Hi, I am working with signal processing fordata collected from a sensor. Its time-series plot looks as follows:

How can I extract the envelope for this signal using in-built functions in Mathematica? I tried using FindPeaks[] and EstimatedBackgroun[] functions, but they are not giving me the correct amplitude extracted waveform.

Thank you for your time.

Hi everybody—we're granting an extension for quiz submissions for this certification through the end of this week (Friday, February 17). For people who earn this certification, we have new certificate links that we'll be sending out soon which include sharable credentials.

Hi Arben,

Can I still add a question? I've started to play around with image processing. Now I'm confused by the output of ImageData and PixelValue. For a color image, I'd expect a list of 3 values for each pixel of the image. However, in the attached notebook, I get 4! What is the extra 1.?

Cheers, Jörn

Are you planning to take the Wolfram Technology Certified Level I exam? If yes, feel free to join our Wolfram Language Certification Prep study group beginning Monday.

Link has been fixed.

Can I express a recurrence expression (and invoke RSolve) using functional programming syntax? I was looking back over the presentation on Symbolics and it didn't talk about that. Could you show how the Fibonacci number example this way? I'll see if I can answer my own question in the mean time...

Any way to tell if our quizzes are done or accepted? Completed all three but other than the screen saying I passed nothing else seems to have happened.

Once again, J. has the right of it. If you see the screen, you should be good to go. When we send out certificates a little while after the due date has passed, if you haven't gotten anything when you expect you should have, you can email us and we'll personally look into it for you.

Hi Arben, I haven't heard anything re the quizzes aside from the fact that I received well over 60% on each of the 3. I did the quizzes by downloading them and getting a score. I assume those get to you but wanted to be sure. Also when is the ETA on the certificate? thanks. Jon

None of my shortcuts for the mathematical notations work in neither Microsoft Edge, nor Chrome, with Wolfram One. How can I change that?

Is there autocomplete for the squared brackets [ ], curly braces { }, and parenthesis ( ) in Wolfram One? I am lost in the brackets.

Noting here that cloud notebooks currently do not support this sort of auto-completion, but it is explicitly on our "to-do" list. As for keyboard shortcuts, I can confirm that it is indeed tricky because browsers intercept keyboard presses like ctrl and limit our ability to implement them for our own shortcuts.

Richard,

From what I can tell, With[] is useful for situations where you want local declarations. The “See Also” section of the With documentation, for example, it references functions like Module, and Block as well as ReplaceAll. From my previous experience, ReplaceAll is the more general and widely used function.

And when I post a comment (like the previous one), I get taken back to the middle of the thread. Why?! Is it a browser issue (Safari on a Mac) or a "feature" of the thread?

I noticed that it takes minutes (!!!) for the body of older messages to all render themselves. Until that's done, the display of the discussion jumps around. In general, I'd say that the forums here don't scale well. They seem to work quite well on topics announcing something -- with a small number of messages. Discourse and Discord are excellent systems for group discussion: they provide a bunch of filters. Among other things, they jump straight to new comments in discussions. Wolfram's forte is computation, visualization, etc. -- computation for the masses! Online chats are not their thing. OTOH, what they have works kinda OK. I think it's going to be a tough sell to convince them to move to one of those responsive modern chat systems.

Stephen noted in his personal blog:

The three main applications I use all day are Wolfram Desktop, a web browser, and email. My main way of working is to create (or edit) Wolfram Notebooks. Here are a few notebooks I worked on today [...]

Everything is in Wolfram Notebooks! Everything! Notes, Todos, personal existence system, corporate management, source code, presentation slides, etc. Stephen's blog entries are just an export from a Notebook. He says he's created over a hundred thousand (!!!) notebooks, and can find the correct old one in a ridiculously small amount of time. And all of them are backwards compatible (!!!) to the original Theo Gray Notebooks ~35 years ago. Very few software systems live that long; I don't know of anyone that managed #!$$ backwards compatibility back to Day 1.

That's extraordinary. It took tremendous amounts of leadership, vision, and just plain stubbornness to pull that off. This company dogfoods their software like nobody else. The downside is that their DNA strongly resists any change to what they've got here. Don't hold your breath for any change.

Thank you for your feedback; it is much appreciated. We are constantly working on trying to resolve these issues.

I ran across a bug when working on Quiz 3. I downloaded the quiz and opened it in Mathematica. When I opened the quiz notebook in Mathematica, all of the quote marks had been stripped out of the four possible answers to the questions. I didn't notice that the text of the quiz had changed. I went back to Quiz 1. The same thing happened, but there were almost no quote marks in the answers of that quiz. One I found was on the fourth answer to Q10 on Quiz 1:

I was going a bit crazy until I noticed the missing quote marks in the notebook questions in the Mathematica window. I didn't notice the quote-stripping when I did Quiz 1. One non-standard thing that could possibly be related to the bug: I'm running Mathematica 12.2.0.0 on my computer.

Hi Jonathan! Each of these entities should have a property corresponding to location, and you can then use Select to get what you want. Looking now (with EntityProperties["AstronomicalObservatory"]), I see that there are a few different properties that relate to position, with one of them explicitly being "country". So:

observatories = EntityList["AstronomicalObservatory"];
observatoriesUS = 
 Select[observatories, #["Country"] == 
    Entity["Country", "UnitedStates"] &]

This isn't super fast because we need to query this huge list of observatory entities (1407 of them) for their countries—and Select does this one by one—but I expect that you could speed it up if you were doing something where speed is more important.

Get all of the countries at once, and extract their names as simple strings:

allCountries=EntityValue[EntityProperty[observatories,"Country"],"Name"];

Now, we can use Pick to quickly pick out the elements according to a test value (in this case, the test is just: "is the element 'United States'?"):

observatoriesUS = Pick[observatories, allCountries, "United States"]

Confirm that this worked:

GeoListPlot[observatoriesUS,GeoRange->"World"]

EDIT: While trying this out, I realize that my initial answer with Select actually doesn't work. While == works to compare most expressions, it doesn't work for entities exactly—basically, if you do have two equivalent entities, it will return True—but if you try and compare, say, the US and Japan, it returns unevaluated. This causes problems for Select, I think—so, using the lessons from the second solution, I think this is optimal in terms of simplicity and performance:

observatoriesUS2 = 
 Select[observatories, 
  EntityValue[#["Country"], "Name"] == "United States" &]

The key in either case is that it's very easy to compare two strings and instantly get back True/False!

Yucko coffee, as it were :). hoffmann_ohno.mp4 has been added to the Sample Data folder!

Hi Richard—really lovely question. I think in this case you'd want to rewrite it such that the f[x,y] appears only once, like you suggest. How to do that, though? Look at the argument:

{0 < y < g[x] && f[x, y] < 0, 0 < y < g[x] && f[x, y] > 0}

We need to find a way to take this piece and rewrite it more simply. I think that having the explicit function (even if it's nasty) would be helpful here, but here's one suggestion:

regionLister[x_, y_] := 
 With[{fVal = f[x, y], gVal = g[x]}, {0 < y < gVal && fVal < 0,
   0 < y < gVal && fVal > 0}]

RegionPlot[Evaluate@regionLister[x, y], {x, 0, 1}, {y, 0, 1}, 
 PlotStyle -> {Red, Blue}]

Basically, I make a new function which, when fed x and y, computes g[x] and f[x,y] once, then creates the list of boolean conditions for that point pair using those computed values. Because the Plot family works by plugging in points in the appropriate domain, it will feed those points to regionLister and get back a result {boole1,boole2}, just like in your example. I used Evaluate to force evaluation so that these points are understood to be a list and show up with different colors.

Without your exact functions, I can't confirm that this works, but it either should work or be close to working.

One simpler option—if acceptable—is to use the PlotPoints option to lower the number of points used to generate the plot.

Let me know how it works! I'm interested in the problem, so keep me updated and we can get into more details if this ends up not working as expected.

Rationalize is working on numbers here, it's just that it can work on (nested) lists of numbers as well. This comes from an attribute of the function called "listability"; you can check these attributes for any given function func by evaluating Attributes[func]. If you see Listable listed among the attributes, you can use the function on a (nested) list without needing to use Map.

https://reference.wolfram.com/language/ref/Listable.html

You know, that's a great question :|. I don't see why it shouldn't have that attribute, so I've asked internally to see if I can get some clarification.

Hi Rohit, hi Arben!

Thanks, this is really useful!

Another function that happily works on lists but doesn't have the Listable attribute is SetPrecision. Very strange.

I also find it unfortunate that the documentation is inconsistent in this regard.

• For some functions (e.g., CanonicalName), the use on lists is given explicitly in the short documentation (the one obtained with ?CanonicalName).
• For some functions (e.g., Attributes), the "Details" section in the Documentation Center explicitly states the attributes.
• Finally, for some functions (e.g., Rationalize), the documentation doesn't mention listability at all.

Looks like a nice cleanup project for an intern. :-)

Cheers, Jörn

Interesting Arben, Then how does Thread[] differ from Map[], and MapThread[]? There seems to be a great deal of overlap (and confusion!) between these functions. :-)

Hi Arben,

Interesting indeed, thanks for clarifying! In light of this, is there a solution to my original question? That is, how do I find out which functions accept (nested) lists as arguments and then work on each list element (at the innermost level)? E.g., for a 2x2 matrix I would like f[{{a,b},{c,d}}] = {{f[a],f[b]},{f[c],f[d]}}.

As mentioned, Rationalize is one example, but I can't see anything in its documentation stating that it works like this.

Cheers, Jörn

How does one take the quiz? I have reviewed the material and I am ready to take quizzes 1 and 2.

Hi Jörn—great observation. I do believe that you've found a bug; I'm inquiring about it and will generate a bug report if I'm correct. (Fortunately, in practice comments are not something that tend to get iconized, so hopefully this doesn't affect your workflow! It also might help to explain why nobody caught it, if it is indeed a bug.)

I have a family member who works at a group doing cancer research at a local university. She would like to systematically (i.e., accurately and thoroughly) extract data from already-published science papers publishing statistical data on clinical trials and papers publishing epidemiological data on certain populations and sub-populations. Management has suggested she "just use machine learning" to make this a slam-dunk. Perhaps Wolfram Language has tools to help build this...

Can you point to any presentations where researchers have had success implementing this kind of science-paper-data-extraction application? Have systems been shown at past Wolfram Technology Conferences? Any published paper about the extraction proper? Given the massive variety of presentations for data in medical papers, this seems like a daunting problem.

phil, I did try to look into this, but I didn't have much luck. Perhaps PDFs can be formatted in a way that makes it easier to extract tables, but the variability there is its own issue. I do think that somebody could manage this with some amount of work, but I think it's beyond me for the time being. Sorry!

Let me know if you find anything useful or interesting once you get around to reading those papers!

Why is an "&" necessary to mark the end of a pure function definition? Can't the front end implicitly know that the definition of the pure function is complete? What's an example where the front end requires the "&" delimiter -- some delimiter -- in order to parse the pure function correctly?

The choices made by Stephen, Theo, and all the others seem rational and well-designed, but I haven't sorted this one out yet.

I just completed Quiz 2 but when I press the "Get Results" button, nothing happens.

Did you download as a notebook on your local machine? I noticed some strange behavior: I had Quiz 1 open for several hours and it cleared out all of its answers spontaneously. Quizzes are deployed from the cloud; perhaps you lost your connection to the server. I'd just reload the webpage, answer the questions again, and promptly [re-]submit it. That's pretty easy to do with quizzes like this.

Added it to the Sample Data folder.

will do. thanks.

Hi Jonathan—it is correct on my end, yes. We did have a key issue with an earlier version, but you shouldn't be experiencing that. I can't discuss quiz answers here, but please see the documentation for Apply. If that doesn't clear things up (which I expect it doesn't, or you probably wouldn't be asking), feel free to email me at my first name, last initial @wolfram.com and we can discuss specifics.

Yesterday's notebook claimed in the section "High-precision Numbers" that numbers outside of the range [ MinMachineNumber,MaxMachineNumber] "are automatically represented using the system that is used for high-precision numbers". What does this mean? Are "high-precision numbers" the same as numbers in "arbitrary-precision arithmetic"?

Hi Jörn—I think that this documentation page will be informative for you. In short: my understanding of what we mean by "high precision" numbers is "any number with a precision higher than $MachinePrecision. These could come from approximations of infinite precision numbers (like rationals, integers, symbolic numbers, results of special functions, and so on), or they could just be manually entered or calculated numbers with precision higher than $MachinePrecision. When we say that they're "automatically represented", we mean that if you perform some operation with the appropriate precision throughout, we won't require you to manually change anything in order for your result to maintain that precision—e.g. you won't have to "type" the variable you save these results too as a special, higher-precision type variable.

More importantly, how does this help me? N[Exp[100000000000000000]] still yields Overflow[].

It helps you because you might want to do calculations which either return an infinite precision result or use numbers beyond $MaxMachineNumber in intermediate steps. That you get an overflow when trying to get that number per se is unavoidable, but you can still have and represent the expression Exp[100000000000000000], and use it in calculations. A clear example is:

N[Exp[100000000000000000]/Exp[100000000000000000 - 10000]]

If numbers greater than $MaxMachineNumber were not representable, then this computation would not be possible. Moreover, this:

N[Exp[100000000000000000]/Exp[100000000000000000 - 10000],10000]

would not be possible either.

where can I find data2D.dat?

Thanks phil!

A few, but I wouldn't sweat it :) Those are the ones I use frequently (in addition to @@@), but I provided a few links showing ~all of the shortcuts in last week's review notebook. Those resources were:

I saw that Richard had asked in today's Q&A about units—we have full support for physical units through the Quantity function. Units will correctly interact with each other and display in a nice way.

Hi Richard—good question. NSolve works mostly like Solve in that it's primarily built for solving polynomial equations and will usually run into trouble for more general equations that can involve transcendental functions. FindRoot is much more general, but the tradeoff is that it needs a starting point and can only return one root at a time because it works iteratively until it finds a solution.

Reduce is (very very hand-wavily) a bit in between these two, and should stay on your radar as a potential solver (as long as you offer sufficient restrictions, e.g. reducing over the reals).

Hi Jonathan,

A couple of ways to do this

data = {1, 4, 3, 5, 2};
plotFunctions = {PieChart, NumberLinePlot, ListPlot, BarChart};

Using Through

Through[plotFunctions[data]] // Partition[#, UpTo@2] & //
 Grid[#,
   Frame -> All,
   Spacings -> {1, 1}] &

Using MapThread is more flexible

options = {
  {ColorFunction -> "Pastel"}, 
  {PlotStyle -> Blue},
  {PlotTheme -> "Scientific"}, 
  {ChartLabels -> Alphabet[][[;; Length@data]], ChartStyle -> "DarkRainbow"}}

MapThread[#[data, #2, PlotLabel -> #] &, {plotFunctions, options}] // 
 Partition[#, UpTo@2] & //
 Grid[#,
   Frame -> All,
   Spacings -> {1, 1}] &

Feel free to email it to me—it's first name, last initial @wolfram.com.

Please see the background information in the attached "Impedance Background" Notebook (including a link to the RMT Ropes "dragon roll" video). Questions: 1. How can I make a simple animation that approximates the path of the centerline of the RMT rope motion? Is there an example of this helical path somewhere? 2. I'd like to compute a path based on the approximate forces on the rope, and show the resistance/reactance forces in a separate panel. I'd like to show the phase relationship between resistance/reactance, but not freak out people unfamiliar with the complex number representation of impedance. Suggestions? 3. Does Mathematica provide a way to visually capture the 3D path of [a marked] centerline of the rope? I may need to stitch the inputs from multiple cameras together? I was thinking of producing a 3DP of this captured path.

One unrelated request: can you capture an audio sample from your cat and show us a Fourier transform of it for the study group? Do we look at Fourier transforms? Maybe your cat just wants to contribute to the presentation. Meeeeeow.

Attachments:

Impedance Background.nb

Tremendous commentary Arben! I'd been wondering why we needed a PhD to be leading this course; I'm wondering no more. I'll almost certainly defer diving into this for the next two weeks, but will definitely pick it back up.

After our work with Point[] yesterday, it would certainly be educational to have an animated point moving around the path (and indicating the changes in velocity). This would be similar to graphically showing the orbits of planets in the solar system on their respective ellipses with a higher velocity as they get closer to the sun located at one foci. That would probably be a better problem to look at first. Do I just need Animate[] to be moving that point along a curve?

Two comments about the RMT Ropes "dragon roll": I'm fairly certain that our bones, muscles, and CNS never ever encountered any movement like this before. While awkward at first, our CNS does figure it out, and then it figures out how to polish the movement to be graceful and efficient. We don't have to know a peep about the physics or its computation; we just do it. When I was moving with the rope this AM, I noticed that it's certainly possible to move through the pattern without touching the ground (i.e., getting any lifting force from that bounce). However, the required forces to get the rope over your head are far smaller if you let the bounce happen. That's the general theme of impedance and gait in the human body: reactance doesn't usually make the movement possible; it makes the movement significantly more efficient. Again, it's astonishing that the CNS just notices that bounce, rolls with it, and figures out how to #!$$ use it. The CNS-controlled biomechanics of the human body are dazzling and humbling.

Thanks, now you've taught us SolveValues, which makes it easy to extract the desired solutions.

Thanks, nice to see how Set works in this context to create an assignment.

Hi again!

Looking at the "Cleaning Up Data" example of day 2, I wanted to generalize the replacement to work on anything that is not a number, not just the specified strings "N/A" etc. So I'd have to replace the parts of a list that yield False when the test function NumberQ is applied. However, something like col /. _?Not[NumberQ] -> 42 doesn't do the trick (where col is a list of numbers and other objects like in the example).

Defining a new test function notNumberQ[x_] := Not[NumberQ[x]] and then using this function in the replacement does work but seems a bit clunky.

Is there a more elegant way to realize replacements with combined test functions?

Ciao, Jörn

Hi Arben!

Afraid not, this replaces the whole list by 42:

Cheers, Jörn

Got it, thanks! Jörn

There are a few ways to do this; perhaps the best (and this is a rare suggestion from me...) is UpValues. For your case, that would look like: g /: g[f[x_], f[y_]] := f[x] f[y] + 1 That actually associates a definition to g, which—while the neatest way to do this, according to my intuition about what you might want—is perhaps a bit much. You can cleverly do this while sticking to Map just with a little level specification:

In[226]:= g[x_, y_] := x y + 1

In[227]:= Map[f, g[x, y], {2}]

Out[227]= 1 + f[x] f[y]

Hi Mitch—yes, I remember this. Attached is my best shot, if I've read what you've said here correctly.

1. For the last plot, I've changed from the default (axis) display to a frame display, choosing to only display the frame on the bottom and left edges (the left frame edge replaces the y axis). I've used this to place not Ticks, but FrameTicks at the very bottom. I set the frame opacity to 0, and then set the frame ticks opacity to 1. This is necessary because without manual specification of the frame ticks style, they inherit the style of their associated frame. I updated the previous two plots to only have left frames; they keep their axes, removed the gridline at x=0, and slightly modified their plot range paddings so that the frames appear more like axes.

2. To put it technically, this can often be a bit of a PITA. In this case, however, because of the way that Epilog works, you can just outright write the color inside the list of graphics options which specifies epilog. I've done that and changed the point sizes to all be equivalent, assuming that you want only the color to be the distinguishing factor. (Easy enough to change back if not, of course.)

Here's what I get for a final result:

I don't love that the points on the edges are cut off... it's due to the PlotRangePadding option. You can change that from {0,.1} to just .1 and it'll fix it, but it adds a liiiiittle space between the plot itself and the frame-edge that's serving as our y axis. If you do that, you probably want to modify the ticks such that the 0 is not included, because it looks cluttered... not sure how to avoid this presently, so pick your poison!

Attachments:

Plot_DerivativeD...nb