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Check out this 3D chart that won Visual Of The Year for 2024 by Visual Capitalist. It's a mashup between a 3D bubblechart and a categorical bar plot yet the only graphical components are the x-axis labels and the legend. Not only does it show relative proportions of material in a laptop but it also shows what the raw material looks like.
I love the idea of analog data visualization. I wonder if any readers have made a analog "chart".
syms u v
atan2alt(v,u)
function Z = atan2alt(V,U)
% extension of atan2(V,U) into the complex plane
Z = -1i*log((U+1i*V)./sqrt(U.^2+V.^2));
% check for purely real input. if so, zero out the imaginary part.
realInputs = (imag(U) == 0) & (imag(V) == 0);
Z(realInputs) = real(Z(realInputs));
end
As I am editing this post, I see the expected symbolic display in the nice form as have grown to love. However, when I save the post, it does not display. (In fact, it shows up here in the discussions post.) This seems to be a new problem, as I have not seen that failure mode in the past.
You can see the problem in this Answer forum response of mine, where it did fail.
At the present time, the following problems are known in MATLAB Answers itself:
- Symbolic output is not displaying. The work-around is to disp(char(EXPRESSION)) or pretty(EXPRESSION)
- Symbolic preferences are sometimes set to non-defaults
I'm beginning this MATLAB-based numerical methods class, and as I was thinking back to my previous MATLAB/Simulink classes, I definitely remember some projects more fondly than others. One of my most memorable was where I had to use MATLAB to analyze electrocardiogram (ECG) peaks. What about you guys? What are some of the best (or worst 🤭) MATLAB projects or assignments you've been given in the past?
The MATLAB Online Training Suite has been updated in the areas of Deep Learning and traditional Machine Learning! These are great self-paced courses that can get you from zero to hero pretty quickly.
Deep Learning Onramp (Free to everyone!) has been updated to use the dlnetwork workflow, such as the trainnet function, which became the preferred method for creating and training deep networks in R2024a.
- Content streamlined to reduce the focus on data processing and feature extraction, and emphasize the machine learning workflow.
- Course example simplified by using a sample of the original data.
- Classification Learner used in the course where appropriate.
The rest of the updates are for subscribers to the full Online Training Suite
The Deep Learning Techniques in MATLAB for Image Applications learning path teaches skills to tackle a variety of image applications. It is made up of the following four short courses:
- Explore Convolutional Neural Networks
- Tune Deep Learning Training Options
- Regression with Deep Learning
- Object Detection with Deep Learning
Two more deep learning short courses are also available:
The Machine Learning Techniques in MATLAB learning path helps learners build their traditional machine learning skill set:
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I've always used MATLAB with other languages. In the early days, C and C++ via mex files were the most common ways I spliced two languages together. Other than that I've also used MATLAB with Java, Excel and even Fortran.
In more recent years, Python is the language I tend to use most alongside MATLAB and support for this combination is steadily improving. In my latest blog post, I show how easy it has become to use Python's Numpy with MATLAB.
Have you used this functionality much? If so, what for? How well did it work for you?
I am inspired by the latest video from YouTube science content creator Veritasium on his distinct yet thorough explanation on how rainbows work. In his video, he set up a glass sphere experiment representing how light rays would travel inside a raindrop that ultimately forms the rainbow. I highly recommend checking it out.
In the meantime, I created an interactive MATLAB App in MATLAB Online using App Designer to visualize the light paths going through a spherical raindrop with numerical calculations along the way. While I've seen many diagrams out there showing the light paths, I haven't found any doing calculations in each step. Hence I created an app in MATLAB to show the calculations along with the visualizations as one varies the position of the incoming light ray.
Demo video:
For more information about the app and how to open it and play around with it in MATLAB Online, please check out my blog article:
Many of my best friends at MathWorks speak Spanish as their first language and we have a large community of Spanish-speaking users. You can see good evidence of this by checking out our relatively new Spanish YouTube channel which recently crossed the 10,000 subscriber mark
Our MathWorks Usability Team is working on an accessibility project and they want to interview people who use MATLAB and also have experience with screen readers.
If you fit the criteria and are interested, sign up here https://www.mathworks.com/products/usability.html?tfa_30=A11Y
Let's say you have a chance to ask the MATLAB leadership team any question. What would you ask them?
I wish I knew more about the intended evolution of the capabilities of the function arguments block. I love implementing function syntaxes using this relatively new form, but it doesn't yet handle some function syntax design patterns that I think are valuable and worth keeping.
For example, some functions take an input quantity that can something numeric, or it can be an option string that descriptively names a particular value of that quantity. One example is dateshift(t,"dayofweek",dow), where dow can be an integer from 1 to 7, or it can be one of the option strings "weekday" or "weekend".
Another example is Image Processing Toolbox that take a connectivity specifier as input. The function bwconncomp is one particular case. Connectivity can be specified using certain scalars, certain arrays, or the option string "maximal".
I think this is a worthwhile function design pattern, but I don't think the arguments block validation functionality supports it well (unless you use a lot of extra code that duplicates standard MATLAB behavior, which undermines the value of the arguments block).
MathWorkers - believe me, I know that it is not in your DNA to discuss future features. But would anyone care to offer a hint about directions for the arguments block functionality?
Just shared an amazing YouTube video that demonstrates a real-time PID position control system using MATLAB and Arduino.
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Inspired by the suggestion of Mr. Chen Lin (MathWorks), I am writing this post with a humble and friendly intent to share some fascinating insights and knowledge about the Schwarzschild radius. My entry, which is related to this post, is named: 'Into the Abyss - Schwarzschild Radius (a time lapse)'.
The Schwarzschild radius (or gravitational radius) defines the radius of the event horizon of a black hole, which is the boundary beyond which nothing, not even light, can escape the gravitational pull of the black hole. This concept comes from the Schwarzschild solution to Einstein’s field equations in general relativity. Black holes are regions of spacetime where gravitational collapse has caused matter to be concentrated within such a small volume that the escape velocity exceeds the speed of light.
This is a rudimentary scientific post, as the matter of Schwarzschild radius - it's true meaning and function, is a much, much, much-more complex "thing" (not known to us entierly, by the third degre of epistemological explanation(s)).
And, very important is to mention: I am NOT an expert - by any means, on this topic, just a very curious guy, in almost anything, that has to do with science.
Schwarzschild Radius (Gravitational Radius)
The Schwarzschild radius (Rₛ) is the critical radius at which an object of mass 
must be compressed to form a black hole, specifically, a non-rotating, uncharged black hole, known as a Schwarzschild black hole. The Schwarzschild radius 
is given by the formula: 
.
must be compressed to form a black hole, specifically, a non-rotating, uncharged black hole, known as a Schwarzschild black hole. The Schwarzschild radius is given by the formula: . Where: 
.
. Key Characteristics are, that for any mass, if that mass is compressed within a sphere with radius equal to 
, the gravitational field is so strong that not even light can escape, thus forming a black hole. The Schwarzschild radius is proportional to the mass. Larger masses have larger Schwarzschild radii.
, the gravitational field is so strong that not even light can escape, thus forming a black hole. The Schwarzschild radius is proportional to the mass. Larger masses have larger Schwarzschild radii.Example:
For the Sun 
: 
.
: .So, if the Sun were compressed into a sphere with a radius of ~3 km, it would become a black hole!
Stellar-mass Black Holes form from the collapse of massive stars (roughly 
). Their Schwarzschild radius ranges from a few kilometers to tens of kilometers.
). Their Schwarzschild radius ranges from a few kilometers to tens of kilometers. Supermassive Black Holes found at the centers of galaxies, such as Sagittarius A in the Milky Way (
), their Schwarzschild radii span from a few million to billions of kilometers!
), their Schwarzschild radii span from a few million to billions of kilometers! Primordial or Micro Black Holes, are the hypothetical small black holes with masses much smaller than stellar masses, where the Schwarzschild radius could be extremely tiny.
A black hole, in general, is a solution to Einstein’s general theory of relativity where spacetime is curved to such an extent that nothing within a certain region, called the event horizon, can escape.
Types of Black Holes:
1. Schwarzschild (Non-rotating, Uncharged):
- This is the simplest type of black hole, described by the Schwarzschild solution.
- Its key feature is the singularity at the center, where the curvature of spacetime becomes infinite.
- No charge, no angular momentum (spin), and spherical symmetry.
2. Kerr (Rotating):
- Describes rotating black holes.
- Involves an additional parameter called angular momentum.
- Has an event horizon and an inner boundary, known as the ergosphere, where spacetime is dragged around by the black hole's rotation.
3. Reissner–Nordström (Charged, Non-rotating):
- A black hole with electric charge.
- A charged black hole has two event horizons (inner and outer) and a central singularity.
4. Kerr–Newman (Rotating and Charged):
- The most general solution, describing a black hole that has both charge and angular momentum.
Relationship Between Schwarzschild Radius and Black Holes
Formation of Black Holes: When a massive star exhausts its nuclear fuel, gravitational collapse can compress the core beyond the Schwarzschild radius, creating a black hole.
Event Horizon: The Schwarzschild radius marks the event horizon for a non-rotating black hole. This is the boundary beyond which no information or matter can escape the black hole.
Curvature of Spacetime: At distances closer than the Schwarzschild radius, spacetime curvature becomes so extreme that all paths, even those of light, are bent towards the black hole’s singularity.
BTW, the term singularity, scientificaly 😊, means that: we do not have a clue what is really happening right there...
Detailed Properties of Black Holes:
a. Singularity:
At the center of a black hole, within the Schwarzschild radius, lies the singularity, a point (or ring in the case of rotating black holes) where gravitational forces compress matter to infinite density and spacetime curvature becomes infinite. General relativity breaks down at the singularity, and a quantum theory of gravity is required for a complete understanding.
b. Event Horizon:
The event horizon is not a physical surface but a boundary where the escape velocity equals the speed of light. For an outside observer, objects falling into a black hole appear to slow down and fade away near the event horizon due to gravitational time dilation, a prediction of general relativity. From the perspective of the infalling object, however, it crosses the event horizon in finite time without noticing anything special at the moment of crossing.
c. Hawking Radiation: (In the post, I told that there is no radiation - to make it simple, although, there is a relatively newly-found (theoretically) radiation. Truth to be said, some physicists are still chalenging this notion, in some of it's parts...)
Quantum mechanical effects near the event horizon predict that black holes can emit radiation (Hawking radiation), a process through which black holes can lose mass and, over very long timescales, potentially evaporate completely. This process has a temperature inversely proportional to the black hole's mass, making large black holes emit extremely weak radiation. (Very trivialy speaking: the concept supposes that an anti-particle is drawn from the vakum and is anihilated with the black's hole matter (particle), and in the process, the black hole looses mass gradually and proportionally to the released energy - very slowly(!)).
This radiation is significant only for small black holes.
Gravitational Time Dilation (here, as well, things become 'super-weird'...)
Near the Schwarzschild radius, the intense gravitational field leads to time dilation. For an external observer far from the black hole, time appears to slow down for an object moving toward the event horizon. As it approaches the Schwarzschild radius, time dilation becomes so extreme that the object appears frozen in time at the horizon.
The time dilation factor is given by: 
Eg. Approaching the Schwarzschild radius and theoretically remaining just outside of it for a few hours would correspond to the passage of approximately several decades on Earth due to relativistic time dilation.
Using relativistic equations, it's estimated that near the event horizon 2 hours (120 minutes) near the black hole Sagittarius A* (as already mentioned ~ 4 million 
) - in the center of our galaxy Milky Way, could correspond to 83 years passing on Earth! However, this varies based on the precise distance from the event horizon (give or take, a decade 😬).
) - in the center of our galaxy Milky Way, could correspond to 83 years passing on Earth! However, this varies based on the precise distance from the event horizon (give or take, a decade 😬).Information Paradox (definte answer on this question, 'hold's the keys of the universe' 😊, maybe...)
The black hole information paradox arises from the seeming contradiction between general relativity and quantum mechanics.
According to quantum mechanics, information cannot be destroyed, yet anything falling into a black hole seems to be lost beyond the event horizon. Hawking radiation, which allows a black hole to evaporate, does not appear to carry information about the matter that fell into the black hole, leading to ongoing debates and research into how information is preserved in the context of black holes, or not...!
Schwarzschild Radius is the key parameter defining the size of the event horizon of a non-rotating black hole. Black Holes are regions where the Schwarzschild radius constrains all physical phenomena due to extreme gravitational forces, forming event horizons and singularities. The interaction between general relativity and quantum mechanics in the context of black holes (e.g., Hawking radiation and the information paradox) remains one of the most intriguing areas in modern theoretical physics.
For detailed and further reading: https://www.sciencedirect.com/topics/physics-and-astronomy/hawking-radiation.
I hope you will find this post, and information provided, interesting.
You can make a lot of interesting objects with matlab primitive shapes (e.g. "cylinder," "sphere," "ellipsoid") by beginning with some of the built-in Matlab primitives and simply applying deformations. The gif above demonstrates how the Manta animation was created using a cylinder as the primitive and successively applying deformations: (https://www.mathworks.com/matlabcentral/communitycontests/contests/8/entries/16252);
Similarly, last year a sphere was deformed to create a face in two of my submissions, for example, the profile in "waking":
You can piece-wise assemble images, but one of the advantages of creating objects with deformations is that you have a parametric representation of the surface. Creating a higher or lower polygon rendering of the surface is as simple as declaring the number of faces in the orignal primitive. For example here is the scene in "snowfall" using sphere with different numbers of input faces:
sphere(100)
sphere(500)
High poly models aren't always better. Low-polygon shapes can sometimes add a little distance from that low point in the uncanny valley.
Go to this page, scroll down to the middle of the long page where you see "Coding Photo editing STEM Business ...." and select "STEM". Voilà!
Next week is MATLAB EXPO week and it will be the first one that I'm presenting at! I'll be giving two presentations, both of which are related to the intersection of MATLAB and open source software.
- Open Source Software and MATLAB: Principles, Practices, and Python Along with MathWorks' Heather Gorr. We we discuss three different types of open source software with repsect to their relationship to MATLAB
- The CLASSIX Story: Developing the Same Algorithm in MATLAB and Python Simultaneously A collaboration with Prof. Stefan Guettel from University of Manchester. Developing his clustering algorithm, CLASSIX, in both Python and MATLAB simulatenously helped provide insights that made the final code better than if just one language was used.
There are a ton of other great talks too. Come join us! (It's free!) MATLAB EXPO 2024
All technical questions
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