A description of the specific steps needed to solve a particular problem in an unambiguous way, expressed in an abstract form.

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An algorithm to produce, not necessarily efficiently, another algorithm that efficiently solves the Rubik cube

How complex is the task to formulate an algorithm that produces, not necessarily efficiently, another algorithm to efficiently solves the Rubik cube? Has it been attempted before? What is the latest ...
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44 views

MCNPX for nuclear simulation [on hold]

is it legal here to ask this problem? I need someone help. I run mcnpx. I try to calculate f4:n using nps:1000. But, it stop directly before culculate f4. There is comment: stack trace terminated ...
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22 views

Finding the time complexity of fibonacci function using recursion tree method [on hold]

I tried it in the following way and I want to know if I am right or wrong
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63 views

HDF5 Many Writers, One External Reader

I have an application where I want to have 3 different machines writing to their own independent HDF5 files at a high rate, but have a way to read data from them externally and combine it. Is HDF5 a ...
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0answers
56 views

How to fix time intervals to store data in a stochastic simulation (continous time markov chain)

I am using FORTRAN to implement Gillespie's stochastic simulation algorithm. I would be running many simulations in parallel (both parallel instances with different seed and parallel functions); if I ...
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1answer
77 views

How to evaluate a series of derivatives?

Consider the function $$f(\mathbf{x}) = \sum_{n=0}^{N} a_n \left( (\mathbf{b}-\mathbf{x})\cdot \nabla \right)^n \frac{1}{r}$$ where $r = |\mathbf{x}| = \sqrt{(x-x_0)^2 + (y-y_0)^2}$ and $a_n$ and ...
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3answers
123 views

Numerical integration algorithm for this set of ODEs

I have to solve numerically the following initial value problem, which physical origin is discussed in this article by G.I. Taylor (1941). Here $\eta$ is the independent variable and ranges beetween ...
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1answer
101 views

Newton iteration for cube root without division

It's a fairly well known trick to avoid division in calculating square-roots to apply Newton's method to finding $1/\sqrt{x}$, and probably better known, using Newton's method to find reciprocals ...
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35 views

Bracket Algebra, Straightening Algorithm

My apologies if the question is simple. I need to write a code for straightening algorithm. Which includes defining bracket algebra. I tried to write it in CoCoA-5, but it wasn't possible because ...
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3answers
140 views

Algorithms for radiation treatment planning

I have a medical physics problem - I want to maximise the dose absorbed by a brain tumour whilst minimising the dose in the rest of the brain, especially certain organs, such as the pituitary gland, ...
3
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1answer
69 views

How to Check a Hyper-Cube for Defects

I would greatly appreciate some help/references on solving the following problem: You are in charge of searching through a n-dimensional hyper-cube $[0,1]^n$ to make sure that it does not contain ...
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2answers
72 views

Faster methods for projecting a mesh onto a hierachally unrelated mesh?

I have a set of independent meshes whose results I would like to project onto another non-hierachally related mesh. Until now, I've been accomplishing this by finding the nearest-distance node in the ...
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74 views

Using SVD to biorthogonalize left and right eigenvectors?

I have a set of left and right eigenvectors from an nonsymmetric eigenproblem, and I'd like to biorthogonalize them. I tried Gram-Schmidt, but this fails for most cases. I then read that the SVD is ...
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3answers
137 views

Algorithm to compute the intersection of two lines given their cartesian equations

I'm looking for a way to compute the coordinates of the intersection of two lines. Each lines are defined with a point and a normal vector. We can assume than the normal vectors are not zero and ...
4
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1answer
126 views

Active Elements in Projected Newton's Method?

To those who are familiar with the projected Newton's method or projected gradient method... We consider a constrained optimization problem with simple bounds. Particularly, minimize f(x) subject to ...
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0answers
41 views

Finding a scalar field in order to generate a solenoidal vector from a given vector

I am working on generating a (complex) solenoidal vector field $\mathbf{A}$ from a prescribed (complex) vector $\mathbf{a}$ and the gradient of a scalar, $b$, such that $$\mathbf{A} = \mathbf{a} + ...
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2answers
87 views

How to prove time complexity of merge sort

I was asked to prove that the time complexity of merge sort is $ O(log_2n)$ but I cannot find a way to continue my method. Any help? $T(n)=2T(\frac{n}{2} )+n$ $T(n)= 2[2T(\frac{n}{4})+n] +n = ...
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1answer
36 views

MAX-SAT and MAX-cut

I have been using MAX-SAT solver to obtain the exact ground state of ising spin glass model: For 1D periodic model, for systems with 50 binary variables and interaction range of 15th nearest ...
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1answer
61 views

Help me analyze the computational cost of two kinds of operations

everyone, I have a question about computational costs for a algorithm. That is: I have two vectors $u_n,\ v_n\in \mathbb{C}^N$, a matrix $A\in \mathbb{C}^{N\times N}$ (can be both sparse and dense) ...
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43 views

Proof of corollary to Chinese remainder theorem

I was puzzled regarding corollary 31.29 of the Chinese remainder theorem as presented in the chapter on number theoretic algorithms by Cormen et al. I found another person who asked the same question ...
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1answer
69 views

Efficient way to compute the cumulative weights of all subtrees rooted at each node in a tree?

I have a tree data structure (rooted, unbalanced, with unbounded branching factor), where each individual node has an associated 'weight'. For every node $n$ in the tree, I'd like to compute the ...
3
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1answer
59 views

Computing the (non-convex) boundary of a set of paths between two points

I have a set of paths between two fixed points (marked in red below). Each of these paths consists of an ordered series of $\{x, y\}$ points (marked in blue). I am trying to find the ordered set of ...
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1answer
46 views

Adjusting Keplerian orbits for thrust with numerical stability

I'm writing a mod for a game that models orbital physics (Kerbal Space Program, or KSP). I'm attempting to model the effects of thrust on spacecraft in certain states where the game only models them ...
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2answers
350 views

A method to determine whether a point can be contained within a circle with no neighbouring points

I have been working on a particularly challenging problem and was hoping for some guidance. Here is my problem. I have a point cloud containing millions of points. For each point in the set, I need to ...
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16 views

Max weighted subset (max sum diversification)

Given a set of elements $V$, with known cost $\pi_S$ for each subset $S \subset V$ and a monotone increasing function on the subsets $f(S)$ . I'm wondering if there is a pseudo-polynomial algorithm ...
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2answers
90 views

fastest and most efficent way to count all combinations in many sets and sum them together

I am a Java programmer who has reached the limits of brute computer power. My relational database (and non relational databases) is not producing results quick enough and I have hit a bottleneck in ...
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137 views

Are there improved method of computing the following expression?

given a symmetric matrix $Y \in \mathbb{R}^{n \times n}$, and an arbitrary matrix $X \in \mathbb{R}^{n \times n}$, and a vector $v \in \mathbb{R}^{n \times 1}$, is it possible to compute the following ...
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1answer
106 views

What is the algorithm that matlab used in its built-in function 'pca'?

Do anyone know what is the algorithm that MATLAB used in its built-in function "pca"? I have the following data set: 148.9820 55.8438 210.2150 149.3030 56.8891 208.4280 151.4400 ...
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1answer
344 views

Patankar's algorithms for Numerical Heat Transfer and Fluid Flow

I am looking for the algorithm of Patankar (for example, SIMPLE, SIMPLER, SIMPLEC and PISO) written in Fortran for the simulation of heat transfer and fluid flow.
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1answer
41 views

What is a general method for identifying how connected parts of a binary volume are?

I have a binary volume consisting of a number of disconnected objects. (coming from a noisy, anatomic dataset) However, some of the objects are 'somewhat' connected. Picture a big cylinder and a ...
2
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0answers
95 views

How to get proper parameters of SPH simulation?

I'm implementing basic fluid flow simulator using SPH method basing on e.g. https://www10.informatik.uni-erlangen.de/Publications/Theses/2010/Staubach_BA10.pdf. So far I've implemented: uniform ...
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3answers
92 views

Algorithm: Extracting motion frequency from video

I was wondering if anyone knows of any algorithms or projects that can detect the frequency of a motion from a video clip. Like if I had a video of a bouncing ball with constant frequency, could an ...
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1answer
238 views

Finding optimal velocity profile using Dynamic Programming

While continuously reading about Dynamic Programming I have a problem, implementing it in a practical application. Let's assume we want to optimize our way to school which we go daily by bicycle. ...
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2answers
132 views

Finding shortest path in a time/distance map

I get a distance map output after using a Fast Marching Method. The PDE involved is the Eikonal equation which take the form : $$\begin{cases} c(x).|\nabla u| =1\\ u(x) =\phi(x) ...
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0answers
69 views

Parameter ESTimation (PEST) algorithm? Steps and purposes? [closed]

I'm reading up on the Parameter ESTimation algorithm, (Link to PEST homepage 1), and having trouble understanding the broad strokes, as I keep getting lost in null spaces, different regularized ion ...
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2answers
70 views

How to measure trajectory regularity?

I have two animal running trajectories. A regular one with repeated back and forth running between point A and B, like the one on top in the figure. The other one is very irregular, animal paused and ...
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35 views

Algorithm for porosity based CFD mesh

I am writing the pre-processing program for a porosity based CFD project. I have a mesh made of cubes, and need to import an object (a stl file: triangular mesh, not solid) over it. The cubes will ...
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1answer
109 views

How to minimize the artefact of a cartesian to polar transform followed by a polar to cartesian transform?

I'm transforming cartesian images into polar images. (x,y) => (angle, radius) I fill the polar image by iterating on each of its pixels and filling them by doing the reverse polar transform. For a ...
4
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1answer
103 views

Numerically compute one-to-one mapping

I have a set of points defined by their coordinates $(x_1,y_1)$ after changing some parameters of the problem I obtain a second set of points defined by their coordinates $(x_2, y_2)$. There exists a ...
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1answer
63 views

Appropriate algorithm for (non-linear) ODE with integral equilibrium constraint: collocation?

I have a problem of the following structure: For some scalar $g$, functions $F(z)$ and $h(z)$ defined on $[0,\bar{z}]$ , and a non-linear operator $\phi(F,z)$ (in reality, $F$ and $h$ are vector ...
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1answer
55 views

Algorithm for distributing members over activites (with individual preferences)

So in my school we have a day where everybody participates in different activities. Each projects can have like 10 members. The whole day is divided in 2 or 3 different blocks, in which the pupils ...
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1answer
65 views

Finding roots without knowing much about the function

Consider solving numerically for roots: $( x_0, y_0): f(x_0, y_0) = 0, g(x_0, y_0) = 0$ where you only know that f, g continuously differentiable but the theoretical differentiation is not a ...
2
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0answers
47 views

Algorithm for optimizing graph interconnectivity

I have a partiuclar kind of graph problem and (not having a background in graph algorithms) I would like to know how this kind of problem is called in the literature and what algorithms exist for ...
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0answers
16 views

Generation of symmetric groups

I've been trying to make an algorithm to generate symmetric groups in order to create graphics like the ones shown here. I've programmed circular and dihedral groups so far, but could someone help me ...
9
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0answers
135 views

Why are Octrees used for Multipole space decomposition?

In most (all?) implementations of the Fast Multipole Method (FMM), octrees are used to decompose the relevant domain. Theoretically, octrees provide a simple volumetric bound, which is useful for ...
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1answer
47 views

How to compute the weight matrix for tomography applications?

I am trying to compute the weight matrix for a set of straight ray paths through a reconstruction region. Ideally, I would like to be able to do this for both a rectangular grid region, where each ...
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74 views

Algorithm for Octree for nearest neighbor seach

Problem Statement: To find the nearest GRID ID of each of the particles using Octree. I have a system of particles(~6k, movable, Fig 1) for which I need to check which grid point (rigid; in ...
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50 views

Algorithm to explore a 3D scalar potential

I have to write an algorithm/code to reconstruct an unknown 3D scalar potential $ V(\mathbf{r})$ up to a specified threshold $E_c$ (assume that the potential is monotonic) The problem has the ...
10
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1answer
562 views

What are the relative benefits of using Adams-Moulton over Adams-Bashforth algorithm?

I am solving a system of two coupled PDE's in two spatial dimensions and in time computationally. Since the function evaluations are expensive, I would like to use a multistep method (initialised ...
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2answers
200 views

How can I create a computational model of the human eye?

I need to create a program that can simulate the optical system of the human eye. The input will be any image, the output would be the image that is projected onto the retina. I need it to be as ...