June 24–July 13, 2018

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Wolfram Summer SchoolFounded in 2003

16th Annual Wolfram Summer School, held at Bentley University June 24–July 13, 2018


Alexandre Ismail

Class of 2005


Alexandre Ismail was born in Jakarta, Indonesia, and grew up mostly in New York City. He graduated as a biochemistry major from Hunter College in the spring of 2005 and is interested in computational biology, particularly protein structure prediction. He has worked with molecular modeling systems based on traditional mathematics (e.g. CHARMM) as an undergraduate. It became apparent that a major challenge in the field was making accurately representative models without the computational expense of fine detail. The NKS paradigm seems capable of great results in the area of modeling biological systems. Alex will begin his Ph.D. program in the fall of 2005. In his spare time, Alex also enjoys fencing, skin diving, fake rock climbing, walking to and fro, and adventures.

Project: An Exploration of Protein Folding Pathways

Protein folding is usually represented as a problem of choice: conformational space is computationally large, and methods of sampling and evaluating conformations must begin with a number of assumptions to reduce it. However, proteins fold in much less time than predicted by an exhaustive search at the speed of the physical system. Here, we postulate that the exploration of folding space is channeled by the sequence of moves one uses to explore it. Further, the rules of movement may render some conformations inaccessible, despite their plausibility by measures of constraint optimization. In summary, the rules of movement (also known as the move-set) may be important in reducing the space searched. In this experiment, we perform an exhaustive exploration of the folding pathway space of a simplified system to assess its general properties. Folding is represented by a multiway system of configurations of a string on a square lattice. Configurations are evaluated by the criterion of solvent entropy maximisation. The system is reviewed for the appearance of solvent entropy maximising conformations, and the growth of the network is examined. The second phase of this experiment (results not published) involves the exploration of the same space with a modified move-set. In this case, solvent entropy is used as a movement rule and not just an evaluation.

Favorite Four-Color, Nearest-Neighbor, Totalistic Rule

Rule chosen: 4524

The "all in one" rule 4524 of the four-color totalistic cellular automata. I chose it because it displays repetitive, nesting, and complex behaviour in a seemingly phase-separated manner. The outer border retains repetitive behaviour while the interior grows more complicated. It appears that repetitive patterns get turned into nested patterns, which give way to progressively more complex behaviour. However, these regions of behaviour are separated into "phases," whose borders grow at the maximum speed and maintain the separation.