# Tagged Questions

1k views

### Convert a WFF to Clausal Form

I'm given the following question: Convert the following WFF into clausal form: \begin{equation*} \forall(X)(q(X)\to(\exists(Y)(\neg(p(X,Y)\vee r(X,Y))\to h(X,Y))\wedge f(X))) \end{equation*} ...
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### Simple ranking/rating algorithm [closed]

Is there a Simple ranking/rating algorithm that calculates a score between 0 and 1 given a number of alerts along with its priority. For example: each system can produce "Low", "Medium" and "High" ...
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### Risk seeking utility

I am stuck on a question in an archived course on BerkeleyX's CS188x Artificial Intelligence. Which of the following would be a utility function for a risk-seeking preference? That is, for which ...
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### Split a map into roughly equal sections directionally and put points in it

I have a 16000 x 9000 grid map and I want to split it into x sections that are preferably of equal size. Then I want to place points on each section are centers of circles with a 2200 unit radius and ...
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### Contradiction in Davis–Putnam–Logemann–Loveland (DPLL) Method?!

As we see on page $10,11$ and $12$ on Google Books we know about Unit Clause (UC) and Pure Literal (PL) in DPLL Algorithms. in the following example if assign value $0$ to variables is prior to ...
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### Is it better to average the log2 for a series of numbers or just the numbers themselves? And, how would you test or prove this?

Lets say I'm trying to compare two vectors for similarity and normalizing them before hand based on some mean or standard deviation combo for the purpose of finding the similarity between the 2 ...
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### AI Parameters for Tetris-like Game

I am building an AI to play a variation of Tetris. The rules are changed in that there are 19 different types of pieces, rotation is not allowed, and the pieces can be placed anywhere in a 10X10 grid. ...
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### Neural Networks: Solving XOR

A perceptron with two inputs $x_1$ and $x_2$ has following linear function and is hence able to solve linear separateable problems such as AND and OR. $f((x_1w_1+b)+(x_2w_2+b))$ $f(x)$ is the basic ...
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### maximizing alpha-beta puning.

I was searching a more pertinent place to post artificial intelligence concerned question, but some results pointed me to similar questions posted here, thus I chose math.se, now let's get through ...
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### Find sectors in a racing line.

Consider the following photo: To magnify image, right click and select open-image in new tab or something similar The photo above is a random race circuit data I've collected. What I'm trying to ...
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### What kind of graph is the StackExchange?

Assuming that we have three distinct layers of nodes called Users, Questions & Answers, connected by the obvious way $(A)$, what kind of graph is the StackExchange? Do such graphs have special ...
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### Boosting v. weighted average

I have been watching an MIT online Artificial Intelligence lecture by Prof. Winston about boosting. The boosting technique uses complicated maths to combine the results from several weak predictors to ...
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### $i,j,k$ Values of the $\Theta$ Matrix in Neural Networks

SO I'm looking at these two neural networks and walking through how the $ijk$ values of $\Theta$ correspond to the layer, the node number. Either there are redundant values or I'm missing how the ...
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### Modern Mathematical Theory for Neural Networks, Cellular Automata, Neuroscience

Is it possible for someone to do research on subjects like neural networks, cellular automata, or neuroscience as an applied mathematician? I have in mind the theoretical development of these fields,...
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### What is the sigmoid *squashing* function?

I've just read the following The basic unit ("neuron" i) performs the following computation to update its state $y_i$: it computes a weighted sum $v_i$ of its inputs $x:j$ which is passed ...
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### Memory of a neural network: is it forever?

As far as I remember a neural network cannot forget anything. Does this mean that no matters how evolved the network is, it's always going to throw me back the right output if I feed it an input? And ...
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### How to Calculate Values from Incoming Messages? - Evidence Propagation in Bayesian Network

I'm currently trying to wrap my head around evidence propagation in bayesian network (simple tree propagation) but I'm having trouble finding information about the process. As an example, let's take ...
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### How to calculate probabilities in a Bayesian network?

Consider the Bayesian network represented by the directed acyclic graph given below: We are given the following probabilities: P(tampering) = 0.02 P(fire) = 0.01 P(alarm | fire ∧tampering) = 0.5 ...
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### What aspects of convex optimization are used in artificial intelligence, if any?

I work on convex optimization with Stephen Boyd's book. As an example, support vector machines are mentioned as an application of separating hyperplanes theorem. I am wondering if there is any other ...
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### Does this equation my professor wrote actually work? [closed]

Does this make sense to you? Peter's classroom example $\frac{1}{2^{(\text{any power})}} = \frac{1^{(\text{any power})}}{2^{(\text{any power})}} = (\frac{1}{2})^{(\text{any power})}$ If that's the ...
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### How do I use resolution refutation in backward reasoning

Suppose I have the following facts in my KB: ∀a,b: g(a,b)→ p(a,b) ∀x: ¬p(x,x) ∀x,y,z: p(x,y)∧ p(y,z)→ p(x,z) ∀w,r: p(w,r)→ g(w,r) I have a questions: If I want ...
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### Dung's Argumentation Framework

Given an extension of Dung's argumentation framework, and all definitions therein, let $$AF_1 = \langle A,Def \rangle$$ be a framework where $$A = \{ A, B, C, D, E, F, G, H \}$$ and Def = \{A def G, ...
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### hamiltonian graph problem (sitting problem)

Hello guys sorry for noob question but i am learning graph theory and i am solving a question . in book it says it have only four solution but i founded that it can more than four so i am confused . ...
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### The mathematics behind Google Deepmind

I'm aware of the following question: The mathematics behind AlphaGo AI and Google Deepmind I'm aware of math behind Perceptron and several other AI concepts: ...
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### The mathematics behind AlphaGo AI and Google Deepmind [closed]

in case you are following the tech news, Google's AlphaGo beat the world Go champion Lee Sedol, not once but twice. Here is the link of the game 2 review: http://gogameguru.com/alphago-races-ahead-2-...
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### Comparing two textbooks for machine learning

I am a Ph.D student in Electrical Engineering. I am going to study the field of machine learning and I found some textbooks to study this field. 1) Probabilistic Graphical Models: Principles and ...
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### How to apply negation to a term?

EDIT: Maybe page 18 of this paper can help. This is a follow up from this question, where I am using ALCQ and I have this: $\lnot(3 \le \exists \text{hasPet}.\text{Animal})$ How to apply the ...
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### Implicit feature space of Power Kernel

For the polynomial kernel, $K(x,y) = (x^Ty+c)^d$, the implicit feature space $\phi$ for which $K(x,y) = \phi(x)^T \phi(y)$ is of finite dimension and well known [1][2]. It is also well known that the ...
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### Solving differential equation using artificial intelligence

Hellow, I want to do my phd on the topics solving differential equation using artificial intelligence. At first I want to read some introductory books on artificial intelligence and then on the topic "...
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### State space complexity of $2d$ and $3d$ tic tac toe

So for a 2d tic tac toe game, we know that the space complexity can be represented as follows. A naive upper bound will be $3^9$ as there is $3$ possibilities (X, Y or blank) in each of the $9$ ...
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### Improving Simulated Annealing based on Measure of Goodness

can anyone answer this question or direct me to a reference that can help? Simulated Annealing returns the current state when the end of the annealing schedule is reached and if the annealing ...
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### binary resolution rule proof

I want to proof the binary resolution rule that is, if we For any two clauses $C_1$ and $C_2$, if there is a literal $L_1$ in $C_1$ that is complementary to a literal $L_2$ in $C_2$, then delete $L_1$ ...
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### Complexity analysis of alpha beta pruning of a full tree

I am trying to understand the derivation of a time complexity for an alpha-beta pruning algorithm but up till now have not found any reasonable recourse. Many recourses claim that if you take a full ...
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### Using differential evolution to evaluate weights

I have an equation I am attempting to optimise of the form: w1x1 + w2x2 + w3x3 Using a pre defined fitness function. Unlike any of the original papers, I also have the constraint: Sum of the ...
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### How does Best First Search Calculate the Heuristic Values in the Graph

I understand that Best First Search uses a sorted open list based on Heuristic Values of the Nodes (priority queue) and a closed list.But how are these Heuristic values of the Nodes calculated? The ...
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### Reducing TIC-TAC TOE State Space by using Symmetry in Artificial Intelligence

Im learning Heuristics in AI.I see that for brute force search there are 9! states.But the textbook says that first 3 levels are reduced by symmetry.How does that work?
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### What would linear neurons be able to model in artificial neural nets

Is it true that linear neurons are only useful in single layer neural nets because adding multiple layers will not allow the net to learn any interesting features because of the linear neurones?
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### Math replacing natural language [closed]

Before reading any further. I ask yous to think creatively on this subject. I was in shower and was pondering over A.I. (Strong A.I. both at human level and beyond human level) as I do from time to ...