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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Best algo for finding no. of steps required to convert a sequence to a palindromic sequence

[My first question of Math SE, so, HI!] I'm not sure of what the rules are around the place, but I have a straightforward question as follows... The sequences 23, 45, 23 and 23, 45, 56, 23, 23, ...
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1answer
92 views

Finding an expression to represent this pattern

Is there a method to find a math expression for a given pattern? I have this pattern and I am very curious to find out how can I generate it. ...
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1answer
72 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) ...
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1answer
173 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 ...
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25 views

What does this quantity measure?

Consider this list of numbers: $$\begin{bmatrix} 59 \\ 148 & 0.60 \\ 200 & 0.26 & 1 \\ 250 & 0.20 & 1.25 \\ 290 & 0.14 & 1.45 \\ 325 & 0.11 & 1.625 \\ 360 & ...
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52 views

Pattern Finding in terms of previous terms

Find the next terms of the pattern: $$ 1,4,24,192,2120,31140,566202 \dots$$ Tell the pattern expression. I have already tried Lagrange interpolation. But it is not accurate enough.
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61 views

What Constitutes a Pattern

Mathematics is often referred to as the "study of patterns." What I'm wondering is whether there is somehow a technical way to describe a pattern. For the length of this question let's assume that ...
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111 views

Find the number that follows the rules of two different series

I have this logic problem where I need to find a number that fits in 2 different series (vertical and horizontal). Each series has a rule, and once you find them, you can determine the answer. $$ ...
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150 views

Point Group of a pattern

I need to determine the point group of the following patterns: I think the one on the left is $D_1$ and the one on the right is $D_2$
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116 views

Adding Numbers Pattern

A few nights ago I couldn't sleep and so started doing this: I would take a number and add up all of its digits to get a new number and then add up all of those digits and so on until there was only ...
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431 views

Guilloché security printing — can it be cracked?

Money uses Security printing, and often uses Guilloché patterns. These curves are inscribed by wheels on wheels on wheels, ten wheels deep in some cases. For example, the back of the US $1 bill has ...
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242 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 ...
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431 views

What does this say about prime numbers?

I was having fun with Sage when I noticed something interesting: ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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0answers
30 views

Calculating a formula for variables with multiple values equaling the same total

I'm having a bit of trouble puzzling a formula for some code I'm using to develop a piece of software. I'm not very savvy with what the technical terms for all of what I'm describing are, but I'll try ...
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0answers
60 views

Elusive closed form for card permutation problem

Does a closed form formula f(n) exist for the two rightmost columns? The two question marks are meant to be 0. The diagram is a summary of the numerical results from original question: Permutations ...
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59 views

Why use two slack variables in the support vector regression formulation?

I am learning support vector regression but cannot fully understand the rational of the slack variable tricks in its formulation. The original optimization problem for SVR is as follows: ...
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26 views

Can KNN theoretically be less accurate than pattern averaging?

My task is pattern recognition. I need to classify 2D matrices into an arbitrary number of classes. The question is: For pattern classification, could k nearest neighbours algorithm ever be less ...
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52 views

Other Patterns in Triples

I have the following 20 triples generated by polynomial distribution: $$\begin{matrix} (2,4,5)&(2,3,4)&(2,3,5)&(1,4,5)&(2,2,4)\\ ...
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26 views

k nearest neighbor density estimation

In k nearest neighbor density estimation we calculate the density using following formula For given 1D sample X={4,5,6,7,9,10,11,12,13,14) if k=3, and we do not consider on boundary samples inside ...
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58 views

Leibniz Binary Representation of Squares

Leibniz claims to have found patterns in the square numbers and their binary representations. I cannot see any patterns at all. Here are the first ten squares and their binary representations, can ...
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286 views

Finding an unknown number in the middle of a number sequence

I've stumbled across a very peculiar number sequence and it was bugging me for a while now, i would really like to find out a way to dissect and work out the number that is missing, here's the ...
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0answers
35 views

Trace of a product of a recursive series of non-full rank matrices

Let $H$ be a $m\times n$ matrix that is not full rank. Hence $H^T H \neq \mathbb{1}_{m\times m}$. Can we say anything about the diagonal entries, or the trace, of matrix products of the form: $P_0 = ...
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333 views

Study the number patterns and fill in the missing number

This problem seems easy but I have been working on it for quite some time with little clue. It is about finding number patterns, I have tried many different ways, which seem to work at first but fail ...
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113 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 ...
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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 ...
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0answers
180 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 ...
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58 views

Is there a pattern that can be seen in this sequence?

I can't seem to find any pattern, perhaps a fresh view from one of you guys can point me to the right direction: 14898997873, 16483634594, 17241926510, 16427260053, 19933377255, 7467660818, ...
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Pattern recognition and machine learning - Bishop: Difficulty deriving (2.111) and (2.112)

I'm having a hard time deriving (2.111) and (2.112) in this book (it's on page 110/703). Here is what it says: Finally, we seek an expression for the conditionalp(x|y). Recall that the results for ...
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31 views

Solving a Recurrence for a Mathematical Game

The problem is: Two players take turns removing coins from a pile. There are initially $n$ coins, and on each turn, a player can remove $a_1, a_2, \dotsc, a_k$ coins. The player who cannot remove ...
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12 views

Frequency of a specific date, time, DoB combination/'palindrome'

Apologies if this isn't the correct forum to ask - I'm a regular Stack code user, this had me scratching my head for a while and just curious if someone a lot smarter than me can tell me how 'unique' ...
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15 views

Need help on Pattern problem

Hi I have problem on Pattern problem as shown picture. I can find only A B C butpending on D. Thanks. E.g. (First table) A = 7-1 =6 B = 7-6 =1 C = 7 + A = 7 + 6 ...
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48 views

Why does this matematical pattern occurs here?

The actual question goes like this A room has N (1 to N inclusive) bulbs and N switches. N people go in one by one. 1st person goes in and toggles none of the switches. 2nd person goes in and ...
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8 views

Discriminant Functions of two classes sharing same covariance matrix

How can i find the discriminant functions of two classes having same diagonal covariance matrix with different means? (their feature vector is two dimensional) Thank you!
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12 views

Recognition rate prediction as a function of number of distractors

What would be a formula for extrapolating behavior of an algorithm that was tested with small number of false positives, say $10$ or $100$ but I want to know the rate with $1000$. E.g., the ...
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0answers
55 views

In kernel rules, why is a regular kernel necessarily bounded?

Request from a dabbler in measure theory. Here a kernel merely designates a real-valued function. Quoted from "A Probabilistic Theory of Pattern Recognition", Luc Devroye, Laszlo Gyorfi, Gabor ...
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30 views

Estimate prior for normal distributed data

I have successfully implemented a bayesian classifier using maximum likelihood. In my case I've got 2 classes and I have calculated the two $\mu$ and $\Sigma$. In my problem with a 3-dimensional ...
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0answers
15 views

Is auto-correlation a particular and simple form of pattern in time series?

In a time serie context and considering the sign of the variation of the variable auto-correlation means that for couple of measures at (time t, time t+1) the ...
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0answers
20 views

Kernel Method for complex valued problems

Kernel Method are widely used in Pattern Recognition and Machine Learning. e.g Kernel PCA and Kernel Regression are used as some extension of the regular PCA and Regression. However all the kernels I ...
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0answers
28 views

Pattern Recognition terms a little fuzzy

I've been trying to learn more about probability and the websites I have visited are not describing the relationship to each other that well (when to use what, for what purpose in conjunction with ...
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0answers
33 views

Common or distinct covariance matrices for mahalanobis distance classifier

I'm very new to pattern recognition so apologies in advance for a newbies question. I've been experimenting with mahalanobis distance to class mean based classifiers to predict diagnoses from ...
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0answers
148 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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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 ...
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436 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
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126 views

Matrix & Partition & Natural Number & Pattern

I would like to know if someone know, how is called a matrix M*N, where m represents the row index in the matrix and the sum of the N columns at this row. Meaning that each row represents a possible ...