Computing in the fractal cloud: modular generic solvers for SAT and Q-SAT variants

Abstract geometrical computation can solve hard combinatorial problems efficiently: we showed previously how Q-SAT can be solved in bounded space and time using instance-specific signal machines and fractal parallelization. In this article, we propose an approach for constructing a particular generic machine for the same task. This machine deploies the Map/Reduce paradigm over a fractal structure. Moreover our approach is modular: the machine is constructed by combining modules. In this manner, we can easily create generic machines for solving satifiability variants, such as SAT, #SAT, MAX-SAT

A Simple n-Dimensional Intrinsically Universal Quantum Cellular Automaton

We describe a simple n-dimensional quantum cellular automaton (QCA) capable of simulating all others, in that the initial configuration and the forward evolution of any n-dimensional QCA can be encoded within the initial configuration of the intrinsically universal QCA. Several steps of the intrinsically universal QCA then correspond to one step of the simulated QCA. The simulation preserves the topology in the sense that each cell of the simulated QCA is encoded as a group of adjacent cells in the universal QCA.Comment: 13 pages, 7 figures. In Proceedings of the 4th International Conference on Language and Automata Theory and Applications (LATA 2010), Lecture Notes in Computer Science (LNCS). Journal version: arXiv:0907.382

Computing Aggregate Properties of Preimages for 2D Cellular Automata

Computing properties of the set of precursors of a given configuration is a common problem underlying many important questions about cellular automata. Unfortunately, such computations quickly become intractable in dimension greater than one. This paper presents an algorithm --- incremental aggregation --- that can compute aggregate properties of the set of precursors exponentially faster than na{\"i}ve approaches. The incremental aggregation algorithm is demonstrated on two problems from the two-dimensional binary Game of Life cellular automaton: precursor count distributions and higher-order mean field theory coefficients. In both cases, incremental aggregation allows us to obtain new results that were previously beyond reach

The genomic landscape of balanced cytogenetic abnormalities associated with human congenital anomalies

Despite the clinical significance of balanced chromosomal abnormalities (BCAs), their characterization has largely been restricted to cytogenetic resolution. We explored the landscape of BCAs at nucleotide resolution in 273 subjects with a spectrum of congenital anomalies. Whole-genome sequencing revised 93% of karyotypes and demonstrated complexity that was cryptic to karyotyping in 21% of BCAs, highlighting the limitations of conventional cytogenetic approaches. At least 33.9% of BCAs resulted in gene disruption that likely contributed to the developmental phenotype, 5.2% were associated with pathogenic genomic imbalances, and 7.3% disrupted topologically associated domains (TADs) encompassing known syndromic loci. Remarkably, BCA breakpoints in eight subjects altered a single TAD encompassing MEF2C, a known driver of 5q14.3 microdeletion syndrome, resulting in decreased MEF2C expression. We propose that sequence-level resolution dramatically improves prediction of clinical outcomes for balanced rearrangements and provides insight into new pathogenic mechanisms, such as altered regulation due to changes in chromosome topology