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We consider the minimum norm interpolation problem in the [Formula: see text] space, aiming at constructing a sparse interpolation solution. The original problem is reformulated in the pre-dual space, thereby inducing a norm in a related finite-dimensional Euclidean space. The dual problem is then transformed into a linear programming problem, which can be solved by existing methods. With that done, the original interpolation problem is reduced by solving an elementary finite-dimensional linear algebra equation. A specific example is presented to illustrate the proposed method, in which a sparse solution in the [Formula: see text] space is compared to the dense solution in the [Formula: see text] space. This example shows that a solution of the minimum norm interpolation problem in the [Formula: see text] space is indeed sparse, while that of the minimum norm interpolation problem in the [Formula: see text] space is not. 

Nowadays an emerging class of applications are based oncollaboration over a shared database among different entities. However, the existing solutions on shared database may require trust on others, have high hardware demand that is unaffordable for individual users, or have relatively low performance. In other words, there is a trilemma among security, compatibility and efficiency. In this paper, we present FalconDB, which enables different parties with limited hardware resources to efficiently and securely collaborate on a database. FalconDB adopts database servers with verification interfaces accessible to clients and stores the digests for query/update authentications on a blockchain. Using blockchain as a consensus platform and a distributed ledger, FalconDB is able to work without any trust on each other. Meanwhile, FalconDB requires only minimal storage cost on each client, and provides anywhere-available, real-time and concurrent access to the database. As a result, FalconDB over-comes the disadvantages of previous solutions, and enables individual users to participate in the collaboration with high efficiency, low storage cost and blockchain-level security guarantees. 

Understanding the complex growth and metabolic dynamics in microorganisms requires advanced kinetic models containing both metabolic reactions and enzymatic regulation to predict phenotypic behaviors under different conditions and perturbations. Most current kinetic models lack gene expression dynamics and are separately calibrated to distinct media, which consequently makes them unable to account for genetic perturbations or multiple substrates. This challenge limits our ability to gain a comprehensive understanding of microbial processes towards advanced metabolic optimizations that are desired for many biotechnology applications. Here, we present an integrated computational and experimental approach for the development and optimization of mechanistic kinetic models for microbial growth and metabolic and enzymatic dynamics. Our approach integrates growth dynamics, gene expression, protein secretion, and gene‐deletion phenotypes. We applied this methodology to build a dynamic model of the growth kinetics in batch culture of the bacteriumCellvibrio japonicusgrown using either cellobiose or glucose media. The model parameters were inferred from an experimental data set using an evolutionary computation method. The resulting model was able to explain the growth dynamics ofC. japonicususing either cellobiose or glucose media and was also able to accurately predict the metabolite concentrations in the wild‐type strain as well as in β‐glucosidase gene deletion mutant strains. We validated the model by correctly predicting the non‐diauxic growth and metabolite consumptions of the wild‐type strain in a mixed medium containing both cellobiose and glucose, made further predictions of mutant strains growth phenotypes when using cellobiose and glucose media, and demonstrated the utility of the model for designing industrially‐useful strains. Importantly, the model is able to explain the role of the different β‐glucosidases and their behavior under genetic perturbations. This integrated approach can be extended to other metabolic pathways to produce mechanistic models for the comprehensive understanding of enzymatic functions in multiple substrates.