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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4answers
106 views

Pattern Recognition - How to solve this problem? [closed]

A general term of the sequence $$ -8,-7,-10,-1,-28,53,\ldots $$ can be expressed as $\dfrac{a-b^{n-1}}{4}$, where $a$ and $b$ are integers. What is the value of $ab$? Teach me how to solve this ...
2
votes
2answers
97 views

What is the next row of this pattern?

I'm attempting to help my little sister with her Algebra 1 homework, and this problem showed up. I can't for the life of me figure out the pattern; I was hoping someone would be able to. Here's the ...
2
votes
2answers
35 views

Find solution to pattern

Ok so I have this pattern [1]0-50 [2]51-150 [3]151-300 [4]301-500 [5]501-750 [6]751-1050 [7]1051-1400 etc forever What I need is to be able to take in the second ...
2
votes
2answers
97 views

What is the relation between this binary number with no two 1 side by side and fibonacci sequence?

I saw this pattern of binary numbers with constraints first number should be 1 , and two 1's cannot be side by side. Now as an example ...
2
votes
5answers
115 views

Why is $ A_1 x + … + A_n x^n $ a solution of $ \sum_0^{n} (-1)^n \frac{x^n}{n!} \frac{d^n y}{d x^n} = 0 $?

I was playing(/fiddling) around with some maths and I saw this pattern( where $ A_n $ is a constant.): $ A_1 x $ is a soultion of: $$ \frac{y}{x} - \frac{dy}{dx} = 0 $$ $ A_1 x + A_2 x^2 $ is a ...
2
votes
1answer
544 views

Mathematical Background for Computer Vision [closed]

I am a PhD student and would like to do deep research in the area of computer vision and pattern recognition. I know to be successful I need strong mathematical background. Could you please introduce ...
2
votes
1answer
179 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 ...
2
votes
1answer
362 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
222 views

Pattern of (1201, 2121, 3142, 4253, 5342)

What could be a part of the following set of numbers: $1201, 2121, 3142, 4253, 5342$ $a) 1317$ $b) 2315$ $c) 2573$ $d) 3456$ Differences between the numbers are $920, 1021, ...
2
votes
1answer
150 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
2
votes
3answers
214 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
35 views

Why Does This Summation Pattern Occur?

This is probably something stupid and for some reason I can't see it, but let's say you are taking the sum of the first $10^{i}$ squares. If $i=1$ we get $385$,$i=2$ we get $338350$, $i=3$ we get ...
2
votes
1answer
105 views

Math Competition Question Singapore 2

In Singapore, there is this competition named SMO. Recently, they released some example questions. The following is one of them... Let $a_1, a_2, a_3$ be an arithmetic progression with $a_1$>0 and ...
2
votes
1answer
80 views

Order a list of sets based on a rule (pretty tough)

I did not know where to turn so I'm looking up anyone who could offer an answer to this interesting problem. I have a set of variables, listed as (A, B, C, D, E, F, G, H) Each variable is couple in ...
2
votes
1answer
103 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 ...
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 ...
2
votes
1answer
178 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
469 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
28 views

Derive a formula for the number of small square base pyramids required to create a bigger pyramid?

To quote from the problem statement: "Pyramids are built using smallest pyramids of "level 1", that are used as building blocks for higher levels. Stacking pyramids of "level 1" to create ...
2
votes
1answer
60 views

How to show that $p(t|x,\mathbf x,\mathbf t)= \int p(t|x,\mathbf w)p(\mathbf w|\mathbf x, \mathbf t)d\mathbf w $

The following paragraph is approximately cited from Bishop's book, Pattern Recognition and Machine Learning. In curve fitting problem, we have training data $\mathbf x$ and $\mathbf t$, along ...
2
votes
1answer
35 views

how to calculate nth term of mth row of this table?

there is a table which grows as 1,1 1,1,2 1,1,3,3 1,1,4,4,6 1,1,5,5,10,10 1,1,6,6,15,15,20 .....and so on If i want to find an specific element of the table ...
2
votes
1answer
81 views

Why 312 Avoiding?

I have recently had the chance to attend a nice talk in Combinatorics, and once the speaker alluded to the famous 312-avoiding pattern problem, I was reminded of the following question I have had ...
2
votes
1answer
83 views

Is there a pattern for this sequence? [closed]

I've been looking at this and I thought there might be a pattern but I can't seem to find it. There are always $4$ elements, and they can be divided into $1, 2, 3, 4$ subsets ("chunks"). For example ...
2
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1answer
55 views

Using primes to create unique character mappings for scrambled substring searching

Problem: given a string needle, and a string haystack determine if there is there an anagram of needle present as a substring of haystack? (Assume case doesn't matter). One solution is to map the ...
2
votes
2answers
77 views

Number pattern problem

I need some help to figure out the following number pattern: Find the next number in the following sequence: $3, 2, 3, 12, 35, 78$. I tired to figure out the difference by ...
2
votes
1answer
911 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 ...
2
votes
1answer
184 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
1answer
116 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
1answer
79 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 ...
2
votes
0answers
35 views

Trade-off among symmetries

Take a set $X \in \mathbb{R}^2$ of nonzero measure $\mu(X) \neq 0$. I am attempting to design a set that has the following symmetries (continuous or discrete) $1.$ Scale symmetry $2.$ Rotation ...
2
votes
1answer
39 views

Finding the best fit of 3 categories ( restaurants/meal/person analogy problem )

I have this problem that sounds tedious and long and I'm not sure if there exist an intuitive way to solve it. The problem is related to image recognition but I will try to give an analogy to it You ...
2
votes
0answers
51 views

Question regarding pattern recognition in a table

Knowing this is a seemingly weird question, I do believe I should provide some additional context . One of our university professor's has a terribly peculiar habit . Namely, each year, the students ...
2
votes
0answers
87 views

Unexplanied pattern from increasing rational sequences

I've stummbled upon some strange pattern when working with series of rational numbers. If anyone could shed light on this phenomenon I will be most greatful. Backgroud: Working in an integer lattice ...
2
votes
0answers
203 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 ...
2
votes
0answers
114 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
0answers
73 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
117 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
213 views

In simple terms what is the sequence 220,171700,167167000,166716670000 a part of?

I know that <1,2,3,...,10>$\cdot$<1 0,9,8,...1>=220 <1,2,3,...,100>$\cdot$<100,99,98,...,1>=171700 <1,2,3,...,1000>$\cdot$<1000,999,998,...,1>=167167000 ...
1
vote
1answer
195 views

Patterns of no formula.

How do I find the next number if the given pattern is $$1,2,3,2,3,4,1,2,6,23,14,19,64,69,12,78,152,93,108,?$$ (Find the question mark)
1
vote
4answers
320 views

Easy as $3.14$ question

I've got the following question with the hint "Easy as $3.14$". $$2003 = 2\\1337 = 4\\7877 = 3\\5732 = 4\\8315 = 3\\4466 = 0\\0354 = 2\\8923 = 2\\8888 = 0\\0000 = 0\\4059 = 1\\2403 = \ ?$$ I need to ...
1
vote
2answers
48 views

This question is for sequences, how would I go about solving this?

Find a general term (expressed as a function of the variable $n$) for the following sequence: $$\{a_1, a_2, a_3, a_4,\dots\}=\left\{\frac{4}{8}, \frac{16}{64}, \frac{64}{512}, ...
1
vote
5answers
34 views

Finding expression for pattern

This seems easy.... Pattern: 3, 6, 10, 15, 21.... How do I find expression for this? It looked easy, but I couldn't find it. I tried graphing it, but it turned out that it is not quadratic... ...
1
vote
2answers
55 views

What is the pattern for this sequence?

I know that it increments by 1 until the (10n + 1)th term, where it increments by the term #. I don't know how to represent this entire pattern as an equation or summation of some sort.
1
vote
2answers
59 views

Find if a number lies in this pattern

I have a sequence of numbers below... $1, 2, 4, 7, 11, 16 ...$ You get this list by starting at $1$ then add $1, 2, 3, 4, 5 ...$ Given a number $n$, how can I determine if it will show up in this ...
1
vote
4answers
113 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.
1
vote
1answer
174 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
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2answers
186 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
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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 ?
1
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2answers
836 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
231 views

How to use a difference table to find a formula for a given sequence?

Given a sequence, how do you get a "rule" from its difference table? For example; 1, 2, 3, 4, 5, 6 1, 1, 1, 1, 1 Or 1, 2, 7, 16, 29 1, 5, 9, 14 4, 4, 4 I haven't really explored this ...