1. From a samples of a small samples of mathematical objects, conjecture a common pattern to all of them. This includes "guess the next terms in the sequence" question (consider checking OEIS first). Please provide as much context as possible. 2. Mathematical ideas related to pattern recognition, ...

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2
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1answer
162 views

Pattern finding for repeating sequences

Find a pattern for the following sequence. 1,1,3,1,3,5,7,1,3,5,7..... Let n= the nth number. Find the nth number of this series
0
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1answer
84 views

Finding a generating function for a pattern

I was working on this projecteuler.com problem, and I was very interested by the premise. Essentially, given n terms, find an ...
0
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1answer
39 views

Making the Smallest Number of Mistakes Possible

I have the following problem. I have a set of $k$ labelled points, $\left\{\mathbf{x}_i, y_i\right\}_{i=1}^{k}$, where $\mathbf{x}_i\in \mathbb{R}^{2}$, and $y_i\in\left\{-1,1\right\}$. I want to ...
7
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1answer
93 views

Finding $x^n$ patterns

I noticed the other day while computing consecutive powers of $2$ that for $n \geq 1$, the numbers in the ones place of the values of $2^n$ repeat every 4 terms $(2, 4, 8, 6,\ldots)$. In the tens ...
2
votes
1answer
189 views

what is the pattern in the distribution of divisors.

I made a table that shows the number of divisors for each number less than 500, and i think that there is a pattern, for example when there is a spike in the number of divisors the surrounding numbers ...
1
vote
1answer
78 views

How to determine which encryption system is being used?

I came across this question in a local contest. I was not able to solve it at that time. Also, no solution was provided. I was wondering if someone can help me to understand how to tackle this kind ...
0
votes
2answers
114 views

Find n term of sequence

A sequence is given: $$1,10,11,100,101,110,111,1000,\dots,a_n,\dots$$ The question is: what is the value of $a_n$ for a given $n$? I have tried a lot of patterns but was not able to meet the ...
2
votes
3answers
219 views

Find Pattern of Numbers

I need some help figuring out a pattern. I have a set of numbers that are dependent on four variables i,j,k, and l. The combination of variables in one set leads to different values in another set. ...
2
votes
1answer
107 views

Calculation for absolute value pattern

I have a weird pattern I have to calculate and I don't quite know how to describe it, so my apologies if this is a duplicate somewhere.. I want to solve this pattern mathematically. When I have an ...
4
votes
1answer
122 views

Some questions about $\gcd(n,m)$ and $\phi(n)$

I was messing around in Excel at the end of work today and made a table where the $(i,j)$ entry $a_{i,j}$, for $j \geq i$, is 1 exactly when $i$ and $j$ are coprime (see snapshot of a portion of the ...
2
votes
1answer
1k views

Mutual Information for clustering

I'm working on a document clustering application and decided to use Normalized Mutual Information as one of the measures of effectivenes. But I don't really understand how to implement this in that ...
0
votes
1answer
366 views

Pattern recognition next shape [closed]

Is there any logic for finding the next shape in the blank? I think it's an hard one.
2
votes
1answer
1k views

Bottom to top explanation of the Mahanalobis distance?

I'm studying Pattern recognition and statistics and almost every book I open on the subject I bump into the concept of Mahanalobis distance. The books give sort of intuitive explanations, but still ...
1
vote
0answers
121 views

Mapping an object's projected 3D path to a pre-defined top-down 2D path.

The title of the question may be misleading and the context simpler. Please suggest more appropriate tags for this question. Consider looking at a plane from two different perspectives. Perspective ...
0
votes
0answers
149 views

Understanding Gray-Level Hit-or-Miss-Transform Definition

From a paper I am using for my Bachelor thesis: The HMT transform by the pair $(A,B)$ associates to a binary image $X$ the set $X\otimes(A,B)$ of positions where the translate of $A$ fits inside ...
1
vote
4answers
116 views

Finding $n^{th}$ term of sequence

$$3,8,17,32,57,\ldots$$ How do we find the $n^{th}$ term? I have been roaming aimlessly for a few minutes now. A definite pattern is in the differences of differences. Hints will be apreciated.
0
votes
1answer
203 views

Expression for Sum of Multivariate Gaussian Random Vectors

Consider two multidimensional random vectors $x$ and $z$ having Gaussian distributions $P(x)=N(x\mid\mu_x,\Sigma_x)$ and $P(z)=N(z\mid\mu_z,\Sigma_z)$, respectively, together with their sum $y=x+z$. ...
5
votes
2answers
259 views

Is This A Derivative?

I am in a little over my head. This all began with my reading how each level of pascals triangle adds to $2^n$, where n=row# starting with n=0. I then though, "wouldn't it be clever if the rows added ...
0
votes
1answer
104 views

How to calculate a result based on an exponentially changing pattern/sequence. [duplicate]

Given any number (including decimals) between 12.5 and 87.5 I need to calculate another number based on these results:  Input = 12.5 | 31.25 | 50 | 68.75 | 87.5 Result = 12.5 | 64.5  | 78 | ...
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1answer
74 views

Is there a shorter way to write an equation with a clear pattern?

I have this simple expression: $$\left(\begin{array}{l} 1\\ +(A)\\ +(A+B)\\ +(A+B+C)\\ +(A+B+C+D)\\ +(A+B+C+D+E)\\ +(A+B+C+D+E+F)\\ +(A+B+C+D+E+F+G)\\ +(A+B+C+D+E+F+G+H)\\ +(A+B+C+D+E+F+G+H) ...
1
vote
3answers
90 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 am tired.I do not even recognize the pattern.I calculated a few ways,but all I want is a ...
2
votes
1answer
192 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 ...
1
vote
1answer
180 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
1answer
162 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 ...
3
votes
3answers
10k 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 ...
1
vote
1answer
162 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 ...
3
votes
2answers
108 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 ...
9
votes
7answers
4k 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 ...
-1
votes
2answers
412 views

Guess the terms in the sequence?

I am writing GRE in 2 two months, and I just can't solve these sequence question. Can anyone tell what the missing terms are and what is the pattern here? Find the next 4 terms in this sneaky ...
1
vote
1answer
181 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
1answer
760 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." ...
0
votes
1answer
154 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
66 views

Identifying a pattern in an array

Is there a way to identifying a pattern and/or recursive function for an array? If yes, how can I do this. Could anyone please help me with some information and/or resource for this? Any help is ...
1
vote
2answers
373 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 ...
2
votes
1answer
159 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 $10\mathrm{F}$ ...
58
votes
7answers
7k views

What's next in this number series? [closed]

340, 680, 1428, 3141.6, _____ This is from an aptitude test. I'm not able to find any pattern in them.
1
vote
2answers
188 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
0answers
48 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 ...
0
votes
0answers
40 views

Estimating $p(x)$ with a nonparametric method

"Pattern Classification" book I study that in nonparametric methods we need to estimate $p(x)$, and we don't want just the averaged version of it. They give an example of theoretical procedure to ...
2
votes
0answers
220 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 ...
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 $xz-1$
0
votes
3answers
2k views

Logical Reasoning: Identify next figure

I came across this logical reasoning/ abstract reasoning question in my logical reasoning book. Can somebody please help me identify the next pattern: Thanks!
1
vote
3answers
2k 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 ?
0
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0answers
461 views

Pattern matching questions

I saw the below questions and was curious regarding the logic behind the answer. I will be grateful is some one could help me So the question is given the patter, identify the next one
7
votes
1answer
223 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 ...
2
votes
2answers
496 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
0answers
115 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 ...
3
votes
1answer
147 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
0answers
247 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 ...
1
vote
1answer
97 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 $\Sigma_0 \in \mathcal{R}^{D\times D}$ ...