0
votes
0answers
27 views

Parameter estimation of Lorenz system (nonlinear dynamical system)

My problem is as follows. I have to estimate parameters of Lorenz system using given data. Lorenz system is described by following system of ODEs: $$ \frac{dx}{dt} = \sigma(x-y) \\ \frac{dy}{dt} = ...
0
votes
1answer
40 views

A good reference to learn the concept of partition function

I am looking for a good reference and easy to learn the concept of partition function in mathematics. Can anyone help me?
2
votes
0answers
71 views

Boltzmann machines - motivation for the energy function

I've been studying Boltzmann machines lately and was wondering if anyone could give me a "high-level" explanation or motivation for the energy function used: $$E = -\sum_{i<j} w_{ij} \, s_i \, s_j ...
2
votes
1answer
59 views

Why are log-probabilities of global states of Boltzmann machines linear in their energies?

While going through the Wikipedia article about Boltzmann machines, I read the following on the probabilities of global states of Boltzmann machines in the "Equilibrium state" section ...
1
vote
1answer
192 views

Kalman filter and data extrapolation

Context of the situation: I have a system set up that can give me the position of a person in a room. I also have a light that shines on this position. However, the light are lagging behind by 0.300 ...
0
votes
1answer
84 views

How to model a system for tracking a person using kalman filter?

I need to model a system for human motion. The following link shows for to build a system for a plane. I am currently reading the documentation for a kalman filter library ...
0
votes
1answer
83 views

Logistic function

Let $$f=\lambda x(1-x)$$ be a logistic map with $\lambda>4$. How to show that set of all periodic points of $f$ in $\Lambda$ is countable and the set of point in $\Lambda$ with dense orbits is ...
3
votes
1answer
63 views

Inverse of itinerary function

Let $S^{-1}:\Sigma \to \Lambda$ be inverse of itinerary function. I showed that $S$ is continuous and bijective. How to show that $S^{-1}$ is continuous?
1
vote
0answers
93 views

Fibonacci like monkey population problem ( population dynamics )

Assume a female and male monkey. Lets call this generation $1$. All males and females have one and one only partner for breeding in their entire life assuming there is at least $1$ available. And ...
1
vote
0answers
76 views

Simultaneous equations for bacteria.

I would like to calculate the value of bacteria on 4 surfaces $i=\{1..4\}$. A person touches some of those 4 surfaces at random and a count is made on their finger after each surface contact ($x_i$). ...