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Dharmendra S. Modha

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Archives for 2007

Dr. Benjamin Mann’s 23 Mathematical Challenges

August 23, 2007 By dmodha

At DARPATECH 2007, Dr. Benjamin Mann presented his list of 23 mathematical challenges in his talk "DSO Mathematics: The Heart and Soul of the Far Side". The reader will no doubt notice that his first challenge is to my liking.

  1. The Mathematics of the Brain:  Develop a mathematical theory to build a functional model of the brain that is mathematically consistent and predictive rather than merely biologically inspired.
  2. The Dynamics of Networks: Develop the high-dimensional mathematics needed to accurately model and predict behavior in large-scale distributed networks that evolve over time occurring in communication, biology and the social sciences
  3. Capture and Harness Stochasticity in Nature: Address Mumford’s call for new mathematics for the 21st Century.  Develop methods that capture persistence in stochastic environments.
  4. 21st Century Fluids: Classical fluid dynamics and the Navier-Stokes Equation were extraordinarily successful in obtaining quantitative understanding of shock waves, turbulence, and solitons, but new methods are needed to tackle complex fluids such as foams, suspensions, gels and liquid crystals.
  5. Biological Quantum Field Theory: quantum and statistical methods have had great success modeling virus evolution.  Can such techniques be used to model more complex systems such as bacteria?  Can these techniques be used to control pathogen evolution?
  6. Computational Duality:  Duality in mathematics has been a profound tool for theoretical understanding.  Can it be extended to develop principled computational techniques where duality and geometry are the basis for novel algorithms?
  7. Occam’s Razor in Many Dimensions: As data collection increases can we “do more with less” by finding lower bounds for sensing complexity in systems?  This is related to questions about entropy maximization algorithms.
  8. Beyond Convex Optimization: Can linear algebra be replaced by algebraic geometry in a systematic way?
  9. What are the Physical Consequences of Perelman’s proof of Thurston’s Geometrization Theorem?  Can profound theoretical advances in understanding three dimensions be applied to construct and manipulate structures across scales to fabricate novel materials?
  10. Algorithmic Origami and Biology:  Build a stronger mathematical theory for isometric and rigid embedding that can give insight into protein folding.
  11. Optimal Nanostructures: Develop new mathematics for constructing optimal globally symmetric structures by following simple local rules via the process of nanoscale self-assembly.
  12. The Mathematics of Quantum Computing, Algorithms, and Entanglement: In the last century we learned how quantum phenomena shape our world.  In the coming century we need to develop the mathematics required to control the quantum world.
  13. Creating a Game Theory that Scales: What new scalable mathematics is needed to replace the traditional PDE approach to differential games?
  14. An Information Theory for Virus Evolution: Why not?
  15. The Geometry of Genome Space: What notion of distance is needed to incorporate biological utility?
  16. What are the Symmetries and action Principles for Biology?  Extend our understand of symmetries and action principles in biology along the lines of classical thermodynamics, to include important biological concepts such as robustness, modularity, evolvability and variability.
  17. Geometric Langlands and Quantum Physics: How does Langlands program, which originated in number theory and representation theory, explain the fundamental symmetries of physics?  And vice versa?
  18. Arithmetic Langlands, Topology, and Geometry.  What is the role of homotopy theory in the classical, geometric, and quantum Langlands programs?
  19. Settle the Riemann Hypothesis: the Holy Grail of number theory.
  20. Computation at Scale: how can we develop asymptotics for a world with massively many degrees of freedom?
  21. Settle the Hodge Conjecture:  the conjecture in algebraic geometry is a metaphor for transforming transcendental computations into algebraic ones.
  22. Settle the smooth Pioncare Conjecture in Dimension 4.  What are the implications for space-time and cosmology?  And might the answer unlock the secret of “dark energy”?
  23. What are the fundamental laws of biology?  Dr. Tether’s question will remain front and center in the next 100 years.  I place this challenge last as finding these laws will undoubtedly require the mathematics developed in answering several of the questions listed above.

Filed Under: Brain-inspired Computing, Interesting People

Rapid Erasure of Long-Term Memory Associations in the Cortex by an Inhibitor of PKM zeta

August 20, 2007 By dmodha

Science published an interseting study (Science 17 August 2007:
Vol. 317. no. 5840, pp. 951 – 953) by Reut Shema, Todd Charlton Sacktor, and Yadin Dudai.

Abstract:

Little is known about the neuronal mechanisms that subserve long-term memory persistence in the brain. The components of the remodeled synaptic machinery, and how they sustain the new synaptic or cellwide configuration over time, are yet to be elucidated. In the rat cortex, long-term associative memories vanished rapidly after local application of an inhibitor of the protein kinase C isoform, protein kinase M zeta (PKM zeta). The effect was observed for at least several weeks after encoding and may be irreversible. In the neocortex, which is assumed to be the repository of multiple types of long-term memory, persistence of memory is thus dependent on ongoing activity of a protein kinase long after that memory is considered to have consolidated into a long-term stable form.

Filed Under: Brain-inspired Computing

The Singularity Summit 2007: September 8-9

August 17, 2007 By dmodha

"The Singularity Institute for Artificial Intelligence presents the Singularity Summit 2007, a major two-day event bringing together 17 leading thinkers to address and debate a historical moment in humanity’s history – a window of opportunity to shape how we develop advanced artificial intelligence." See their website for details.

Filed Under: Accomplishments, Brain-inspired Computing, Presentations

DARPATECH 2007

August 16, 2007 By dmodha

Last week, I had the opportunity to attend DARPATECH 2007 at which DARPA presented its vision. The Urban Challenge was also announced. The event attracted huge media attention:

http://www.popularmechanics.com/technology/military_law/4220413.html
http://blog.wired.com/defense/2007/08/darpatech-the-b.html
http://www.hardocp.com/news.html?news=Mjc0MDMsLCxoZW50aHVzaWFzdCwsLDE=
http://www.engadget.com/2007/08/09/new-military-robots-showcased-at-darpatech-2007/
http://science.slashdot.org/article.pl?sid=07/08/11/1527243
http://www.designnews.com/blog/320000232/post/1590012959.html

Filed Under: Brain-inspired Computing, Leadership

Elizabeth Torres: Three building blocks of the mind to autonomously control the body

July 25, 2007 By dmodha

Elizabeth TorresWe had a wonderful talk today from Dr. Elizabeth Torres who is currently at CalTech.

Abstract:

We propose three necessary components for autonomous behavior that any biological organism with sensors, a nervous system subject to the inevitable sensory-processing internal delays and equipped with memories should have. The first component deals with spatio-temporal disparities between the internal and the external mediums of the organism to facilitate comparisons of signals that may be misaligned in space and time. The second component evaluates the similarities between current and old (memories) information to select a course of action (storing a new memory from scratch, using an old memory as it is, or updating an old memory to turn it into a new one as part of a family). The third component regulates the level of relevance for storage, retrieval and update of memories according to the consequences that a given situation my have for the survival and reproduction of the organism.

We provide an example of how these three blocks manifest in primates within the domain of voluntary arm movements. As other systems in the brain, the sub-systems involved in these autonomous behaviors have to deal with sensory-motor maps and transformations involving disparate spatio-temporal representations, internal sensory-processing delays and memories (in the motor domain). Thus these subsystems need to store, retrieve and update memories, which (in primates) we define as associations between the allocentric representation of internal delays (anchored to an early sensory receptor like those in the retina) and a given set of external contextual cues according to their relevance (consequence). We show empirical data from humans and monkeys that strongly suggest that in primates, given a situation such binding computation can be allocentric encoded retinotopically independent of body motions. This evidence changes the way in which we currently think of episodic memory and provides a fresh look at how our conscious notion of the passage of time may have come about.

Filed Under: Interesting People

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