New Horizons

For more than a year or so, I am completely amazed to realize that what I would call the random approach , both in terms of computational algorithm and hardware design, has unexpected but very encouraging properties. Microprocessor come up with a many error-correcting processes, using a large amount of overall CPU resources (energy, wall-clock time, etc). By allowing the hardware to make a few mistakes, managed to be under some probability law, scientists of the Rice-NTU Institute for Sustainable and Applied Info dynamics (ISAID) lead by Krishna Palem, showed that significant gain could be possible, both in term of energy demand and performance. Also by trimming away ( pruning in the jargon) some rarely used portions of the chip and confining locally voltage requirements researchers  have been able to take advantage in energy requirements. “In the latest tests, we showed that pruning could cut energy demands 3.5 times with chips that deviated from the correct valu...

As you probably may (or may not!) know, molecular biology often study biological functions from interaction network between molecules rather than studying each component one-by-one. It's the opposite of the universal divide-and-conquer strategy, I would call it the all-inclusive strategy. Those interactions networks involves myriads (10.000) of molecules that interacts by various chemical ways, which is generally represented as an oriented graph between each molecular compound. The transcriptional networks describe the relationship between genes and proteins, the protein-protein network s defines the cascades of interactions between some, ingenuously lumped, proteins, the metabolic networks attempt to mimic the flush of metabolic reactions inside living organisms.  So the idea is to understand how the  main 'thing' works from all those interactions linked together. Of course, other kind of networks are used in many different domain to study more-or-less linked ...

Here is a nice video of sketch based visualization tool of fluid systems. I'm quite amazed by the complexity of the systems that can be modeled that way, and I find the graph version very practical. It's a nice idea to have a rough idea of your subsystem connectivity, specially when the model is a mess of tubes, valves and containers. I like that !   Source Sourxce

This blog entry will be entirely dedicated to a subject that absorbed me for more than one year: support graph preconditioners . When one have to solve say a laplacian equation on a mesh the numerical discretization  the problem to solve is generally of the form Ax=b, where A is a sparse matrix with many zero entries. More importantly the non-zero entries have a pattern direclty inherited from the mesh connectivity. For linear elements, (i,j) entry is non void if and only if there is an edge between node i and node j (what's cool with the laplacian is that a node is a degree of freedom). So, as long as the mesh has a moderate connectivity pattern, the matrix inherits  that pattern and is therefore relatively sparse. If you factorize your matrix with a direct solver then the work your computer has to do is directly linked to the connectivity of the underlying mesh. For instance if the underlying mesh is a tree , then the complexity of the direct solver will be linear with r...