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2answers
47 views

Estimating the mean with least median of squares target

I have a set of real numbers $x_1,\ldots,x_n$. I would like estimate the mean of the set, $y$, such that the median of squares will be minimal : $\operatorname{median}(x_i-y)^2$ Is there a closed ...
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1answer
8 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 ...
1
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1answer
65 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
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1answer
101 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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1answer
33 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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1answer
37 views

what are the possible patterns of the sequence?

Given sequence 12, 10, 9 ,7 ,6, 8 what are the possible patterns you could think? I was thinking 12 + 6 = 18, 10 + 8 = 18, ..., which is very awkward.
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1answer
47 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 ...
0
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1answer
73 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
31 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 ...
9
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0answers
493 views

Are there “mental calculator” persons that can recognize closed-form expressions?

There are people, sometimes called mental calculators, who is capable of performing fast calculations in their head, involving multiplication, factorization, finding logarithms and roots of a high ...
5
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0answers
125 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 $D_2$
3
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0answers
80 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 ...
3
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0answers
199 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
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0answers
290 views

What does this say about prime numbers?

I was having fun with Sage when I noticed something interesting: ...
2
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0answers
105 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
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0answers
68 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
20 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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0answers
167 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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0answers
73 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 ...
1
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0answers
40 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
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0answers
104 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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0answers
128 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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0answers
7 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
15 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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0answers
21 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 ...
0
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0answers
65 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
15 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 ...
0
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0answers
65 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
34 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 ...
0
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0answers
38 views

KMP with given state - reproduce the pattern

PROVE OR DISPROVE: suppose you are given the array state[m] which was created by the KMP algorithm for a pattern P of length m as following: (1 <= i <= m), state[i] = (0 if i is odd) and (1 if ...
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0answers
108 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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0answers
46 views

Multivariate Gaussian with 3 Partitions

Given that we partition a Gaussian random vector $\textbf{x}$ into three groups, $\textbf{x}_a$, $\textbf{x}_b$, and $\textbf{x}_c$, with a corresponding partitioning of the mean vector $\mu$ and of ...
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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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0answers
269 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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0answers
120 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 ...
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0answers
100 views

Solution Manual to Accompany Pattern Classification

I'm looking for the book "Solution Manual to Accompany Pattern Classification" by O.Duda, but it seems impossible to find (I looked also in amazon.com but there isn't). Someone of you has a copy to ...