Alexey Radul gave a talk on the "Art of Propagator" [1]. His slides are available at [2].  

Here are the key points raised during the talk and during the subsequent discussion. The notes are also available at [3]. There could be mistakes in the scribe notes. Feel free to correct if you find any.  

Alexey: A propagator is an abstract machine that reads some cells and writes to some cells.

Lalana: Does it allow rewriting cells? And what about the temporal aspects of the system?

Alexey: The state is explicitly exposed in the cells, and the propagator system network is stateless. It's  always on, asynchronous and stateless.

Joe: Does it accept, for example, a Clcok Pulse Input?

Alexey: We are avoiding the consequece of time.

Alexey: Gave the examples of the mutually inverse propagators using the adder and subtractor example, and the multi-directional computation example useing Celcius -> Fahrenheit -> Kelvin temperature conversion.

Alexey: A cell can get multiple input. This can lead to many problems, even if the cells hold different but compatible values. Therefore, the cells hold *information* about the values, and not the values.

Ian:  Information flow is decided by the constraints of the propagator network.

Alexey: Information is flexible and ideally monotonic. The constraints compose into multi-directional computations which can grow incrementally without adjusting explicit controls. Interval arithmetic provides a solution to temporal inconsistencies between the different values obtained from different sources.

Alexey: The paper was about low level propagtor networks. But the same concept can be applied to higher level abstractions such as the "Deadbeat Dad" scenario.

Lalana: Functionality wise, how does a propagator network different from a regular TMS?

Alexey: This can be thought of as a distributed TMS

Gerry: The propagator network distribute the computation across the cells.

Kenny: The cells are global?

Alexey: No

Joe: Are cells unique?

Alexey: Yes

K: There are many issues related to data management and controlling access to data. Data from multiple sources could be synchronized to compose a compound answer or the answer could be taken from a single original source.

[scribe note: the question was not that clear to me (was distracted for some reason). So, please add / correct me if I am wrong]  

Gerry: Compound answer might be better.

Ian: What is the difference between Actor model[4] and this?

Gerry: Actor model is mainly for concurrency computation. But the Propagators do not implement concurrency.

Kenny: Can you give more examples for the Partial Information scenario?

Alexey: TMSes, machine learning results, Waltz's line labelling algortihm, Real number constraint satisfaction algorithms (?), Probability Distribution Networks

Lalana: How are you readings the cells? Through URIs as identifiers? Pub-Sub protocol?

Alexey: Right now they are just pointers to the computer's memory. This is still a model of computation at a very low level.

Oshani: If we use URIs as the contents of the cells, don't we have to assume the cells to be immutable?

Gerry: We can use Versioning as a proof of what the current state is.

Alexey: This is entirely a simulation of a compuatation model. No concurrency implemented yet. Only allow one propagator at a time.

Gerry: My main worry is about the garbage collection.

Kenny: What are the future plans of this project?

Alexey:

1. Partial Information over Compound data structures  

2. Abstraction - Put a boundary around  the propagotor network

3. Probablisitic model of data structure for interencing - How can we do continuous instead discrete?  

[1] http://dspace.mit.edu/handle/1721.1/44215

[2] http://dig.csail.mit.edu/2009/DIG_Seminar/0312-alexey.pdf

[3] http://dig.csail.mit.edu/2009/DIG_Seminar/notes/0312.xhtml

[4] http://en.wikipedia.org/wiki/Actor_model