Applied Mathematics

Hi guys, I really need help with this question :/ (my sketch: https://www.geogebra.org/classic/abeyyk7p ) Let ABC be an acute, non-isosceles triangle with D is any point on segment BC. Take E on the side AB and take F on the side AC such that ∠DEB = ∠DFC. The lines DF, DE cut AB, AC at M, N, respectively. Denote (I1), (I2) as the circumcircle of DEM, DFN. Let (J1) be the circle that internal tangent to (I1) at D and also tangent to AB at K, let (J2) be the circle that internal tangent to (I2) at D and also tangent to AC at H. Denote P as the intersection of (I1…

Hi, I was reading an article related to MonteCarlo Method. The link of the article is: http://ib.berkeley.edu/labs/slatkin/eriq/classes/guest_lect/mc_lecture_notes.pdf I found the equation in the following attached image. 1)In the equation related to the attached image, we are assigning a value to a function. What does this mean? 2)What the expected function will do with this value? 3)Please guide me by providing examples of function fX(ꭓ), E(g(X)) and g(ꭓ). Zulfi.

A team or a player who has 20 wins in 20 games is better than a team or a player who has 40 wins and 20 losses in 60 games. Whereas the both have wins-losses=20. And a team or a player that has 200 wins in 200 games is better that a team or a player who has 1200 wins and 1000 losses in 2200 games. Whereas the both have wins-losses=200. Therefore the correct rating is not wins-losses, but (wins-losses)/(number of games)=(w-l)/g, which is equivalent to (wins+0.5draws)/(number of games)=(w+0.5d)/g. But a team or a player who has (1+0.5*0)/1=1 almost certainly is much more weaker than a team or a player who has (90+0.5*0)/100=0.9, therefore the (w+0.5d)/g needs two modificati…

I have done empirical research for 10+ years and I'd say I'm familiar with statistical methods, both Bayesian and classical. So, I have a question: Why do people use Bayesian methods? Can anybody give a good reason? I'm all ears because I can give three obvious disadvantages: They're damn slow. People don't really check that the Markov chains have converged. (Ideally, you should do this by formal statistics like effective sample size, but most people just eyeball the trace and the scientific journals don't require formal tests.) Nobody checks how the prior affects the results. Again, the journals don't require you to do this, and you just use…

This thread is an attempt to quantify the methods used to communicate a mathematical concept to another person for the purpose of applying the concept. Each response should ideally contain: A single math concept, as you would present it to an inexperienced colleague in your field, who asks for help. Any additions that you would include for the average person. Optional comments. Provide as many examples as you like, including historical examples, but please send each as its own post for ease of evaluating responses. There are no restrictions on field or complexity. The only restrictions on length and format are the practical limitations…

So, I'm spinning my wedding ring on the table, (I'm right-handed, so spin it anti-clockwise, with my right thumb on the bottom and my left forefinger on the top). If I look down on it from above, it goes through a number of phases (has to be spun quite fast): 1. starts spinning anti-clockwise 2. the centre forms a triangle shape 3. slows and starts spinning clockwise 4. slows and starts spinning anti-clockwise and the centre forms a square 5. slows and starts spinning clockwise 6. slows and starts spinning anti-clockwise and the centre forms a pentagon 7. slows and starts spinning clockwise 8. slows and starts spinning anti-cl…

Hello Looking for someone to point me in the right direction so I can start researching a solution to the problem below: Problem Linear regression with high dimensionality - p=29, n = 5000ish, input variables are generally quite highly correlated When using the model for prediction, data sets regularly have a missing input parameter(s). At the moment I just refit a LSQ solution from the training data with that input deleted. This seems to lead to quite unstable results. Stability is important for my application, more so than absolute accuracy in some senses. -- Regularisation (e.g. Ridge) feels like it should help, but (and I'm not formally …

I was talking with a buddy on the train a couple of years ago, and he asked me what I thought about men who complain about some women not liking "nice" guys and instead going for "bad" guys. I asked him if he meant that those women don't like the "nice" guys because they are "nice", or despite them being "nice, and he said that it was despite them being "nice". I said the fact that they are "nice" is irrelevant then, since we can assume those women would still not like those "nice" men if they were "bad", and there must be other factors making them unattractive to those women. Eventually this got us talking about whether or not it was worth it to try to change one's perso…

is it just me or does this mathematical principal seem to be something we all should have learn in high school? also called benfords law. If you realize the potential of this like I do please comment or argue if you like.

Hello, Lets assume I have time history data from pressure probe placed in a duct where a gas flows. Of course, when using Fourier transformation (DFT or FFT) I may resolve significant frequencies occurring in the duct. If I create an attractor from these data, can this transformation bring some additional information compared to DFT/FFT ? Does attractor visualization and its post-processing bring "some better point of view" ?

Hello everyone,, I'm a college sophomore in an applied math BS program with a statistics concentration at a state university. I originally came from a computer science background, but I decided to pursue this after really enjoying my AP Stats class my senior year of high school. I'm currently taking my first mathematical statistics class and in an R job with a professor. Even though I still enjoy the subject in the classroom, I'm not 100% informed on what's out there as for career options (leaning towards data science right now). While still in college, how should one prepare for the best chance at a statistics job? Is going on to graduate school recommende…

Is there a command in Mathematica to transform a Beta function to Gamma function,actually when the output it is written in Beta function to transform that in Gamma function.If there is not a command for that can someone if he/she has a code to post here about this topic. Thanks for the answer.

Hi there everyone, I'm Koen Van Loon from Belgium and there is something that has been laying on my mind for quite some time now, but I'm not smart enough/don't have the proper education to solve it myself, so I thought you guys might be able to help. I was thinking about evolution and came up with an experiment which I would like to know the answer to. Lets say we have a highly sophisticated robot, either biological or mechanical (like those things from Boston dynamics). If we would randomly change this robot, the chance that it would become worse is naturally higher than the chance that the robot would be improved by this chance. This …

Some of the latest posts in Speculations have led me to this attempt at clarification, because I see that some people are very confused when it comes to handling equalities. The point is their meaning. It's subtle, but it's not moot in general; although in some cases it may be. Not all equalities are the same. There are at least these variants: Definition (or substituting symbol or replacing symbol, etc.) Example: fine structure constant, \[\alpha\overset{{\scriptstyle \textrm{def}}}{=}\frac{e^{2}}{4\pi\epsilon_{0}\hbar c}\] Identity (or universal equivalence under known or specified set of previous rules that may be algebraic, geometric, etc.) …

Hey everyone, At some part during my studies I had to read and subsequently discuss a paper, I remember this as one of the more difficult papers I had ever read, although after the discussion understood everything. I recently looked back at the paper and now see that I do not understand it anymore (or maybe never did). https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5474757/ My question is specifically about the false discovery rate metric used here (see text and picture at the end of this post). For context, I will briefly explain what they do in this paper before asking my question: In this paper the researchers introduced random mutations into cells (on average …

I was refreshing my memory of the derivation of ridge solution and realised I haven't got some of the intuition quite right in my head. Specifically - by using regularisation when fitting a very high order polynomial, intuitively the regularisation part of the objective function should kill off some of the higher order terms. However since the penalty is on the L2 norm of the weights, it will penalise larger weights preferentially and on first glance this would appear to penalise the lower order terms first. Since the data should be normalised this is not a problem in reality (ie. higher order terms in the data matrix are reduced, so their weights larger). …

Hello, Thank you for read this question. I am trying to understand dynamic programming to find a solution to a optimization problem. I understand optimization through linear programming but it is not enough to solve my problem. What I would like to know is how dynamic programming deal with the optimization of the process as a whole, I mentioned LP because I can see how LP works (objective and constraints) and maybe DP has similitudes. Maybe the answer of my question is studying more DP but any advise would be good. I feel like a loop should be closed like in LP but I do not see the concept or concepts which ensure that. I’ll apreciate any comment…

Can anyone hep me understand this solution I have attached both question and solution I can see the application of Fourier's law to the right hand side of the solution, but why is right hand side multiplied by area?, also to the left, what has happened to Ko. Thanks

Hey there! I am part of a research project on the intuitive understanding of probabilities in contour plots and we are seeking for participants for a short online experiment. Participation is completely anonymous and will take less than 15min of your time. Just go with the browser of your laptop or desktop PC (no mobile phones!) to: https://survey.fl.dlr.de/index.php/627715?lang=en With you participation in the experiment you directly contribute to current basic research of the Friedrich-Schiller-University Jena and the German Aerospace Center. We would be very happy if you could support our work. Thank you!

Hi there, I have just started going through a python programming book and one of the functions presented is the error function. I understand it is not very necessary for me to understand the mathematics behind it, but I would just like to. Now from looking at, reading a bit about it and watching a video how it is derived, it is my current understanding that the function computes the probability that a Random Variable (if assumptions of normal distribution, standard deviation and expected value are all met) can be found within [-x, x]. I think two things are unclear for me, firstly: what exactly is a Random Variable, the wiki article and some other websites tal…

The following image shows a set of points (A,,B,C,p) rotated (in this example 360/21°) anticlockwise around the origin o. The resultant set of points (A', B', C') are then rotated clockwise (18°) around the resultant point p'. My goal is to derive a single centre of rotation that will rotate the set of points [A,B,C] to [A' ',B' ', C' '], given only the position of p, and the two rotations: Graphically, by projecting normals to the centres of the lines A-A' ', B-B' ', C-C' ', (also p-p' '), where they cross at point r, gives me the center of a single rotation I seek. Question: how to do that mathematically given only: p = (7.160299318411282, 0) rotation1…

Hlw. Still I failing to understand the difference between Linear, semilinear and Quasilinear pde even after reading from Google. Can anyone clarify for me please.

Can someone please help me with this question?

I need help with understanding this question.