Leaderless deterministic chemical reaction networks

This paper answers an open question of Chen, Doty, and Soloveichik [1], who showed that a function f:N^k --> N^l is deterministically computable by a stochastic chemical reaction network (CRN) if and only if the graph of f is a semilinear subset of N^{k+l}. That construction crucially used "leaders": the ability to start in an initial configuration with constant but non-zero counts of species other than the k species X_1,...,X_k representing the input to the function f. The authors asked whether deterministic CRNs without a leader retain the same power. We answer this question affirmatively, showing that every semilinear function is deterministically computable by a CRN whose initial configuration contains only the input species X_1,...,X_k, and zero counts of every other species. We show that this CRN completes in expected time O(n), where n is the total number of input molecules. This time bound is slower than the O(log^5 n) achieved in [1], but faster than the O(n log n) achieved by the direct construction of [1] (Theorem 4.1 in the latest online version of [1]), since the fast construction of that paper (Theorem 4.4) relied heavily on the use of a fast, error-prone CRN that computes arbitrary computable functions, and which crucially uses a leader.Comment: arXiv admin note: substantial text overlap with arXiv:1204.417

High harmonic generation and periodic level crossings

Published versio

SWiM: Secure Wildcard Pattern Matching From OT Extension

Suppose a server holds a long text string and a receiver holds a short pattern string. Secure pattern matching allows the receiver to learn the locations in the long text where the pattern appears, while leaking nothing else to either party besides the length of their inputs. In this work we consider secure wildcard pattern matching WPM, where the receiver\u27s pattern is allowed to contain wildcards that match to any character. We present SWiM, a simple and fast protocol for WPM that is heavily based on oblivious transfer (OT) extension. As such, the protocol requires only a small constant number of public-key operations and otherwise uses only very fast symmetric-key primitives. SWiM is secure against semi-honest adversaries. We implemented a prototype of our protocol to demonstrate its practicality. We can perform WPM on a DNA text (4-character alphabet) of length $10^5$ and pattern of length $10^3$ in just over 2 seconds, which is over two orders of magnitude faster than the state-of-the-art scheme of Baron et al. (SCN 2012)

Determination of genetic structure of germplasm collections: are traditional hierarchical clustering methods appropriate for molecular marker data?

Despite the availability of newer approaches, traditional hierarchical clustering remains very popular in genetic diversity studies in plants. However, little is known about its suitability for molecular marker data. We studied the performance of traditional hierarchical clustering techniques using real and simulated molecular marker data. Our study also compared the performance of traditional hierarchical clustering with model-based clustering (STRUCTURE). We showed that the cophenetic correlation coefficient is directly related to subgroup differentiation and can thus be used as an indicator of the presence of genetically distinct subgroups in germplasm collections. Whereas UPGMA performed well in preserving distances between accessions, Ward excelled in recovering groups. Our results also showed a close similarity between clusters obtained by Ward and by STRUCTURE. Traditional cluster analysis can provide an easy and effective way of determining structure in germplasm collections using molecular marker data, and, the output can be used for sampling core collections or for association studies