Structure, stability and elasticity of DNA nanotube

DNA nanotubes are tubular structures composed of DNA crossover molecules. We present a bottom up approach for construction and characterization of these structures. Various possible topologies of nanotubes are constructed such as 6-helix, 8-helix and tri-tubes with different sequences and lengths. We have used fully atomistic molecular dynamics simulations to study the structure, stability and elasticity of these structures. Several nanosecond long MD simulations give the microscopic details about DNA nanotubes. Based on the structural analysis of simulation data, we show that 6-helix nanotubes are stable and maintain their tubular structure; while 8-helix nanotubes are flattened to stabilize themselves. We also comment on the sequence dependence and effect of overhangs. These structures are approximately four times more rigid having stretch modulus of ~4000 pN compared to the stretch modulus of 1000 pN of DNA double helix molecule of same length and sequence. The stretch moduli of these nanotubes are also three times larger than those of PX/JX crossover DNA molecules which have stretch modulus in the range of 1500-2000 pN. The calculated persistence length is in the range of few microns which is close to the reported experimental results on certain class of the DNA nanotubes.Comment: Published in Physical Chemistry Chemical Physic

Fixing the NTK: From Neural Network Linearizations to Exact Convex Programs

Recently, theoretical analyses of deep neural networks have broadly focused on two directions: 1) Providing insight into neural network training by SGD in the limit of infinite hidden-layer width and infinitesimally small learning rate (also known as gradient flow) via the Neural Tangent Kernel (NTK), and 2) Globally optimizing the regularized training objective via cone-constrained convex reformulations of ReLU networks. The latter research direction also yielded an alternative formulation of the ReLU network, called a gated ReLU network, that is globally optimizable via efficient unconstrained convex programs. In this work, we interpret the convex program for this gated ReLU network as a Multiple Kernel Learning (MKL) model with a weighted data masking feature map and establish a connection to the NTK. Specifically, we show that for a particular choice of mask weights that do not depend on the learning targets, this kernel is equivalent to the NTK of the gated ReLU network on the training data. A consequence of this lack of dependence on the targets is that the NTK cannot perform better than the optimal MKL kernel on the training set. By using iterative reweighting, we improve the weights induced by the NTK to obtain the optimal MKL kernel which is equivalent to the solution of the exact convex reformulation of the gated ReLU network. We also provide several numerical simulations corroborating our theory. Additionally, we provide an analysis of the prediction error of the resulting optimal kernel via consistency results for the group lasso.Comment: Accepted to Neurips 202

propnet: A Knowledge Graph for Materials Science

Discovering the ideal material for a new application involves determining its numerous properties, such as electronic, mechanical, or thermodynamic, to match those of its desired application. The rise of high-throughput computation has meant that large databases of material properties are now accessible to scientists. However, these databases contain far more information than might appear at first glance, since many relationships exist in the materials science literature to derive, or at least approximate, additional properties. propnet is a new computational framework designed to help scientists to automatically calculate additional information from their datasets. It does this by constructing a network graph of relationships between different materials properties and traversing this graph. Initially, propnet contains a catalog of over 100 property relationships but the hope is for this to expand significantly in the future, and contributions from the community are welcomed

Rapid Generation of Optimal Generalized Monkhorst-Pack Grids

Computational modeling of the properties of crystalline materials has become an increasingly important aspect of materials research, consuming hundreds of millions of CPU-hours at scientific computing centres around the world each year, if not more. A routine operation in such calculations is the evaluation of integrals over the Brillouin zone. We have previously demonstrated that performing such integrals using generalized Monkhorst-Pack k-point grids can roughly double the speed of these calculations relative to the widely-used traditional Monkhorst-Pack grids, and such grids can be rapidly generated by querying a free, internet-accessible database of pre-generated grids. To facilitate the widespread use of generalized k-point grids, we present new algorithms that allow rapid generation of optimized generalized Monkhorst-Pack grids on the fly, an open-source library to facilitate their integration into external software packages, and an open-source implementation of the database tool that can be used offline. We also present benchmarks of the speed of our algorithms on structures randomly selected from the Inorganic Crystal Structure Database. For grids that correspond to a real-space supercell with at least 50 angstroms between lattice points, which is sufficient to converge density functional theory calculations within 1 meV/atom for nearly all materials, our algorithm finds optimized grids in an average of 0.19 seconds on a single processing core. For 100 angstroms between real-space lattice points, our algorithm finds optimal grids in less than 5 seconds on average

optimade-python-tools: a Python library for serving and consuming materials data via OPTIMADE APIs

In recent decades, improvements in algorithms, hardware, and theory have enabled crystalline materials to be studied computationally at the atomistic level with great accuracy and speed. To enable dissemination, reproducibility, and reuse, many digital crystal structure databases have been created and curated, ready for comparison with existing infrastructure that stores structural characterizations (e.g., diffraction) of real crystals. Each database will typically have a bespoke, stateless, web-based Application Programming Interface (API); users can submit a query via specially-crafted URLs. Such esoteric and specialized APIs incur maintenance and usability costs upon both the data providers and consumers, who may not be software specialists. The OPTIMADE API specification (Andersen et al., 2020, 2021), released in July 2020, aimed to reduce these costs by designing a common API for use across a consortium of collaborating materials databases and beyond. Whilst based on the robust JSON:API standard (Katz et al., 2015), the OPTIMADE API specification presents several domain-specific features and re- quirements that can be tricky to implement for non-specialist teams. The repository presented here, optimade-python-tools, provides a modular reference server implementation and a set of associated tools to accelerate the development process for data providers, toolmakers and end-user