# Tagged Questions

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### Mathematical preparation for postgraduate studies in Linguistics

I am an undergraduate student in Mathematics and I would like to continue my postgraduate studies in the harder, more mathematical aspects of Linguistics. What exactly would that include is unknown ...
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### Mathematics base for data mining and artificial intelligence algorithms. [closed]

Could you give me some clarification about data mining and artificial intelligence algorithms? What mathematics base they used for? Could you give me starting point, in mathematics, to understand ...
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### Application of computers in higher mathematics

Currently the main application of computers in mathematics seems to be to compute things, i.e. to solve equations, evaluate integrals, etc. It is at all possible to delegate the thinking of a ...
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### What would be the shortest path between 2 points when there are objects obstructing the straight path?

How would an algorithm find the shortest distance between 2 points on a horizontal 2d plane , especially when a straight path is not possible? Could it be something on the lines of calculating least ...
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### Applications of Differential Geometry in Artificial Intelligence

I am new to this wonderful site. I searched around a bit but I couldn't find any well-discussed posts on applications of differential geometry to artificial intelligence, or more generally to computer ...
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### What about Genetic Algorithms from a mathematical point of view?

Last year I've attended an Artificial Intelligence course (it was very simple, just a summary of the main ideas); we've seen what a genetic algorithm is and the idea seems very interesting to me. Now ...
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### AI strategies for losing positions [closed]

I have a card game that I am analyzing with Maple. Actually, it's a series of card games, one for every parameter k, where k is a natural number (representing the number of ranks of cards used in the ...
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### First order logic.

In Artificial intelligence, I saw the following question and answer in website. Question: Politicians can fool some people all of the time, and they can fool all people some of the time, ...
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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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### Are there some functions that cannot be optimized using calculus?

I've been working on a project to maximize a functions output using a genetic algorithm. However, from the limited calculus I know I thought there were methods to find the maximum of a mathematical ...
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### Recursively Solving a Bellman Equation

Problem Overview I am to figure out $v_\pi$ of a certain Markov state. Given Information A set of actions, $a$ containing ${up, down, left, right}$ $v_\pi(12), v_\pi(13), v_\pi(14)$ (I am given ...
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### State space for 8-queen problem

While reading Artificial Intelligence a Modern Approach I came across the following formulation for the 8-queen problem: Initial state: No queens on the board. States: Arrangements of n queens (0 &...
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### 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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### Mathematics in cognitive sciences

Which areas of Maths can be formally studied in a cognitive sc major? Or: which areas of maths can support the study of brain. Some areas that seem relevant would be: mathematical logic, graph theory, ...
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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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### $i,j,k$ 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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### Games with human edge [closed]

Which are some two- or one-player games, where humans far outperforms the best computer programs? And how does the relative edge scale with time allowed to think? (In time frame 1 sec to 8 hours per ...
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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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### Some doubts about the differences between logic implication and inference rule

I am studying for an Artificial Inteligence university exam that includes a section dedicated to mathematical logic. I am finding some difficulty in understanding the difference between logical ...
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### Boolean Algebra Question

my problem is ,Please give the algorithm: how can rewrite an arbitrary propositional formula alfa(α) into a proposional formula beta(β) so that beta does not contain disjunction(âˆ§) and alfa ...
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### Markov Decision Process - Utility Function

Reward R(S) in a Markov Decision Process is a mapping from a State S -> Bounded number. I want to know how a Utility Function is defined for an MDP. I think it has to be a mapping from a sequence of ...
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### Testing critical points using newton-raphson method

I'm working on a homework assignment for my artificial intelligence course and I became a bit stuck on one part. The problem asks to retrieve the optima of the function and then to tell for each ...
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### Markov Decision Process - Optimal policy invariance to scaling in the Utility Function

The title says it all. If i use a discounted Utility Function, why is the optimal policy invariant with respect tot the scaling of the Utility Function by a positive Factor?
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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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### 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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### 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 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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### 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 ...
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### How to calculate Full joint probability distribution

This is a past exam question, I did it wrong in the exam, I'm reviewing it right now. The question is to compute the full joint probability of the problem below: I draw the full joint ...
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### Gradient descent/ nonlinear optimization intuition needed

all. I'm taking an introductory AI class, and we're using the gradient descent algorithm to find the optimized/ lowest cost of a set of thetas (variable coefficients) to best fit a regression line. In ...
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### Books on AI, programming, optimization

I'm studying math (just started) and I like programming as well (just started this too), is there a career or a branch of research including deep aspect of this two aspects? Is there someone among you ...
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### First Order Logic

Is it possible to represent the english sentence with numerical value in First order Logic. For example if the sentence is: Nobody has more than one mother. I am wandering who can i show the ...
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### Contradiction in Davisâ€“Putnamâ€“Logemannâ€“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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### Using implication with the Universal quantifier

While reviewing my AI textbook, I came across a paragraph that baffled me. It attempts to explain why the truth table for implication turns out to be perfect, as ...
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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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### 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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### LOGIC - Completeness vs Consistent

One of my exams questions were the following (translated from Hebrew) Course is in Artificial Intelligence, and is about Logic in this question. What is a consistent logic system? What is a ...
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### Can you give a simple CDCL example?

I am trying to understand how Conflict-Driven Clause Learning works. After reading through the lecture slides, wikipedia article and some additional slides I found online I realized that I still can't ...
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### Proving that a Hessian Matrix is positive definite

I'm currently stuck on a problem for my Artificial Intelligence class. The assignment is provided at the following link: http://courses.engr.illinois.edu/cs440/HW1.pdf The problems that I'm stuck on ...
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### CHeck my proof of how I arrived at my answer

Show proof for: (P --> Q), P ^ (~ ~R & ~ ~ Q), (S --> ~ R), ~(P & Q) : (~S ^ ~Q) is this correct? (P --> Q) Premise P ^ ( ~ ~R & ~ ~Q) Premise (S --> ~R) ...
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### Ranked Preference Matching Algorithm

first dropping the link that will serve as reference: NRMP Residency Matching I have a sort of side project (nothing riding on it, computational performance not an issue, so feel free to go wild, I ...
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I have to questions about the chess game: please help me to understand it. 1- How can a computer program know if this move or that move is better? It calculates all possbile continuation and examine? ...
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### Which books /tutorials will be good for these topics for AI computer science student

I have found from the internet that I need to know these topics for understanding Artificial Intelligence: Matrix algebra: most machine learning models are represented as matrices and vectors. ...
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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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### 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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### How to find the optimal linear basis functions of an MDP?

Given a set of basis functions, there are many papers on finding a weight vector to linearly approximate the value function. Is there any paper on how to find the basis functions? Is it possible to ...
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### Neural network cost function - why squared error?

Question: Why is the squared error most often used for training neural networks? Context: Neural networks are trained by adjusting the link weights. The key factor that informs these adjustments is ...
The question is as the title. Mathematically, I want to know does the following inequation always hold for any vector $\mathbf b$? \$\mathbf b^T \mathbf B \mathbf B^+ \mathbf b \, \ge \, \mathbf b^T \...