices affect the consumer experience and thus sales." The paper, "Marketing actions can modulate neural representations of experienced pleasantness," was published January 14 in the early online edition of the Proceedings of the National Academy of Sciences. Source: CalTech ### #2 Racoon Racoon Politically Incorrect • Members • 3,650 posts Posted 20 January 2008 - 10:34 AM All the more reason to support the more local vineyard. Nice bit of wine growing here in Oregon and California. I can't tell much difference between a$15 local and a $40 import. the local Pinot Noirs are great quality and low price. No reason to be snobbish with the$100 bottles.

I don't doubt that price affects brain activity concerning perception of the merchandise.

### #3 freeztar

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Posted 24 January 2008 - 07:00 PM

It's so funny because people are conscious of this but not one person will try to change.

I would say that it is the people who are conscious about it who *have* changed.

I almost always determine my purchases based on value.
An example of an exception might be when I go to purchase, say, a bottle of wine, and I make the decision to buy a bottle in a certain price range before I get to the store (ie a $20 bottle opposed to the usual$10 bottle). Not being a wine connoisseur, I usually pick something I haven't tried. Sometimes it's good, sometimes it's bad.
Either way, I don't let it influence my taste perception. Or at least I think I don't.

### #4 freeztar

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Posted 24 January 2008 - 07:57 PM

I don't think think so...people are conscious about so many things yet they act as if they didn't know.I think it's because they simply don't care . Let's take a simple example like smoking cigarettes. People know it's bad for their health, for various reasons, yet they continue to smoke! Now, why is that?

Probably for the same reason that certain obese people continue to gorge themselves on fatty foods, it feels good (or as the researchers in this study say, it's "pleasant").

Why even pick up a cigarette even if it's only to try it if you know it's going to damage your health???

Humans do irrational things all the time that have no relevance to price. In fact, the first cigarette I ever smoked (wish I couldn't say that) was given to me for "free".

In the article it shows how because the price of the wine is high people believe it taste better. That's conditioning lol!

That's really what the researchers who did the experiment were trying to show; that people are conditioned to think a certain way and it goes beyond wine, i mean, this was about wine but they could have done this with anything else. I think the article exposes how conditioned people are into thinking something is good or bad.[/B]

It's important to note that this experiment deals with very specific situations, namely pleasantness with wine according to price. Without seeing the original journal article, it's impossible to know the level of influence price has and it's also impossible to use the data to extrapolate to external, of the said experiments, stimulii. Rangel even says, "it is hard to believe that this is not affecting their actual experience somehow, but we don't have hard evidence for that."
How substantial is that belief, with you, without being able to see the data?

An even better question is: What other factors are involved?

### #5 freeztar

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Posted 26 January 2008 - 03:06 PM

I have a different view from yours.