Return

OBSOLETE! Page is now in Diff-Segm
  • related to Gibson's concept of optical flow and affordance perception
  • used in many applications: movement detection, video compression, frame reconstruction, image stabilization etc.  

 

Survey of Algorithms

 

[poz 191023] proposals:

 

 
  • clustering algorithms 
  • rewriting systems (how to think it more abstract?)
  • cellular automata
  • referntial transparency

maket the input signal part of the program

It assumes that the flow is essentially constant in a local neighbourhood of the pixel under consideration, and solves the basic optical flow equations for all the pixels in that neighbourhood, by the least squares criterion

 

(in relation to the disposition of 'Differential Segmentation')

the 10 most important algorithms for:

  1. Graph algorithms 
  2. Dynamic programming 
  3. Searching and Sorting: 
  4. Number theory and Other Mathematical 
  5. Geometrical and Network Flow Algorithms 
  6. Data Structures

{hhr 191120} more random thoughts:

  • Quorum sensing
  • Particle swarm optimisation
  • Something opposed to the concrete structure; thus biological growth, plants, living organism...

More on P Systems:

  • {L} J.Kleijn and M.Koutny, "Synchrony and Asynchrony in Membrane Systems" - "The aim of our work, however, is different in that we are interested in describing what is actually going on during an execution of a membrane system; alternatively, one might say that we are interested in computations rather than computability." and "Tissue membrane systems In this case objects are transported through channels rather than membranes. Thus the nested tree-like structure of membranes is replaced by a graph, with its edges representing channels connecting compartments in a completely arbitrary way."

{hhr 191121} more random thoughts:

  • (Minimum) Spanning Trees
  • Clustering
  • Region Segmentation

in series (chomsky)

in parallel (lindenmayer)

 
  • rewriting system
  • self similarity
  • easy to communicate

 
axiom: 0
1st recursion: 1[0]0
2nd recursion: 11[1[0]0]1[0]0
3rd recursion: 1111[11[1[0]0]1[0]0]11[1[0]0]1[0]0

 

 

[L] John R. Rice (1975), The Algorithm Selection Problem

P Systems

 

elements:

  • environment
  • membrane
  • symbols
  • catalysts
  • rules
  • application process

 

[hhr 191024] Reading through WP article, I think that's very interesting in that it operates with these "abstractions" or "metaphors", as the article tries to describe the commonalities between various "P systems". That's kind of the abstract description of "algorithm" that I would deem suitable for exploration, as it doesn't prescribe yet how all of this is operationalised.

 

Example: "Membranes are the main “structures” within a P system. A membrane is a discrete unit which can contain a set of objects" ... that's both very particular and open at the same time.

 

[hhr] P system seems to be more a model of computation than a particular algorithm, perhaps it could be called an algorithmic or computation strategy? The dissolution of membranes I find rather beautiful.

criteria for selection

  • renowned / unknown
  • classical (input->run->output) vs non-terminating

 

a simple neural network (with python examples)

theorem 9

rule 110

simulation: "As there is no current method of directly implementing a P system in its own right, their functionality is instead emulated"

(this is then used to define nested membrane structures)

Abstract Rewriting

"Confluence (abstract rewriting)": https://en.wikipedia.org/wiki/Confluence_(abstract_rewriting)

 

Knuth-Bendix "rules": delete / compose / simplify / orient / collapse / deduce

 

"Trace Monoid": "In computer science, a trace is a set of strings, wherein certain letters in the string are allowed to commute, but others are not. It generalizes the concept of a string, by not forcing the letters to always be in a fixed order, but allowing certain reshufflings to take place."

 

Peitgen: Multiple-reduction copying machine

 

Liskov substitution principle

 

"Symbolic chemical system based on abstract rewriting system and its behavior pattern": https://link.springer.com/article/10.1007/BF02471142

; ARMS - abstract rewriting system on multisets

 

P System: "A P system is a computational model in the field of computer science that performs calculations using a biologically-inspired process. They are based upon the structure of biological cells, abstracting from the way in which chemicals interact and cross cell membranes."

dedicated subpage for rewriting processes

[hhr] What I find interesting about rewriting systems is

  • that they may potentially run forever, as a process
  • that they usually assume "symbols" or an "alphabet", making the connection to sound and signal processing not directly obvious (it's a challenge).
  • that they relate to graphs and topologies

Clustering

 

Data Structures

 

time: 45m30s

file: IT5/191024/cut/ZOOM0017cut.wav

DP

Rule 110 is one of these simple ML rules, with which you can build turing complete machines. Build means that you have a 2D cellular automaton, where you place the beginning points and then the machine computes something. And it's really funny to look at, it has a very machine-like movement that is really interesting. 

 

HHR

It's probably similar to these artificial life people that take ants or bees and make them compute something. 

 

DP

Yeah. But that's interesting for me because there's a very strong aesthetics of where computation is in nature. I mean, Wolfram, who was one of the guys who used these things, he thinks that nature computes. It's a massive statement, right? And all these kind of things are based on this idea, which is a very strong aesthetic. 

[in SC]

 

Machine Learning (terms, ideas)

 

  • neural gas
  • novelty detection
  • unsupervised learning
  • backpropagation
  • clustering
  • self-organising (maps)
  • Hebbian theory
  • Autoassociative memory

simple graph rewriting rule application in a computer program: replace multiplication-by-two by addition-with-itself