Questions tagged [diffusion]
The diffusion tag has no usage guidance.
18
questions
0
votes
0answers
5 views
How to generate a log-linear frequency distribution of walk durations with a random walk?
Imagine that I have a random walk of n-individuals running to time t. There is a lower absorbing boundary z at which each individual stops walking when encountered. Steps are randomly drawn from any ...
2
votes
0answers
33 views
What is the likelihood function of the starting time of diffusion?
I need to find the likelihood that a set of molecules was instantaneously released at time $t_0$, say $t_0=0$.
Toy System Example:
Let $N$ be the set of molecules released from a specific point in a ...
2
votes
0answers
15 views
How to apply the diffusion maps when the matrix is PSD but not positivity preserving?
In order to apply the diffusion maps in a matrix $C\in\mathbb R^{n\times n}$ , that matrix must obey some restrictions,
C is symmetric: $C_{ij} = C_{ji}$,
C is positivity preserving (PP): $\forall ...
0
votes
0answers
27 views
Hopefully a quick semantics question (Maximum Likelihood Estimator)
I was working through a portion of this paper, when I came across something that seemed odd to me.
In Appendix E (pg24), equation (E4), the following line pops up:
$\widehat{D} = \frac{\widehat{\...
1
vote
0answers
23 views
Diffusion tensor as a covariance matrix
TLDR: In nuclear magnetic resonance (NMR), to study molecular diffusion we assume that molecules displace in 3D space according to a trivariate gaussian distribution. The variables are then the ...
2
votes
1answer
175 views
What is the distribution of the peak time of the first hitting time process
I need to find the distribution of the random variable $T_{peak}$ where $T_{peak}$ represents the peak time of the first hitting time process.
Detailed Explanation of the System:
There are $N^{Tx}$ ...
2
votes
0answers
53 views
Stochastic Differential equation: CAPM
Let $R = (R_1, \dots , R_M)'$ denote a vector of excess returns of $M$ assets observed at $n$ time points, $0 < t_1 < t_2 < \cdots < t_n < T$, within a time span $T > 0$.
We wish ...
3
votes
0answers
25 views
Increase the number of samples when the PDF is invariant
Background:
$$\frac{\partial C}{\partial t} = D \frac{\partial^2 C}{\partial x^2}$$ is given by Fick's second law, in which $D$ is the diffusion coefficient.
The solution to this equation (given the ...
0
votes
1answer
51 views
Why is the sample variance equal to the average sample size for random processes?
I am learning auto-correlation function for fluorescence correlation spectroscopy (FCS) on fcsXpert.com. The web page says:
For random processes such as diffusion, the average of the square of the ...
0
votes
1answer
48 views
Distribution of the step size of diffusion in 3-dimensional space
I need to find the distribution of the random variable
$$Y=\sqrt{X_1^2+X_2^2+X_3^2}$$
where $X_i\sim{\cal{N}}(0,\sigma^2)$ and $\sigma^2$ is related to diffusion coefficient. All $X_i$s are ...
2
votes
0answers
215 views
How to simulate anomalous diffusion of a 1D point like particle?
I want to simulate 3 types of diffusion processes:
normal diffusion $[\langle x^2(t)\rangle \propto t ]$.
subdiffusion $[\langle x^2(t)\rangle \propto t^\alpha ; \alpha<1 ]$
superdiffusion $[\...
1
vote
0answers
73 views
Computing properties of non-uniform random walk/diffusion
I have a lot of numerical data which I'm looking to characterise as a (possibly continuous) random walk with variable (in space) step size, for example, along $x$ between $-1$ and $1$ with a step size ...
1
vote
0answers
232 views
2 Dimensional Random Walk Simulation
I am trying to simulate random diffusion of particles using a random walk diffusion model. I have used probabilities of movement of particles in a 2D area, to be 1/4 in all 4 directions. The confusion ...
1
vote
2answers
426 views
confusion about root mean squared distance in 1 dimensional random walk
I was just introduced to the concept of a random walk while reading the Feynman lectures on physics, Volume 1. There was something in the explanation there that confused me, so I tried looking online ...
5
votes
0answers
332 views
Theoretical link between the graph diffusion/heat kernel and spectral clustering
The graph diffusion kernel of a Graph is the exponential of its Laplacian $\exp(-\beta L)$ (or a similar expression depending on how you define the kernel). If you have labels on some vertices, you ...
3
votes
0answers
393 views
Diffusion coefficient from double-normal probability density function
The spread of individuals of species is often described by so-called dispersal kernels. The main parameter of spread is then often the variance defined as the average squared movement distance of a ...
9
votes
0answers
196 views
What is tantile regression?
My question follows on this discussion of medials and tantiles vs medians and quantiles from earlier this year:
When would we use tantiles and the medial, rather than quantiles and the median?
As ...
3
votes
2answers
2k views
Probability distribution of the magnitude of a circular bivariate random variable?
I'm very new to this topic. I have a distribution similar to the picture below but with the center at zero.
As I said, I'm very new to this, but if I understand correctly, if there was no hole in ...
