PM_ME_VINTAGE_30S
@PM_ME_VINTAGE_30S@lemmy.sdf.org
Why don’t you have a second account?
Lazy. Don’t care if my shit gets fucked. But if you do care if your shit gets fucked, then you shouldn’t rely on centralized social media.
—PM_ME_VINTAGE_30S@vlemmy.net, Professional Life Regretter, about a week before his shit got fucked
- Comment on mphf 2 days ago:
I mean I upvoted 😆
- Comment on mphf 2 days ago:
To whomever created this: it would have cost you zero dollars to not bring this abomination into the world 😆
- Comment on Can you explain your grad school research to relatives over Thanksgiving Dinner? - Journal of Astrological Big Data Ecology 5 days ago:
If I’m understanding your comment correctly, wavelets are a kind of discrete and/or finite quantization of the “full” infinite Fourier transform, by way of using more complex “basis vectors” than pure sine waves?
The second part is basically correct, but the first part needs a little bit of explanation.
So depending on what you need to do, you can actually use continuous-time (or continuous-space) wavelet transforms, or discrete-time (or discrete-space) wavelet transforms. The continuous-time wavelet transform is, practically, “just as exact” as the continuous-time Fourier transform. So instead of being “better” or “lesser” than the Fourier transform, it’s really a “different perspective” on the same space of signals by choosing a different set of “basis” vectors [1].
Also, wavelets often are “more complicated” than sine waves, but not necessarily. In fact, one of the first wavelets discovered was this, the Haar wavelet:
To be completely clear: this waveform is defined for any real number; it’s not sampled, and it is not a quantized version of some “better” wave! It is just 1 for any inputs between 0 and 1/2, -1 for any inputs between 1/2 and 1, and 0 everywhere else [2]. Although this wavelet happens to have a finite range (so not even countably infinite, you get {-1,0,1} and you don’t get upset), if you slap enough of these things together (possibly infinity of them), you can get back any “reasonable” waveform, where “reasonable” is precisely defined in Mallat’s book (it’s L^2® if you’ve been exposed to L^p spaces).
Hope you enjoy the book as much as I have!
[1] “Basis” is in quotes because it depends on what you mean by “basis”. Typically, a “basis” in linear algebra means that you need to be able to exactly recover any element in the vector space with a weighted finite sum of the bases — a Hamel basis. In signal processing, in particular in Mallat’s book, we typically extend the notion of basis to allow for infinite linear combinations with limits. This means that we need to choose a topology, which is absolutely a reasonable requirement in signal processing, but not necessarily in “pure” linear algebra. I believe that the definition for “(orthonormal) basis” in Mallat’s book (in Appendix A) is called a(n orthonormal) Schauder basis in other parts of applied math.
By contrast, “vectors” is not in quotes above because, using the “generic” definition of a vector space, the basis elements are indeed vectors, i.e. members of a space that you “cannot leave” by scaling or adding finite numbers of the basis elements.
Lastly, “signals” and “vectors” are mostly interchangeable within the signal processing discipline. In signal processing, we typically assume that signals have been given an inner product (“correlation”, “dot product”), therefore a norm (“length”) from the inner product, and therefore a topology (“abstract geometry”) from the norm. I.e., “signals” in signal processing usually have more structure than “vectors” in applied math.
[2] The values of the Haar wavelet at exactly {0,1/2,1} are in the plot. However, since continuous wavelet transforms are integral transforms, the values at the points {0,1/2,1} can be changed to whatever you want as long as it’s finite. Rigorously, the Lebesgue integrals in the wavelet transform definitions are “blind to” a “small” (measure zero) set like {0,1/2,1}. From a signal processing perspective, changing the signal only on “small” sets like {0,1/2,1} is not enough to change the signal energy.)
I think there is a reason why the choice of values at {0,1/2,1} given in the plot makes sense. Mathematically, the choice makes the Haar mother wavelet right-continuous and upper semi-continuous, but I can’t remember off the top of my head why this is helpful for applications.
- Comment on Can you explain your grad school research to relatives over Thanksgiving Dinner? - Journal of Astrological Big Data Ecology 1 week ago:
That’s fucking cool!
- Comment on Can you explain your grad school research to relatives over Thanksgiving Dinner? - Journal of Astrological Big Data Ecology 1 week ago:
Okay here are the 🫘:
Wavelets:
So the best way to begin explaining wavelets is through analogy to music. (I’m cheating a bit since this explanation is alluded to in the article 😆)
It is a nontrivial practical fact that you can express any reasonable sound as a sum of sine waves. Yes, by combining enough sine waves (which individually “move” for all time) in just the right weights, you can come up with “any” sound you want. And then, it turns out that if you give me just the weights, I can give you back the sound itself. And as a final physical fact, it turns out that we hear the weights of any given sound, averaged over some finite window of time (more on this window in a minute). Hence why we can pick out instruments from a band. And lastly, some phenomenon are easier to analyze by looking at the weights; music is an excellent example. In fact, when I mix music in my rapidly diminishing free time, I am often staring at a graph of the weights and seeing this these weights add together and make the instruments work together.
Formally, we use one of the Fourier transform frameworks. Each weight is associated to one unique sine with a given frequency. The size of the weight is called the frequency response at that frequency.
Now for many, many purposes, breaking up a signal in terms of sines is a perfectly appropriate choice. However, what you lose when you choose to look at just the weights is all timing information. (This is why I included the detail about the window in how you hear stuff. If you heard all frequencies over all time with no window, you would not be able to perceive rhythm.) The solution in music often is to simply impose a window on the signal and slide it as the play head moves.
However, we must now leave the realm of music to talk about wavelets in a domain where they are typically used. Now imagine you want to apply all your intuition about music [more accurately, theory of sound, not music theory] to seismic signals. Well… unfortunately, we really do care about the timing of these signals. So instead of ditching all the magical techniques of linear algebra and transform analysis, we can pick a new set of waves and decompose in terms of those. I.e., we use a transform “midway” between the Fourier transform and the identity transform (doing nothing, just working with the raw signal).
One way to do this is to start with a wavelet: any waveform with zero average and finite “length”. Then, you take this mother wavelet, and you create child wavelets by stretching and/or shifting the mother wavelet. Then, you break up your signals in terms of the wavelets. (I think you pick wavelets based on what you want to find. For example, if you want to find sharp changes, you can pick a Haar wavelet, which is basically a family of rectangles. And then, you can pick wavelets based on their statistics so that the variances and higher order statistics vanish.)
My favorite book on Wavelets, and one of my personal favorite books, is A Wavelet Tour of Signal Processing: The Sparse Way by Mallat. It’s a bit mathematically challenging, but it’s such a fun read. One of the few books I actually own in print. And it’s one those cool fields in math where you basically just start with like pure math and end up with some incredibly practical results and algorithms.
Research:
My background is in control theory. I work on analyzing dynamical systems, specifically large-scale, complicated (typically people use the word “complex”, but I really mean complicated, because all the systems I work on evolve in real spaces) systems that evolve in time according to differential equations (e.g. electronic circuits, mechanical systems, power systems) or difference equations (e.g. sampled versions of the above). The goal of my research is to make just enough assumptions and prove it using calculus so future generations don’t have to do so much calculus…because you have to do so much calculus that not even a supercomputer can solve it.
PM me for more details since I’m not quite ready to dox myself 😆
- Comment on Can you explain your grad school research to relatives over Thanksgiving Dinner? - Journal of Astrological Big Data Ecology 1 week ago:
Goddammit now I want to talk about wavelets and my research 😆
- Comment on Insulin 1 week ago:
Do you know? Curious where folks pick this stuff up.
I do know that Maoists use it, but I think I picked it up when I read about some Black Panthers using it (I mean they probably were Maoists). And also I started doing this when some snarky shitlibs were like “oh you shouldn’t say ‘America’ because Central America is ‘America’” so I’m just like “then I guess we’re doing this now” 😆.
I’m an anarchist so of course not a Maoist, but I absolutely do not disagree with Maoists about the particular issue of America not being a good thing.
- Comment on Insulin 1 week ago:
Unfortunately I have a terminal case of CBA (can’t be arsed)
- Comment on Insulin 1 week ago:
Being “slightly less than servile to AmeriKKKan sensitivities while anarchist” is not being “a tankie”.
- Comment on Insulin 1 week ago:
If you don’t mind sharing, did you have to pay the exit tax? Actually, what was your way out?
- Comment on Insulin 1 week ago:
No I’m pretty sure you’re a liberal, right? We probably do not agree almost at all. See this video for more information.
- Comment on Insulin 1 week ago:
Oh well
- Comment on Insulin 1 week ago:
you’re absolutely insufferable.
Agreed lol I don’t like me either
When the people who agree with you
No I actually suspect we disagree, but you think we agree. This isn’t the first time I’ve seen you comment.
- Comment on Insulin 1 week ago:
Fine, just do Ctrl+F, replace each instance of AmeriKKKa with {insert preferred term for the United States}, and move on with your life. It’s almost like you have a problem with what I’m saying and not how I’m saying it…
- Comment on Insulin 1 week ago:
Yeah I hope I get the mental help I obviously need…oh no wait I’m in the US so no I won’t
- Comment on Insulin 1 week ago:
A: It completely undercuts the seriousness of your comment and makes the whole thing come off as a tirade by an edgy teenager.
So you disagree with the tone and not what I’m saying? Because if so, that sounds like a “you” problem, i.e. you’re more interested in the tone of a message than its content.
B: Jokes don’t get funnier every time you repeat them, it was mid the first time and eye roll worthy by the 3rd.
It’s not a joke and it’s not supposed to be funny. I genuinely hate the USA and everything it stands for.
- Comment on Insulin 1 week ago:
My comment was in response to a comment about AmeriKKKans having “Stockholm Syndrome”, which as it turns out is not a real or valuable diagnosis. However, I do not disagree with the implied critique of AmeriKKKan people as being feckless and servile people.
- Comment on Insulin 1 week ago:
Does anyone really need to live? What you need is to be producing value for your company!
/S
- Comment on Insulin 1 week ago:
AmeriKKKa is a settler-colonialist project, and the entity and its defenders deserve zero respect. You are literally on an anarchist Lemmy instance, why TF is this controversial to you?
- Comment on Insulin 1 week ago:
Reminder that the term Stockholm Syndrome was coined to blame victims for being rightly more afraid of the police than their captors:
In [Jess Hill’s] 2019 treatise on domestic violence See What You Made Me Do, Australian journalist Jess Hill described the syndrome as a “dubious pathology with no diagnostic criteria”, and stated that it is “riddled with misogyny and founded on a lie”; she also noted that a 2008 literature review revealed “most diagnoses [of Stockholm syndrome] are made by the media, not by psychologists or psychiatrists.” In particular, Hill’s analysis revealed that Stockholm authorities, responded to the robbery in a way that put the hostages at greater risk from the police than from their captors (hostage Kristin Enmark, who during the siege was granted a telephone call with Swedish Prime Minister Olof Palme, reported that Palme told her that the government would not negotiate with criminals); as well, she observed that Bejerot’s diagnosis of Enmark was made without ever having spoken to her.
- Comment on You can do anything at Zombocom 3 weeks ago:
The power of Bogatin compels you! Image
- Comment on If you truly love your girlfriend, then you need to buy her an expensive engagement ring. If you don’t have the money, then you don’t deserve to be in a relationship. 3 weeks ago:
It’s almost beautiful how terrible of an opinion this is 🖕😆🖕
- Comment on When we eat the billionaires, we should spare Gabe Newell? No? 3 weeks ago:
The working class
- Comment on When we eat the billionaires, we should spare Gabe Newell? No? 3 weeks ago:
No lol.
- Comment on I promise I'm not 4 weeks ago:
I am crazy but the only help I need is the abolition of all forms of domination and hierarchy
- Comment on i hate myself and i want to die lol 5 weeks ago:
Re: thread about your PhD manuscript. Strongly recommend waiting until not shit faced 😆
Short answer: send whatever you have
Long answer:
So I’m taking a course on advanced machine learning. I know pretty well how to use SkLearn, Pytorch, and HuggingFace transformers to implement machine learning algorithms.
But the thing is that my research is in dynamical systems, specifically power system dynamics. (I’m the “control guy” in my group, i.e. I know more about math (specifically control theory) than I do power systems.)
So my group is really interested in getting theoretical guarantees because … well, ultimately we’re literally trying to keep the lights on. So I’m taking this machine learning course to learn about asymptotic analysis and finite-sample analysis of the convergence of ML algorithms, i.e. to mathematically analyze machine learning algorithms. Power systems are extremely high-dimensional and nonlinear, and as more wind and solar PV plants are added to the grid, we’re actually going to have to change how we control the grid because they don’t “act like” synchronous machines (i.e. hydro, fossil, nuclear, biodiesel plants).
And to the ML professor’s credit, he has taught these things and he’s clearly very careful about the mathematics. But he really does over-rely on LLMs which … I’m having trust issues.
So one thing our group does is data-driven analysis of dynamical systems. For controlling or observing a dynamical system (like a power grid) our group has been looking into the Koopman operator framework. The Koopman operator is a composition operator that converts a nonlinear dynamical system into an infinite-dimensional linear dynamical system. Unlike standard linearization, this method makes no approximation. Now, by approximating this infinite-dimensional linear operator with a finite-dimensional linear operator, i.e. a matrix. Then in this framework, we can do data-driven control (take the system to an arbitrary state), estimation (get the internal state, for example see if the system is in a dangerous state), and identification (for a mechanical example: you know that you have a pendulum and you have recorded the trajectory of the pendulum, but you want to know the mass and length of the pendulum).
So we have a huge interest in machine learning and it’s impressive results, but we are also going be honest with whatever theoretical guarantees we can prove. So yeah if you have any literature on machine learning, specifically supervised and reinforcement learning, please send.
- Comment on i hate myself and i want to die lol 5 weeks ago:
I mean I’m taking a class on machine learning and … well … on the one hand it’s supposed to be a “rigorous” theoretical class, and the project at least is going to actually be that because I get to choose the topic and I’m obviously gonna be doing my own math … but on the other hand, my professor keeps saying “ask the LLMs for more details” 😭😭😭😭😭. I guess he decided teaching students real analysis is hard and ChatGPT is easy.
- Comment on i hate myself and i want to die lol 5 weeks ago:
Machine learning?
- Comment on i hate myself and i want to die lol 5 weeks ago:
Hell yeah! What’s your research about?
- Comment on Are bots on lemmy? 5 weeks ago:
There are definitely bots but I think people are good about making their bots known, and most of the content you see is posted by humans… because who tf would pay to run a bot farm on our little corner of the Internet?
If you want to see absolutely no accounts that self-report as bots, there’s a setting for that in Lemmy.
