Using three-dimensional microfluidic networks for solving computationally hard problems

This paper describes the design of a parallel algorithm that uses moving fluids in a three-dimensional microfluidic system to solve a nondeterministically polynomial complete problem (the maximal clique problem) in polynomial time. This algorithm relies on (i) parallel fabrication of the microfluidic system, (ii) parallel searching of all potential solutions by using fluid flow, and (iii) parallel optical readout of all solutions. This algorithm was implemented to solve the maximal clique problem for a simple graph with six vertices. The successful implementation of this algorithm to compute solutions for small-size graphs with fluids in microchannels is not useful, per se, but does suggest broader application for microfluidics in computation and control.

Gene recognition via spliced sequence alignment.

Gene recognition is one of the most important problems in computational molecular biology. Previous attempts to solve this problem were based on statistics, and applications of combinatorial methods for gene recognition were almost unexplored. Recent advances in large-scale cDNA sequencing open a way toward a new approach to gene recognition that uses previously sequenced genes as a clue for recognition of newly sequenced genes. This paper describes a spliced alignment algorithm and software tool that explores all possible exon assemblies in polynomial time and finds the multiexon structure with the best fit to a related protein. Unlike other existing methods, the algorithm successfully recognizes genes even in the case of short exons or exons with unusual codon usage; we also report correct assemblies for genes with more than 10 exons. On a test sample of human genes with known mammalian relatives, the average correlation between the predicted and actual proteins was 99%. The algorithm correctly reconstructed 87% of genes and the rare discrepancies between the predicted and real exon-intron structures were caused either by short (less than 5 amino acids) initial/terminal exons or by alternative splicing. Moreover, the algorithm predicts human genes reasonably well when the homologous protein is nonvertebrate or even prokaryotic. The surprisingly good performance of the method was confirmed by extensive simulations: in particular, with target proteins at 160 accepted point mutations (PAM) (25% similarity), the correlation between the predicted and actual genes was still as high as 95%.

Transforming neural computations and representing time

Motifs of neural circuitry seem surprisingly conserved over different areas of neocortex or of paleocortex, while performing quite different sensory processing tasks. This apparent paradox may be resolved by the fact that seemingly different problems in sensory information processing are related by transformations (changes of variables) that convert one problem into another. The same basic algorithm that is appropriate to the recognition of a known odor quality, independent of the strength of the odor, can be used to recognize a vocalization (e.g., a spoken syllable), independent of whether it is spoken quickly or slowly. To convert one problem into the other, a new representation of time sequences is needed. The time that has elapsed since a recent event must be represented in neural activity. The electrophysiological hallmarks of cells that are involved in generating such a representation of time are discussed. The anatomical relationships between olfactory and auditory pathways suggest relevant experiments. The neurophysiological mechanism for the psychophysical logarithmic encoding of time duration would be of direct use for interconverting olfactory and auditory processing problems. Such reuse of old algorithms in new settings and representations is related to the way that evolution develops new biochemistry.

An O(N log N) algorithm for shape modeling.

We present a shape-recovery technique in two dimensions and three dimensions with specific applications in modeling anatomical shapes from medical images. This algorithm models extremely corrugated structures like the brain, is topologically adaptable, and runs in O(N log N) time, where N is the total number of points in the domain. Our technique is based on a level set shape-recovery scheme recently introduced by the authors and the fast marching method for computing solutions to static Hamilton-Jacobi equations.