We present a novel approach, the Local Edge Machine, for the inference of regulatory interactions directly from time-series gene expression data. We demonstrate its performance, robustness, and scalability on in silico datasets with varying behaviors, sizes, and degrees of complexity. Moreover, we demonstrate its ability to incorporate biological prior information and make informative predictions on a well-characterized in vivo system using data from budding yeast that have been synchronized in the cell cycle. Finally, we use an atlas of transcription data in a mammalian circadian system to illustrate how the method can be used for discovery in the context of large complex networks.Electronic supplementary materialThe online version of this article (doi:10.1186/s13059-016-1076-z) contains supplementary material, which is available to authorized users.

The topic of statistical inference for dynamical systems has been studied extensively across several fields. In this survey we focus on the problem of parameter estimation for nonlinear dynamical systems. Our objective is to place results across distinct disciplines in a common setting and highlight opportunities for further research. arXiv:1204.6265v3 [math.ST]

Let $X$ be an irreducible shift of finite type (SFT) of positive entropy, and let $B_n(X)$ be its set of words of length $n$. Define a random subset $\omega$ of $B_n(X)$ by independently choosing each word from $B_n(X)$ with some probability $\alpha$. Let $X_{\omega}$ be the (random) SFT built from the set $\omega$. For each $0\leq \alpha \leq1$ and $n$ tending to infinity, we compute the limit of the likelihood that $X_{\omega}$ is empty, as well as the limiting distribution of entropy for $X_{\omega}$. For $\alpha$ near 1 and $n$ tending to infinity, we show that the likelihood that $X_{\omega}$ contains a unique irreducible component of positive entropy converges exponentially to 1. These results are obtained by studying certain sequences of random directed graphs. This version of "random SFT" differs significantly from a previous notion by the same name, which has appeared in the context of random dynamical systems and bundled dynamical systems.Comment: Published in at http://dx.doi.org/10.1214/10-AOP636 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

No abstract

We consider the asymptotic consistency of maximum likelihood parameter estimation for dynamical systems observed with noise. Under suitable conditions on the dynamical systems and the observations, we show that maximum likelihood parameter estimation is consistent. Our proof involves ideas from both information theory and dynamical systems. Furthermore, we show how some well-studied properties of dynamical systems imply the general statistical properties related to maximum likelihood estimation. Finally, we exhibit classical families of dynamical systems for which maximum likelihood estimation is consistent. Examples include shifts of finite type with Gibbs measures and Axiom A attractors with SRB measures.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1259 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

The effectiveness of vaccinating males against the human papillomavirus (HPV) remains a controversial subject. Many existing studies conclude that increasing female coverage is more effective than diverting resources into male vaccination. Recently, several empirical studies on HPV immunization have been published, providing evidence of the fact that marginal vaccination costs increase with coverage. In this study, we use a stochastic agent-based modeling framework to revisit the male vaccination debate in light of these new findings. Within this framework, we assess the impact of coverage-dependent marginal costs of vaccine distribution on optimal immunization strategies against HPV. Focusing on the two scenarios of ongoing and new vaccination programs, we analyze different resource allocation policies and their effects on overall disease burden. Our results suggest that if the costs associated with vaccinating males are relatively close to those associated with vaccinating females, then coverage-dependent, increasing marginal costs may favor vaccination strategies that entail immunization of both genders. In particular, this study emphasizes the necessity for further empirical research on the nature of coverage-dependent vaccination costs.

We define the finite extension property for d-dimensional subshifts, which generalizes the topological strong spatial mixing condition defined in [3], and we prove that this property is invariant under topological conjugacy. Moreover, we prove that for every d, every d-dimensional block gluing subshift factors onto every d-dimensional SFT with strictly lower entropy, a fixed point, and the finite extension property. This result extends a theorem from [2], which requires that the factor contain a safe symbol.

In this work we consider an ensemble of random Z dshifts of finite type (Z d -SFTs) and prove several results concerning the behavior of typical systems with respect to emptiness, entropy, and periodic points. These results generalize statements made in [26] regarding the case d = 1.Let A be a finite set, and let d ≥ 1. For n in N and α in [0, 1], define a random subset ω of A [1,n] d by independently including each pattern in A [1,n] d with probability α. Let X ω be the (random) Z d -SFT built from the set ω. For each α ∈ [0, 1] and n tending to infinity, we compute the limit of the probability that X ω is empty, as well as the limiting distribution of entropy of X ω . Furthermore, we show that the probability of obtaining a nonempty system without periodic points tends to zero.For d > 1, the class of Z d -SFTs is known to contain strikingly different behavior than is possible within the class of Z-SFTs. Nonetheless, the results of this work suggest a new heuristic: typical Z d -SFTs have similar properties to their Z-SFT counterparts.