The pattern-recognition tag has no wiki summary.
35
votes
19answers
5k views
Getting the sequence $1, 0, -1, 0, 1, 0, -1, 0, \ldots$ without trig?
What's the simplest way to write a function that outputs the sequence:
1, 0, -1, 0, 1, 0, -1, 0, ...
... without using any trig functions?
I was able to come up ...
9
votes
7answers
656 views
Pattern to last three digits of power of $3$?
I'm wondering if there is a pattern to the last three digits of a a power of $3$? I need to find out the last three digits of $3^{27}$, without a calculator.
I've tried to find a pattern but can not ...
7
votes
3answers
631 views
How to find pattern in $1,2,8,9,15,20,26,38…$ infinite sequence?
While I was investigating some specific types of prime numbers I have faced with the following infinite sequence :
$1,2,8,9,15,20,26,38,45,65,112,244,303,393,560,....$
I tried to find recursive ...
7
votes
1answer
155 views
What is the pattern or relation in this table?
Here is the table:
$$\begin{array}{c}
0\\
1\\
1& 1\\
3& 2& 3\\
5& 3& 3& 5\\
11 &8 &10 &8 &11\\
21 &13 &14 &14 &13 &21\\
43 ...
6
votes
1answer
263 views
How to Characterize Clumps in a Large, Semi-Random Graph
Consider large (100,000+ vertices, say) graphs, which we think of as representing some population with edges representing some form of symmetric relation. They might be the Friend graph of Facebook, ...
5
votes
2answers
180 views
Formula to this pattern?
I have this pattern:
1
11
21
1211
111221
I'm guessing it's a fibo pattern, been at it for hours now. Anyone know?
3
votes
3answers
264 views
Notation for factorial-type pattern with a skip/step of two instead of one?
I came across a peculiar pattern when solving a recurrence relation today:
Some sequence $a_n$ looks as such:
$a_0 = 1$
$a_2 = \frac{1}{2 \cdot 1}$
$a_4 = \frac{1}{4 \cdot 2 \cdot 1}$
$a_6 = ...
3
votes
1answer
134 views
What is the Galois group of $x^n + (x-1)^n $?
What is the Galois group of $x^n + (x-1)^n $ over the rationals in terms of the integer $n$ ?
In case that is too hard , what is it for the first 20 integers ?
3
votes
2answers
41 views
Recognize a valid binary Golay codeword
Are there any properties of a binary [24,12,8] Golay code which would allow me to say, for example, that a given 24-bit word is or is not a Golay codeword for some generator matrix? That is to say, is ...
3
votes
1answer
71 views
finding all pairs $(x,z)$
How to find all pairs $(x,z)$ of integers for which $2(z+1)^3$ is divisible by $xz-1$
3
votes
3answers
165 views
Using Correlation for mouse gesture recognition
I am in need to build a mouse gesture recognition system which will compare given recognition to the the gestures in training data and will say where a given gesture best fits.
I am planning to use ...
3
votes
0answers
125 views
Pattern puzzle help
I've spent hours on this puzzle, which shouldn't be too hard, and I'm sure I've got the right answer, but apparently it's wrong. The problem statement:
You are guessing a positive number X. You ...
3
votes
0answers
234 views
What does this say about prime numbers?
I was having fun with Sage when I noticed something interesting:
...
2
votes
1answer
79 views
Mathematical formula for a pattern
I was cooking and saw a chart of temperature vs cooking time like so:
$154\mathrm{F}$ - $36$ hours
$164\mathrm{F}$ - $18$ hours
$174\mathrm{F}$ - $9$ hours
Basically for every $10\mathrm{F}$ ...
2
votes
2answers
55 views
Finding formula for the nth partial sum
A few days ago, I asked for some clarification about pattern recognition and the n-th partial sum for infinite series. Although the explanation given was top-notch (thanks again), I'm still having ...
2
votes
1answer
199 views
Function for number patterns
I'm primarily a programmer and am pretty rusty at math... so forgive me if this is a stupid question.
I have four number patterns as follows:
a) 3, 13, 31
b) 5, 17, 37
c) 7, 21, 43
d) 9, 25, 49
...
2
votes
1answer
32 views
How to calculate smallest pattern size based on set of ratios
So I have x number of items, each one has its own appearance ratio for making a pattern, of which I'm trying to determine the smallest possible pattern. The appearance ratios for all items total up to ...
2
votes
2answers
201 views
Pattern matching circle, square or triangle
I have a set of x, y co-ordinates that are actually taken from hand drawings of a circle, square or a triangle. Using the set of points, I need to mathematically find if the points approximately fit a ...
2
votes
1answer
98 views
How can one classify (match within a certain confidence interval) gestures based on accelerometer readings?
I am using an accelerometer-enabled device (mobile phone, to be specific) that enables sampling acceleration at a rate of about 20 samples per second. The samples contain three values, each ...
2
votes
0answers
75 views
Multiplication structure for finite abelian rings of order $p^2$.
Consider an odd prime $p$ and a positive integer $a$ as close to 2 as possible that is not a quadratic residue $mod$ $p$.
If we extend the ring $mod$ $p$ with the element $b = a^{\frac{1}{2}}$ then ...
2
votes
1answer
172 views
What kind of recursion or series is this?
I am developing a language learning program, and would like to know the mathematical expression and description for what I have (perhaps incorrectly) calling a recursive series method of learning the ...
2
votes
0answers
61 views
Algorithm to predict next 3D points
For example, having this data:
year x/y/z
2007 10/20/70
2008 20/10/70
2009 30/10/60
2010 40/10/50
2011 40/15/45
We want to predict what will be the x/y/z in ...
2
votes
1answer
93 views
Selecting and Grouping a set of points in a 2D plane
I am currently working on a project that requires to solve the following problem:
Let's say that each time a user access a specific resource on the network from his mobile device, a system stores his ...
1
vote
2answers
64 views
I need to figure out a pattern
Finish the Pattern to the nearest number: 0 0 3 20 115
I need to add in a few more sentences to make this problem meet the standards. If you could solve this pattern, it would help me out alot, its ...
1
vote
3answers
305 views
What is the next picture in this sequence?
I was reading a book on logical reasoning and came across the following:
Can anyone give me the answer to the question. We want the next sequence ?
1
vote
2answers
303 views
How to find the pattern?
I'm challenging myself to figure out the mathematical expression of the number of possible combinations for certain parameters, and frankly I have no idea how.
The rules are these:
Take numbers ...
1
vote
2answers
34 views
finding nth term
Let
3,8,17,32,57 . . . . .
be a pattern.How do we find the nth number?My brains are completely jammed.I do not even recognize any pattern.I calculated a few ways,but all I want is a little hint,not ...
1
vote
1answer
78 views
Is there a pattern in figures whose perimeter is the same as their area?
Here's what I've found so far.
Circumference of a circle with identical circumference and area: $4\pi$
Side length of a triangle with identical perimeter and area: $4\sqrt{3}$
And so on...
...
1
vote
2answers
80 views
Learning patterns and the maths
I am interested in learning more about patterns.
My objective is to learn about how to analyse a set of numbers (not infinite but a large set of numbers in sequence) and see the patterns and then ...
1
vote
2answers
130 views
Trying to figure out the pattern in this series (2)
I could use some help figuring out what the next row is in the pattern below (and what the rule is generally for each number in the series). I put it in a triangle because I'm pretty sure it has ...
1
vote
1answer
38 views
Can rainbows be considered to have mathematical patterns?
Of course it is evident that there is physics and mathematics involved in a rainbow, but my question is (as the title suggests) are there patterns to be found in rainbows? By patterns I mean ...
1
vote
3answers
183 views
Patterns in Sequences
I've heard in a movie that for any sequence of numbers, there is a nice formula for generating that sequence. So, for example if I write:
1,2,1,2,3,3,1,2,3,1,2,4,...
There is a formula for ...
1
vote
1answer
40 views
Understanding the fundamentals of pattern recognition
I'm learning now about sequences and series: patterns in short. This is part of my Calc II class. I'm finding I'm having difficulty in detecting all of the patterns that my text book is asking me to ...
1
vote
1answer
96 views
Softmax function and modelling probability distributions
Hinton in his neural network course on Coursera says that "Any probability distribution P over discrete states (P(x) > 0 for all x) can be represented as the output of a softmax unit for some inputs." ...
1
vote
1answer
65 views
Dimensionality effect on Fisher's Score
Consider Fisher's Linear Discriminant Analysis (LDA).
Let $\mu_0 \in \mathcal{R}^D$ and $\mu_1 \in \mathcal{R}^D$ be means of the two classes. Similarly, let $\Sigma_0 \in \mathcal{R}^{D\times D}$ ...
1
vote
1answer
141 views
Stuck with handling of conditional probability in Bishop's “Pattern Recognition and Machine Learning” (1.66)
I've just started working through the book, and I'm stuck with how the author handles conditional probability in (1.66).
The context is as follows. In this chapter we are working with a curve ...
1
vote
1answer
107 views
Pattern Recognition with basic probability
I am a college student and have Pattern Recognition as a course this semester and I am really struggling with it, reasons could be difference in teaching style of the instructor and different type of ...
1
vote
1answer
37 views
How can I count clockwise vs counterclockwise cycles in a series of (modular) integers?
I'm working with a Markov process that has a state and transition diagram like in the picture:
The transition probabilities are not listed, but they are always positive, but not necessarily ...
1
vote
0answers
34 views
Find a pattern in key => value?
Sorry if this isn't the correct place but it did seem to be! Basically, I'm coding a small test with a bouncing ball. All works well, but the problem is I need to work out the ...
1
vote
0answers
45 views
Is kernel density estimation a GMM with uniform mixture weight?
recall that for a Gaussian Mixture Model, the density of p(x) (multivariate) is
$$P(x) = \Sigma_{i=1}^{C}\pi(c_i)\mathcal{N}(\mu_i,\Sigma_i)$$
On the other hand, non-parametric density estimation ...
1
vote
0answers
78 views
Theoretical proof of convergence of sequential weight update procedure (Neural Networks and Machine Learning)
My question is at the bottom.
(Most of the descriptive words come from Chris. Bishop's Neural Networks for Pattern Recognition)
let $w$ be the weight vector of the neural network and $E$ the error ...
1
vote
1answer
68 views
Question regarding Dynamic Programming for Audio Recognition
Currently I am implementing a DTW (Dynamic Time Warping) algorithm for my project. As some will know it has the complexity of O(n^2). Considering a sound file of length 1-h with 44100 sampling. How ...
0
votes
2answers
175 views
Probability of market movement / Trends
If you imagine a scale from -100 to 100, if the market has moved up from 0 to 40, what is the probability is will continue to 100?
There is a 50-50 chance to move up or down from 0, but what is the ...
0
votes
2answers
59 views
Need help modifying this binomial expansion
The binomial theorem states that
$$(A+B)^n=\sum_{k=1}^{n}{n \choose k}A^{n-k}B^k$$
I need help expressing the following summation as a modified binomial expression:
$$\sum_{k=1}^{n}n!{n-1\choose ...
0
votes
1answer
102 views
Trying to figure out the pattern in this series
I'm trying to figure out the rule that's producing the series below. The first column is the factorials $1!,2!,3!,4!,5!,6!$ But I can't figure out what else is going on. So I know the next row will ...
0
votes
1answer
185 views
Logical reasoning question: what is the next diagram [closed]
I have to identify the next diagram. Can somebody please help with this!
Thanks!
0
votes
1answer
74 views
A lemma regarding cones covering $\mathbb{R}^d$
Added: Pointers to some references with the same conclusion as the wolloing lemma may be helpful to understand it, and are appreciated.
In A Probabilistic Theory of Pattern Recognition By Luc ...
0
votes
1answer
72 views
Game statistics: Extracting interesting patterns out of users and level
I made a small game and in course of time collected fair amount of data between users and level
The level chart is long (120 levels) but looks somewhat like this
$$
\begin{array}{|c|c|}
...
0
votes
1answer
76 views
What is the pattern here? Q-function - SOLVED
I've got the following problem: The difinition of the funtion: Q(S,M).
The purpose is to find the max number of possibilities how to write the funcition.
...
0
votes
1answer
306 views
Math problem in Pattern Recognition and Machine Learning
I had been carefully following Bishop's Pattern Recognition book and came across some of difficulties due to my merely basic math ground.First begin by the Gaussian section on page 80.
The ...
