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Current advances in computational modelling and simulation have led to the inclusion of computer scientists as partners in the process of engineering of new nanomaterials and nanodevices. This trend is now, more than ever, visible in the field of deoxyribonucleic acid (DNA)-based nanotechnology, as DNA's intrinsic principle of self-assembly has been proven to be highly algorithmic and programmable. As a raw material, DNA is a rather unremarkable fabric. However, as a way to achieve patterns, dynamic behavior, or nano-shape reconstruction, DNA has been proven to be one of the most functional nanomaterials. It would thus be of great potential to pair up DNA's highly functional assembly characteristics with the mechanic properties of other well-known bio-nanomaterials, such as graphene, cellulos, or fibroin. In the current study, we perform projections regarding the structural properties of a fibril mesh (or filter) for which assembly would be guided by the controlled aggregation of DNA scaffold subunits. The formation of such a 2D fibril mesh structure is ensured by the mechanistic assembly properties borrowed from the DNA assembly apparatus. For generating inexpensive pre-experimental assessments regarding the efficiency of various assembly strategies, we introduced in this study a computational model for the simulation of fibril mesh assembly dynamical systems. Our approach was based on providing solutions towards two main circumstances. First, we created a functional computational model that is restrictive enough to be able to numerically simulate the controlled aggregation of up to 1000s of elementary fibril elements yet rich enough to provide actionable insides on the structural characteristics for the generated assembly. Second, we used the provided numerical model in order to generate projections regarding effective ways of manipulating one of the the key structural properties of such generated filters, namely the average size of the openings (gaps) within these meshes, also known as the filter's aperture. This work is a continuation of Amarioarei et al., 2018, where a preliminary version of this research was discussed.

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We describe two new discrete symmetries of the inviscid Burgers (or Riemann–Hopf) equation ut+uux=0. We derived both of them using a local, formal approach of Hopf algebraic renormalization, a tool recently used in algorithmic computations. We prove that one of them is a Lie point transformation. Symmetries generate new exact solutions from the known solutions and provide useful frames of reference in the study of shock wave formation. © 2020 The Author(s)

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In a recent paper, using one of the algorithmic assembly formalisms of DNA nanotechnology, we proved that one tile can self-assemble length n structures and n x n squares, which are basic shapes in the study of DNA origami. This new result within a classic Tile Assembly Model (TAM) would not have been possible without the following programming topics: how can we simulate one-dimensional staged self-assembly using the signal-passing TAM, and how can we program staged self-assembly using the available software? We provide probabilistic approaches for investigating the assembly of tile-based one-dimensional structures. We obtain a probabilistic proof of Han's hook length formula in Enumerative Combinatorics. We identify algebraic and combinatorial structures underlying these algorithmic and information theory results.

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We give examples of 2-parameter bounded quadratic dynamical systems with 3 finite singularities, which have at least 4 limit cycles around a singularity (in the (4,0)-configuration)-the first example of this type - and in a (3,1)-configuration. The paper mentions the Nanobiotechnological origins of these experimentally discovered systems with interesting properties.

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The Tile Assembly Model, and its many variants, is one of the most fundamental algorithmic assembly formalism within DNA nanotechnology. Most of the research in this field is focused on the complexity of assembling different shapes and patterns. In many cases, the assembly process is intrinsically deterministic and the final product is unique, while the assembly process might evolve through several possible assembly strategies. In this study we consider the controlled assembly of one dimensional tile structures according to predefined assembly graphs. We provide algorithmic approaches for developing such controlled assembly protocols, using the signal-passing Tile Assembly Model, as well as probabilistic approaches for investigating the assembly of such tile-based one-dimensional structures. As a byproduct, we build a generalized TAS (tile assembly system) which generate specific non-local non-associative algebraic computations and we assamble n x n squares using only one tile, which is a better efficiency compared to the staged assembly model. (C) 2019 The Authors. Published by Elsevier B.V.

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The TAM (Model Tile Assembly Model) is a mathematical paradigm for modeling DNA self-assembling according to various given shapes, using DNA-tiles (rectangular shape) with sticky ends on each of the four edges that bound together on various shapes desired by the researcher. Although there are various models in the literature, the focus in this manuscript is on a rule based model, specifically the authors present an overview of the one-dimensional hierarchical self-assembly model of DNA tiles. The authors also present the evolution of number of tiles in partial assemblies, the average assembly size and of the number of partial assemblies of sizes 2 through 10 over the total running time. All simulations were run using the NFSim simulator on a preset period of time.