The probability distribution describing the state of a Stochastic Reaction Network evolves according to the Chemical Master Equation (CME). It is common to estimated its solution using Monte Carlo methods such as the Stochastic Simulation Algorithm (SSA). In many cases these simulations can take an impractical amount of computational time. Therefore many methods have been developed that approximate the Stochastic Process underlying the Chemical Master Equation. Prominent strategies are Hybrid Models that regard the firing of some reaction channels as being continuous and applying the quasi-stationary assumption to approximate the dynamics of fast subnetworks. However as the dynamics of a Stochastic Reaction Network changes with time these approximations might have to be adapted during the simulation. We develop a method that approximates the solution of a CME by automatically partitioning the reaction dynamics into discrete/continuous components and applying the quasi-stationary assumption on identifiable fast subnetworks.Our method does not require user intervention and it adapts to exploit the changing timescale separation between reactions and/or changing magnitudes of copy numbers of constituent species. We demonstrate the efficiency of the proposed method by considering examples from Systems Biology and showing that very good approximations to the exact probability distributions can be achieved in significantly less computational time.Keywords: adaptive hybrid models, stochastic reaction networks, quasi-stationary, adaptive piecewise deterministic markov processes 1

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We introduce a new method that efficiently computes a set of viewpoints and trajectories for high-quality 3D reconstructions in outdoor environments. Our goal is to automatically explore an unknown area and obtain a complete 3D scan of a region of interest (e.g., a large building). Images from a commodity RGB camera, mounted on an autonomously navigated quadcopter, are fed into a multi-view stereo reconstruction pipeline that produces high-quality results but is computationally expensive. In this setting, the scanning result is constrained by the restricted flight time of quadcopters. To this end, we introduce a novel optimization strategy that respects these constraints by maximizing the information gain from sparsely sampled viewpoints while limiting the total travel distance of the quadcopter. At the core of our method lies a hierarchical volumetric representation that allows the algorithm to distinguish between unknown, free, and occupied space. Furthermore, our information gain-based formulation leverages this representation to handle occlusions in an efficient manner. In addition to the surface geometry, we utilize free-space information to avoid obstacles and determine collision-free flight paths. Our tool can be used to specify the region of interest and to plan trajectories. We demonstrate our method by obtaining a number of compelling 3D reconstructions, and we provide a thorough quantitative evaluation showing improvement over previous state-of-the-art and regular patterns.

Intracellular oscillators entrain to periodic signals by adjusting their phase and frequency. However, the low copy numbers of key molecular players make the dynamics of these oscillators intrinsically noisy, disrupting their oscillatory activity and entrainment response. Here, we use a combination of computational methods and experimental observations to reveal a functional distinction between the entrainment of individual oscillators (e.g., inside cells) and the entrainment of populations of oscillators (e.g., across tissues). We demonstrate that, in the presence of intracellular noise, weak periodic cues robustly entrain the population averaged response, even while individual oscillators remain un-entrained. We mathematically elucidate this phenomenon, which we call stochastic population entrainment, and show that it naturally arises due to interactions between intrinsic noise and nonlinear oscillatory dynamics. Our findings suggest that robust tissue-level oscillations can be achieved by a simple mechanism that utilizes intrinsic biochemical noise, even in the absence of biochemical couplings between cells.