Bonnie Kirkpatrick

Reachability Bounds for Chemical Reaction Networks and Strand Displacement Systems

Chemical reaction networks (CRNs) and DNA strand displacement systems (DSDs) are widely-studied and useful models of molecular programming. However, in order for some DSDs in the literature to behave in an expected manner, the initial number of copies of some reagents is required to be fixed. In this paper we show that, when multiple copies of all initial molecules are present, general types of CRNs and DSDs fail to work correctly if the length of the shortest sequence of reactions needed to produce any given molecule exceeds a threshold that grows polynomially with attributes of the system.

Divide-and-Conquer With Sequential Monte Carlo

ABSTRACT We propose a novel class of Sequential Monte Carlo (SMC) algorithms, appropriate for inference in probabilistic graphical models. This class of algorithms adopts a divide-and-conquer approach based upon an auxiliary tree-structured decomposition of the model of interest, turning the overall inferential task into a collection of recursively solved subproblems. The proposed method is applicable to a broad class of probabilistic graphical models, including models with loops. Unlike a standard SMC sampler, the proposed divide-and-conquer SMC employs multiple independent populations of weighted particles, which are resampled, merged, and propagated as the method progresses. We illustrate empirically that this approach can outperform standard methods in terms of the accuracy of the posterior expectation and marginal likelihood approximations. Divide-and-conquer SMC also opens up novel parallel implementation options and the possibility of concentrating the computational effort on the most challenging subproblems. We demonstrate its performance on a Markov random field and on a hierarchical logistic regression problem. Supplementary materials including proofs and additional numerical results are available online.

Reachability bounds for chemical reaction networks and strand displacement systems

Chemical reaction networks (CRNs) and DNA strand displacement systems (DSDs) are widely-studied and useful models of molecular programming. However, in order for some DSDs in the literature to behave in an expected manner, the initial number of copies of some reagents is required to be fixed. In this paper we show that, when multiple copies of all initial molecules are present, general types of CRNs and DSDs fail to work correctly if the length of the shortest sequence of reactions needed to produce any given molecule exceeds a threshold that grows polynomially with attributes of the system.

Non-identifiable pedigrees and a bayesian solution

Some methods aim to correct or test for relationships or to reconstruct the pedigree, or family tree. We show that these methods cannot resolve ties for correct relationships due to identifiability of the pedigree likelihood which is the probability of inheriting the data under the pedigree model. This means that no likelihood-based method can produce a correct pedigree inference with high probability. This lack of reliability is critical both for health and forensics applications. Pedigree inference methods use a structured machine learning approach where the objective is to find the pedigree graph that maximizes the likelihood. Known pedigrees are useful for both association and linkage analysis which aim to find the regions of the genome that are associated with the presence and absence of a particular disease. This means that errors in pedigree prediction have dramatic effects on downstream analysis. In this paper we present the first discussion of multiple typed individuals in non-isomorphic pedigrees,

A new model for approximating RNA folding trajectories and population kinetics

\mathcal{P}

Design of nucleic acid strands with long low-barrier folding pathways

and

Haplotype Inference for Pedigrees with Few Recombinations

\mathcal{Q}

Correcting for Cryptic Relatedness in Genome-Wide Association Studies

, where the likelihoods are non-identifiable,

Bayesian Pedigree Analysis using Measure Factorization

Pr[G~|~\mathcal{P},\theta] = Pr[G~|~\mathcal{Q},\theta]

Fast Computation of the Kinship Coefficients.

, for all input data G and all recombination rate parameters θ . While there were previously known non-identifiable pairs, we give an example having data for multiple individuals. Additionally, deeper understanding of the general discrete structures driving these non-identifiability examples has been provided, as well as results to guide algorithms that wish to examine only identifiable pedigrees. This paper introduces a general criteria for establishing whether a pair of pedigrees is non-identifiable and two easy-to-compute criteria guaranteeing identifiability. Finally, we suggest a method for dealing with non-identifiable likelihoods: use Bayes rule to obtain the posterior from the likelihood and prior. We propose a prior guaranteeing that the posterior distinguishes all pairs of pedigrees.