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**Published in:** LIPIcs, Volume 314, 30th International Conference on DNA Computing and Molecular Programming (DNA 30) (2024)

Life is chemical intelligence. What is the source of intelligent behavior in molecular systems? Here we illustrate how, in contrast to the common belief that energy use in non-equilibrium reactions is essential, the detailed balance equilibrium properties of multicomponent liquid interactions are sufficient for sophisticated information processing. Our approach derives from the classical Boltzmann machine model for probabilistic neural networks, inheriting key principles such as representing probability distributions via quadratic energy functions, clamping input variables to infer conditional probability distributions, accommodating omnidirectional computation, and learning energy parameters via a wake phase / sleep phase algorithm that performs gradient descent on the relative entropy with respect to the target distribution. While the cubic lattice model of multicomponent liquids is standard, the behaviors exhibited by the trained molecules capture both previously-observed phenomena such as core-shell condensate architectures as well as novel phenomena such as an analog of Hopfield associative memories that perform recall by contact with a patterned surface. Our final example demonstrates equilibrium classification of MNIST digits. Experimental implementation using DNA nanostar liquids is conceptually straightforward.

Cameron Chalk, Salvador Buse, Krishna Shrinivas, Arvind Murugan, and Erik Winfree. Learning and Inference in a Lattice Model of Multicomponent Condensates. In 30th International Conference on DNA Computing and Molecular Programming (DNA 30). Leibniz International Proceedings in Informatics (LIPIcs), Volume 314, pp. 5:1-5:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chalk_et_al:LIPIcs.DNA.30.5, author = {Chalk, Cameron and Buse, Salvador and Shrinivas, Krishna and Murugan, Arvind and Winfree, Erik}, title = {{Learning and Inference in a Lattice Model of Multicomponent Condensates}}, booktitle = {30th International Conference on DNA Computing and Molecular Programming (DNA 30)}, pages = {5:1--5:24}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-344-7}, ISSN = {1868-8969}, year = {2024}, volume = {314}, editor = {Seki, Shinnosuke and Stewart, Jaimie Marie}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.30.5}, URN = {urn:nbn:de:0030-drops-209330}, doi = {10.4230/LIPIcs.DNA.30.5}, annote = {Keywords: multicomponent liquid, Boltzmann machine, phase separation} }

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**Published in:** LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018)

Inspired by nature and motivated by a lack of top-down tools for precise nanoscale manufacture, self-assembly is a bottom-up process where simple, unorganized components autonomously combine to form larger more complex structures. Such systems hide rich algorithmic properties - notably, Turing universality - and a self-assembly system can be seen as both the object to be manufactured as well as the machine controlling the manufacturing process. Thus, a benchmark problem in self-assembly is the unique assembly of shapes: to design a set of simple agents which, based on aggregation rules and random movement, self-assemble into a particular shape and nothing else. We use a popular model of self-assembly, the 2-handed or hierarchical tile assembly model, and allow the existence of repulsive forces, which is a well-studied variant. The technique utilizes a finely-tuned temperature (the minimum required affinity required for aggregation of separate complexes).
We show that calibrating the temperature and the strength of the aggregation between the tiles, one can encode the shape to be assembled without increasing the number of distinct tile types. Precisely, we show one tile set for which the following holds: for any finite connected shape S, there exists a setting of binding strengths between tiles and a temperature under which the system uniquely assembles S at some scale factor. Our tile system only uses one repulsive glue type and the system is growth-only (it produces no unstable assemblies). The best previous unique shape assembly results in tile assembly models use O(K(S)/(log K(S))) distinct tile types, where K(S) is the Kolmogorov (descriptional) complexity of the shape S.

Cameron Chalk, Austin Luchsinger, Robert Schweller, and Tim Wylie. Self-Assembly of Any Shape with Constant Tile Types using High Temperature. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 14:1-14:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{chalk_et_al:LIPIcs.ESA.2018.14, author = {Chalk, Cameron and Luchsinger, Austin and Schweller, Robert and Wylie, Tim}, title = {{Self-Assembly of Any Shape with Constant Tile Types using High Temperature}}, booktitle = {26th Annual European Symposium on Algorithms (ESA 2018)}, pages = {14:1--14:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-081-1}, ISSN = {1868-8969}, year = {2018}, volume = {112}, editor = {Azar, Yossi and Bast, Hannah and Herman, Grzegorz}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2018.14}, URN = {urn:nbn:de:0030-drops-94773}, doi = {10.4230/LIPIcs.ESA.2018.14}, annote = {Keywords: self-assembly, molecular computing, tiling, tile, shapes} }

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**Published in:** LIPIcs, Volume 57, 24th Annual European Symposium on Algorithms (ESA 2016)

We analyze the number of stages, tiles, and bins needed to construct n * n squares and scaled shapes in the staged tile assembly model. In particular, we prove that there exists a staged system with b bins and t tile types assembling an n * n square using O((log n - tb - t log t)/b^2 + log log b/log t) stages and Omega((log n - tb - t log t)/b^2) are necessary for almost all n. For a shape S, we prove O((K(S) - tb - t log t)/b^2 + (log log b)/log t) stages suffice and Omega((K(S) - tb - t log t)/b^2) are necessary for the assembly of a scaled version of S, where K(S) denotes the Kolmogorov complexity of S. Similarly tight bounds are also obtained when more powerful flexible glue functions are permitted. These are the first staged results that hold for all choices of b and t and generalize prior results.
The upper bound constructions use a new technique for efficiently converting each both sources of system complexity, namely the tile types and mixing graph, into a "bit string" assembly.

Cameron Chalk, Eric Martinez, Robert Schweller, Luis Vega, Andrew Winslow, and Tim Wylie. Optimal Staged Self-Assembly of General Shapes. In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 57, pp. 26:1-26:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{chalk_et_al:LIPIcs.ESA.2016.26, author = {Chalk, Cameron and Martinez, Eric and Schweller, Robert and Vega, Luis and Winslow, Andrew and Wylie, Tim}, title = {{Optimal Staged Self-Assembly of General Shapes}}, booktitle = {24th Annual European Symposium on Algorithms (ESA 2016)}, pages = {26:1--26:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-015-6}, ISSN = {1868-8969}, year = {2016}, volume = {57}, editor = {Sankowski, Piotr and Zaroliagis, Christos}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2016.26}, URN = {urn:nbn:de:0030-drops-63776}, doi = {10.4230/LIPIcs.ESA.2016.26}, annote = {Keywords: Tile self-assembly, 2HAM, aTAM, DNA computing, biocomputing} }

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