Applied Mathematics

I'm an anthropology student. I'm currently studying the inter-relatedness of most- if not all- human beings alive today. I also have an interest in statistics so I am using probability theory to come up with estimates. Here is something I go This is just for my own theory- something I can up with. According to the Law of Truly Large Numbers... "that with a sample size large enough, any outrageous thing is likely to happen. This law was made by Persi Diaconis and an associate . This means that this "unlikely event" has a probability of 63.2% of happening if 1000 chances are given, or over 99.9% for 10,000 chances. In other words, a highly unlikely event, given enough t…

Hi all, I am working on a couple of exercices due this Saturday in Theory of Optimization. I was wondering if someone is proficient to assist me as I'm struggling on some questions, mainly on minimum norm duality. Please let me know if you can help me and i would be pleased to tell you more. Thank you very much.

I have found a new solution to the Travelling Salesman Problem. I have tried the solution on all the "complete" graphs of the examples in the 2 textbooks given in the reference section in the post given below. The solution is as follows :- Starter Edge method for an improved solution for the Travelling Salesman Problem Abstract This paper is mainly about a solution to the graph problem of Figure 5.23 given in the book 'Elements of Discrete Mathematics' by C.L.Liu. General note In the starter edge method, the edge with the least weight in a graph is selected as the beginning edge to be taken to b…

This thread paraphrasing an old interesting one in this same forum. As always fascinated by the power of units and after a post of dear Swansont, here are some thoughts: _as an Architect, I use quite commonly a method to measure the slope of a piece of land, or the slope of a ramp, expressed as a percentage. For example say you have a ramp 10 meters long going one meter up, that gives a slope of 10% What did you do? You took the eight divided by the length (the horizontal projection), that is: 1m/10m=0,10 or 10% In fact you divided meters by meters and ended up with a unitless number. This unitless number represents something physical thoug…

After reading this outstanding pdf arxiv first provided on this forum by DH in this thread post #11: It is stated and commonly accepted that C is a fundamental quantity. (Trialogue on the number of fundamental constants Authors: M. J. Duff, L. B. Okun, G. Veneziano, 3.1, page 4) Why then C has no "fundamental unit" (a unit of velocity, call it for example "velocimetre" or "velociconds") and is paradoxically exprimed as a ratio of 2 other units, metres and seconds? How come that the metre or the second is a part of something fundamental? or Ultimately, is it possible to have something that is a part of something fundamental ? In the third part of the sam…

I'm not sure this is the exact right place for this is if I am allowed to do this or not. I was wanting to post two topics for this but in two separate place, but at least we can discuss this here, or if A mod reads this they can move it to where it should go, if you are going to do this, this idea is a good one but really two ideas there is the mathematical side which is where I really need some help with, I am ready for another scientist whether mathematically gifted or gifted with Omniverse Theory. To help me with my research, I know I can do it on my own, but I know two people can work faster than one. I'm want to tell all I have theorized in its entirety. I have a ve…

For example, I know that r^2 of linear regression is, in certain cases, related to the correlation coefficient (goodness of fit) but is there are precise mathematical definition? Perhaps with a geometric interpretation? Any and all references would be helpful.

Interesting article on CNN on applied use of Markov Chains in scheduling (or rather NOT scheduling) buses at Georgia Tech. Waiting for a Bus? Math May Help - Lightyears Blog, CNN.com

I have an assignment http://www20.speedys...nload/image.png which is a bit different, I have to use Mathematics Handbook for Sience and Engineering to solve the problem, I can look it up in tables. But the tables for binomial functions is only up to 20, Normal Distribution to 3.4 and Poisson up to 24 in some cases. So how do I do it? Approximation of some kind?

I have time series data of experimental observations for two related processes. I want to measure correlation for use in further analysis. Correlation of the series changes over time and across different length sliding windows on the data. To clarify, I might want to look at correlation over 5, 6, 7, 8, 9, 10, ..., n periods, each of these essentially sliding windows across the data. Kind of analogous to looking at a range of simple moving average windows. Historically and over future observations, one of these correlation windows will prove a better representation of the data than the rest. But the random nature of the underlying processes (whose distribution one…

example(equation) where diff.eqs. are useful in computer science

I am starting this thread as a response to the blog by Captain Refsmat. as I do not get on well with blogs. Two thoughts 1) There is another use of statistics that is totally usually ignored in such discussions and revalations. That of engineering statistics, where conditions are carfully controlled to give validity to the technique. This leads to the articles giving the false impression that statistical testing is generally invalid. 2) The is another recent populist book on the subject, which is the outcome of a BBC program series into the subject. The Tiger That Isn't Michael Blastland & Andrew Dilnot go well Edit http://www.sciencef…

Hello all, i have some kind of task where i want to use a Netowrk with one hidden layer. the simpliest version of task is to find argmax of each summed row in matrix. (ofcourse in practice this task is a bit different - outuput is not argmax but some experemental answer that should be very similiar to it ) for example input [ 1 3 4 5 1 1 2 2 2 ] wir make sum on each row 1+ 3 +4 = 8 and etc. 5 + 1 +1 = 7 2 +2+2 = 6 and as output wir should receive [2 1 0 ] - this means that row 1 - is maximum all inputs are normalized t 0 - 1 Neural network works not very fine already on 3x3 matrix - it has max precision ~70% on Train ~1000 i…

Hi. i need to use a tri-cubic splines method for interpolation of a function F(x,y,z). i understand that the function is interpolated by F=sum(A(i,j,k)*x*y*z) the coefficients matrix is calculated from by using a constant matrix of 64*64. That matrix is mentioned in several places from Wikipedia (http://en.wikipedia.org/wiki/Tricubic_interpolation) to papers such as the one in (http://www.google.com.au/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CFMQFjAA&url=http%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fdownload%3Fdoi%3D10.1.1.89.7835%26rep%3Drep1%26type%3Dpdf&ei=qZoHUIT9E-jUigfQ6PycBA&usg=AFQjCNEz-WxceAImsf2mA43xY5IFDzVZew). howeve…

This topic in applied mathematics concerns the rating of chess players so that rating differences will imply odds, convergent with increasing data a the mathematically deduced best rate possible without causing anomalies. Applied to Swiss Tournaments, computer simulations verify perfect ranking and unprecedented convergence for odds calculation. The calculation of odds is a unique feature, and allows objective analysis of simulation results. The formulae can be applied to any endevour between pairs of competitors, where success may be guaged as two parts of the whole. In chess o, 1/2, or 1 are the only results used.

There are 9 cities. The ciities ar ordered from 1 to 9 and they are always visited in order from 1 to 9. From city n to city n+1 there are 4 routes, let's call them 1, 2, 3 and 4 . The distances doesn't matter. There are 4^8 possible routes from city 1 to city 9. Is it possible to find out the minimum number of ways to go from city 1 to city 9, such that the route would differ at one and only one segment from the one considered to be the right route? In other words: Possible vectors: (1,1,1,1,1,1,1,1) (1,1,1,1,1,1,1,2) (1,1,1,1,1,1,1,4) (1,1,1,1,1,1,2,1) (1,1,1,1,1,1,2,2) . . . (4,4,4,4,4,4,4,4) Person A chooses any of those. What …

Hi all, I have written this article: .link removed I'd love to have your reactions. Thanks. Lê.

Is there an easier way to find the sum of all whole numbers between x and y (including x and y themselves) than to just sit there and painstakingly add every one up individually? Like, for example, I know that an easier way to find the cumulative product of all whole numbers between 1 and x all multiplied together is to simply punch in the equation "x!" into a calculator, so you don't have to painstakingly multiply 1*2*3*4*5...*x. Is there a similar "shortcut" for addition?

A bow string pushes an arrow say at 50N force for 0.05 seconds. If the arrow is made of lead, it will not reach very far. If the arrow is made of balsa wood, it will not reach very far. If the arrow has certain mass, will 'match' and will reach the farthest. How to calculate the optimal matching mass for an arrow in order to reach the farthest; for a given force / impetus ?

Description: Normal decision tree algorithms are designed to handle simple data (single valued data belongs to one class). This Algorithm is an extension of classical decision tree algorithm in order to handle multi valued, multi labeled data. How do you rate such a modified Algorithm,Is there any scope for it.Please share your views..

(a) A particle of mass 4 kg moves under a force: F = 6t^2i - tj - 4k in Newtons. Assuming that the particle is initially at the origin with velocity v = i + k in m/s, find its position after 1s. (b) A ball of mass m travels with velocity 3 m/s and collides with a second ball with mass 2m at rest. After the collision the 2m ball moves with speed 1 m/s in a direction 60degrees to the original direction of the ball m. (i) What is the final velocity of the ball m ? (ii) What is the angle between the paths of the two balls after the collision ? If you could answer and explain how to do either or even both of these it will possibly save me from failing an exam to…

Is there a book that will introduce probability to me without requiring that I already know the maths involved. I want to learn the mathematics in the process. I know precaclulus but no calculus. I don't know any probability besides the little discrete probability I learned in precalculus I. I'm good at math. On a state-sponsored test administered during highschool, I scored in the ninety-fifth percentile of my school for mathematics, although I was never placed in an advanced class. Most books on probability are expensive, although I found a few books on probability or statistics that I can get for cheap. Probability: An Introduction (Goldberg) is approximat…

In a lottery 6 numbers are extracted out of 90 (numbers 1 to 90). The numbers extracted are not put back in the bin. One can win guessing 3, 4, 5 or 6. Betters play combinations of at least 6 numbers each. I play 15 randomly composed "entirely unique" combinations of 6 numbers each. I mean that each combination is completely different from any other, so that collectively I play all 90 numbers. Each combination differing from every other in all six numbers. This way I have 100% probability of making "at least 1" which gives me a degree of satisfaction, if I switch off my brain. Also when the winning combination is extracted, I memorize the first four numbers and …

Hello All, Can anyone find an analytic solution (preferred, not implicit) to the following equation: \dot{x} = -alpha \sqrt{x} + \xi(t) x(0) > 0, t \in [0, T] and T such that, x(t) > 0. \alpha > 0 and \xi(t) is any smooth function. A solution for a any specific non-trivial \xi(t) is also appreciated. Best, Miki

From the Wikipedia article "Turgot Map of Paris": In 1734 Michel-Étienne Turgot, chief of the municipality of Paris as provost of merchants, decided to promote the reputation of Paris for Parisian, provincial or foreign elites by implementing a new map of the city. He asked Louis Bretez, member of the Royal Academy of Painting and Sculpture and professor of perspective, to draw up the plan of Paris and its suburbs. Detail from maps 11 & 15 with the Louvre In the eighteenth century, the trend was to abandon portraits of cities (inherited from the Renaissance) for a geometric plan, more technical and mathematical. But the plan de Turgot goes against this…