A new class of highly efficient exact stochastic simulation algorithms for chemical reaction networks

We introduce an alternative formulation of the exact stochastic simulation algorithm (SSA) for sampling trajectories of the chemical master equation for a well-stirred system of coupled chemical reactions. Our formulation is based on factored-out, partial reaction propensities. This novel exact SSA, called the partial propensity direct method (PDM), is highly efficient and has a computational cost that scales at most linearly with the number of chemical species, irrespective of the degree of coupling of the reaction network. In addition, we propose a sorting variant, SPDM, which is especially efficient for multiscale reaction networks.Comment: 23 pages, 3 figures, 4 tables; accepted by J. Chem. Phy

Multicomponent low molecular weight gelators

Low molecular weight gelators (LMWG) self-assemble in solution into one-dimensional objects such as fibres or tapes. The entanglement of these fibres or tapes results in the formation of a network and a gel. In general, LMWG are investigated as single component systems. However, there are significant potential opportunities from mixed LMWG systems, which are rarely investigated. Here, we discuss the potential of multicomponent systems, and critically discuss the challenges

A Consistent Histogram Estimator for Exchangeable Graph Models

Exchangeable graph models (ExGM) subsume a number of popular network models. The mathematical object that characterizes an ExGM is termed a graphon. Finding scalable estimators of graphons, provably consistent, remains an open issue. In this paper, we propose a histogram estimator of a graphon that is provably consistent and numerically efficient. The proposed estimator is based on a sorting-and-smoothing (SAS) algorithm, which first sorts the empirical degree of a graph, then smooths the sorted graph using total variation minimization. The consistency of the SAS algorithm is proved by leveraging sparsity concepts from compressed sensing.Comment: 28 pages, 5 figure

Optimizing a Certified Proof Checker for a Large-Scale Computer-Generated Proof

In recent work, we formalized the theory of optimal-size sorting networks with the goal of extracting a verified checker for the large-scale computer-generated proof that 25 comparisons are optimal when sorting 9 inputs, which required more than a decade of CPU time and produced 27 GB of proof witnesses. The checker uses an untrusted oracle based on these witnesses and is able to verify the smaller case of 8 inputs within a couple of days, but it did not scale to the full proof for 9 inputs. In this paper, we describe several non-trivial optimizations of the algorithm in the checker, obtained by appropriately changing the formalization and capitalizing on the symbiosis with an adequate implementation of the oracle. We provide experimental evidence of orders of magnitude improvements to both runtime and memory footprint for 8 inputs, and actually manage to check the full proof for 9 inputs.Comment: IMADA-preprint-c

Self-Sorting Microscale Compartmentalized Block Copolypeptide Hydrogels

Multicomponent interpenetrating network hydrogels possessing enhanced mechanical stiffness compared to their individual components were prepared via physical mixing of diblock copolypeptides that assemble by either hydrophobic association or polyion complexation in aqueous media. Optical microscopy analysis of fluorescent-probe-labeled multicomponent hydrogels revealed that the diblock copolypeptide components rapidly and spontaneously self-sort to form distinct hydrogel networks that interpenetrate at micron length scales. These materials represent a class of microscale compartmentalized hydrogels composed of degradable, cell-compatible components, which possess rapid self-healing properties and independently tunable domains for downstream applications in biology and additive manufacturing