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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3answers
102 views

Finding the $n$th term for the sequence $1, \frac{1}{2}, 3, \frac{1}{4}, 5, \frac{1}{6}, \dots$

I have tried using a negative exponent. I need one statement not two, the pattern is $$1, \; \frac{1}{2}, \; 3, \; \frac{1}{4}, \; 5, \; \frac{1}{6}, \dots$$
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2answers
272 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 ...
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1answer
150 views

What is the 6th term of the sequence? [closed]

Sequence: ABC; 1A1B1C; 111A111B111C; 311A311B311C; ... What is the 6th term of the sequence? ...
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2answers
63 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 ...
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1answer
142 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 ...
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3answers
93 views

Triangular Numbers that are odd, less than 2000

The diagram below shows the $1$st, $2$nd, $3$rd and $4$th triangular numbers. (1 spot) : $1$ (3 spots) : $3$ (6 spots) : $6$ (10 spots) : $10$ The formula $n(n + 1)/2$ can be ...
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2answers
62 views

Evaluate an unknown operator

I have a simple question but I can't seem to be able to solve it. Given that: 25 ╧ 17 = 267 35 ╧ 23 = 373 45 ╧ 15 = 465 what is ...
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2answers
34 views

What is the general stragety for conjecturing a formula based off a pattern?

Is it simply to guess and evolve a answer until it gets closer or is there an approach? Ex: Find the formula for: $a_k = \frac{a_{k-1}}{2} + 1$ where $a_0 = 1$. One would go: $a_1 = 3/2, a_2 = ...
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4answers
152 views

How to represent the $n$th number in the sequence $1,3,5,7,1,3,5,7,\dots$ as a closed form?

I'm given the repeating sequence $1,3,5,7,1,3,5,7,\dots.$ I must determine a formula for the $n$th term of the sequence. I have tried the triangle method, but since this is a repeating series it is ...
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1answer
134 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 ...
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1answer
438 views

Logical reasoning question: what is the next diagram [closed]

I have to identify the next diagram. Can somebody please help with this! Thanks!
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3answers
101 views

Given the sequence $3, 4, 11, 16, 42\ldots $ how can I derive a general formula for it?

Given a sequence $3, 4, 11, 16, 42\ldots $ how can I derive a general formula for this sequence? Is there any optimised approach? My approach: the given series is equal to summation of $\binom{n}{k}$ ...
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1answer
67 views

Creating coexistent patterns, with several pattern-less systems

I'm a young musician, as well as a computer programmer. My understanding of math is formed well to my needs, but I am by no means a mathematician, but the field is very interesting to me. I have come ...
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1answer
207 views

Find the next number in this sequence

I have a homework. It seems to be an easy sequence but I can't get the answer. So, What is the next element? $$2, 7, 10, 13, 23, 34,?$$ What would be the solution out of these numbers? 45 or 49 or 58 ...
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2answers
88 views

Finding pattern (2,7,8,3,5)

What would replace $Z$ in the following sequencing? $$\begin{matrix} 2 & 3 & 4 \\ 7 & 6 & 5 \\ 8 & 7 & 1 \\ 3 & 0 & Z \\ 5 & ...
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1answer
91 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 ...
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1answer
77 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|} ...
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1answer
48 views

Determine Patterns

I have some weather data that I would like to analyze. I have about a millions rows of data, and each row has about 100 attribute values. Each attribute value represents some measurement (i.e., ...
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1answer
36 views

Anyone recognize this pattern? Plotting relationship between two parameters and their response.

First time asking a question here so hopefully I can provide enough information to you guys without explaining more than necessary. I'm doing some amateurish numerical analysis in MATLAB on some ...
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2answers
63 views

closed formula for a series

The first column below is n (iterator), the second is the value, I'm trying to understand if there is a closed formula that I can use for obtaining the value given a fixed n $$n=0: a$$ $$n=1: ...
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2answers
31 views

Equation for value of p given x

I have a set of numbers: $\begin{array}{r(22)}x \in \{ 1,& 2,& 3,& 4,& 5,& 6,& 7,& 8,& 9,& 10,& 11,& 12,& 13,& 14,& 15,& 16,& 17,& ...
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1answer
46 views

How can I figure out the total solutions in this Combinatorics problem?

Imagine you have a sequence of cards, each having a unique set of features. Example features : letter (A, B, C), number (1, 2, 3), and color (Red, Green, Blue) Some example cards : A1Red, B1Blue, ...
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1answer
144 views

Find the pattern, what is the correct number in that spot, explain the answer

we are given the following matrix: $\begin{pmatrix} 9 & 38 & 47 &4 \\ 6 & 35 & 42 & ? \\ 12 & 21 & 23 & 27\end{pmatrix}$ The number that goes in $?$ is $-5$. I ...
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1answer
133 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 $y=x+z$. ...
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1answer
127 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. ...
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1answer
56 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 ...
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1answer
130 views

Finding the mean (or pattern) of a set of related values in a matrix discarding those that are too different.

this is my first question here so I am not sure if it is a valid one. I am currently facing a mathematical problem that is not so hard to solve, but given the accuracy i need in the results I would ...
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1answer
453 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 ...
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1answer
426 views

Equations and Pattern formulas problem solving

I have this question to answer and I need help with finding or creating a equation. You own a license plate manufacturing company. Write a formula or equation that takes a population and ...
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1answer
36 views

Finding a formula for a pattern

I have this pattern which is an infinite sequence (I have placed commas so it's easy to see the pattern)... $1 ,1 2, 1 2 3, 1 2 3 4, 1 2 3 4 5 ...$ Is there any formula governing this sequence, ie, ...
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2answers
337 views

Logic of numerical series

One of our colleagues has written a numerical series to the whiteboard in our breakroom. Nobody until now could solve the logic behind this series: ...
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0answers
43 views

Pattern recognition next shape pattern

which one of the above do you think is the the right answer? i guess it's B but not sure, maybe C. http://tinypic.com/r/nwfqpx/8 thanks.
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0answers
12 views

LDA find densities

I have the predictor-response (X,Y) with response Y={-1,+1}. The predictor X is a pair (X1,X2) independent, uniformly distributed on [0,1]. I am given the prediction rule for Y=+1, eta(X1,X2)= ...
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0answers
17 views

Computing Object Classification with bayesian statistics

Say I want to know if there is a zebra $\theta$, in an image $x$. According to Bayes statistics applies to image recognition, I should be computing: ...
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0answers
19 views

Pattern embedding method

There are three defined functions; $a_n=A(n), b_n=B(n), c_n=C(n)$ and an unknown function $d_n=D(n)$. It has been found out that $d_1=a_1$$d_2=b_1$$d_3=c_1$$d_4=a_2$$d_5=b_2$..... Is there a method ...
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1answer
35 views

How to complete a table of probabilities ?

Im baffling myself as to why I cannot understand where it came from. Someone please explain to me like I'm five. $$\begin{array}{c|c} x & p(x) \\ \hline 0 & 0.73 \\ 1 & ? \\ 2 & 0.06 ...
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0answers
32 views

How can I conceptually visualize a Gaussian Mixture Model?

I'm struggling to get my head around Gaussian Mixture Models & Processes from a conceptual level; my intention is to use a GMM for image segmentation but I'm struggling to understand it. The way ...
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0answers
84 views

Number of differently-sized squares needed to fill a rectangle; is there a visible formula? [Pattern spotting]

Consider a game in which we tile a given rectangle with the largest squares that will fit. We record the number of squares of each size that we can use, until the rectangle is completely covered. ...
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0answers
18 views

Finding properties of Inter arrival times

I apologise in advance if this is a bad question or if it's in the wrong place. Say I get a sample of inter arrival times, I'd like to have some kind of a measure which would tell me whether the ...
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1answer
60 views

Digit sum of the sum equals digit sum of the addends

This may be a simple question and I am not a mathematician. I recently noticed that 11+12+13 = 36 whose digit sum is 9. And that the digit sum 1+1+1+2+1+3 also equals 9. Is there a pattern here that ...
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0answers
70 views

What makes a pattern in a sequence?

Assume a stream of characters$(c)$ where $ c \in (A, B, C ... Z)$. I need to identify patterns available in the stream. As per the definition of a pattern I should be looking for a recurring string. ...
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0answers
43 views

Creating feature vectors with a high degree of entropy from the actual training data for neural network?

Note: My upper level math skills are not in good shape and end around 1st semester calculus. I am looking for guidance that would help me find a known algorithm that does what I need in the open ...
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1answer
75 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 ...
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1answer
34 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 ...
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1answer
234 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.
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0answers
113 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 ...
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1answer
78 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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0answers
35 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 ...
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3answers
1k 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!
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0answers
313 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