3 Search Results for "Gray, Andrew P."

Document
DOI: 10.4230/LIPIcs.DNA.30.1
Geometric Enumeration of Localized DNA Strand Displacement Reaction Networks

Authors: Matthew R. Lakin and Sarika Kumar

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

Abstract
Localized molecular devices are a powerful tool for engineering complex information-processing circuits and molecular robots. Their practical advantages include speed and scalability of interactions between components tethered near to each other on an underlying nanostructure, and the ability to restrict interactions between more distant components. The latter is a critical feature that must be factored into computational tools for the design and simulation of localized molecular devices: unlike in solution-phase systems, the geometries of molecular interactions must be accounted for when attempting to determine the network of possible reactions in a tethered molecular system. This work aims to address that challenge by integrating, for the first time, automated approaches to analysis of molecular geometry with reaction enumeration algorithms for DNA strand displacement reaction networks that can be applied to tethered molecular systems. By adapting a simple approach to solving the biophysical constraints inherent in molecular interactions to be applicable to tethered systems, we produce a localized reaction enumeration system that enhances previous approaches to reaction enumeration in tethered system by not requiring users to explicitly specify the subsets of components that are capable of interacting. This greatly simplifies the user’s task and could also be used as the basis of future systems for automated placement or routing of signal-transmission and logical processing in molecular devices. We apply this system to several published example systems from the literature, including both tethered molecular logic systems and molecular robots.
Cite as

Matthew R. Lakin and Sarika Kumar. Geometric Enumeration of Localized DNA Strand Displacement Reaction Networks. In 30th International Conference on DNA Computing and Molecular Programming (DNA 30). Leibniz International Proceedings in Informatics (LIPIcs), Volume 314, pp. 1:1-1:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{lakin_et_al:LIPIcs.DNA.30.1,
  author =	{Lakin, Matthew R. and Kumar, Sarika},
  title =	{{Geometric Enumeration of Localized DNA Strand Displacement Reaction Networks}},
  booktitle =	{30th International Conference on DNA Computing and Molecular Programming (DNA 30)},
  pages =	{1:1--1:24},
  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.30.1},
  URN =		{urn:nbn:de:0030-drops-209294},
  doi =		{10.4230/LIPIcs.DNA.30.1},
  annote =	{Keywords: Localized circuits, reaction enumeration, DNA strand displacement, geometry, molecular computing}
}
Document
DOI: 10.4230/LIPIcs.SEA.2024.27
Improved Cut Strategy for Tensor Network Contraction Orders

Authors: Christoph Staudt, Mark Blacher, Julien Klaus, Farin Lippmann, and Joachim Giesen

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract
In the field of quantum computing, simulating quantum systems on classical computers is crucial. Tensor networks are fundamental in simulating quantum systems. A tensor network is a collection of tensors, that need to be contracted into a result tensor. Tensor contraction is a generalization of matrix multiplication to higher order tensors. The contractions can be performed in different orders, and the order has a significant impact on the number of floating point operations (flops) needed to get the result tensor. It is known that finding an optimal contraction order is NP-hard. The current state-of-the-art approach for finding efficient contraction orders is to combinine graph partitioning with a greedy strategy. Although heavily used in practice, the current approach ignores so-called free indices, chooses node weights without regarding previous computations, and requires numerous hyperparameters that need to be tuned at runtime. In this paper, we address these shortcomings by developing a novel graph cut strategy. The proposed modifications yield contraction orders that significantly reduce the number of flops in the tensor contractions compared to the current state of the art. Moreover, by removing the need for hyperparameter tuning at runtime, our approach converges to an efficient solution faster, which reduces the required optimization time by at least an order of magnitude.
Cite as

Christoph Staudt, Mark Blacher, Julien Klaus, Farin Lippmann, and Joachim Giesen. Improved Cut Strategy for Tensor Network Contraction Orders. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 27:1-27:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{staudt_et_al:LIPIcs.SEA.2024.27,
  author =	{Staudt, Christoph and Blacher, Mark and Klaus, Julien and Lippmann, Farin and Giesen, Joachim},
  title =	{{Improved Cut Strategy for Tensor Network Contraction Orders}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{27:1--27:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.27},
  URN =		{urn:nbn:de:0030-drops-203924},
  doi =		{10.4230/LIPIcs.SEA.2024.27},
  annote =	{Keywords: tensor network, contraction order, graph partitioniong, quantum simulation}
}
Document
DOI: 10.4230/DagSemProc.07071.5
An Inner/Outer Stationary Iteration for Computing PageRank

Authors: Andrew P. Gray, Chen Greif, and Tracy Lau

Published in: Dagstuhl Seminar Proceedings, Volume 7071, Web Information Retrieval and Linear Algebra Algorithms (2007)

Abstract
We present a stationary iterative scheme for PageRank computation. The algorithm is based on a linear system formulation of the problem, uses inner/outer iterations, and amounts to a simple preconditioning technique. It is simple, can be easily implemented and parallelized, and requires minimal storage overhead. Convergence analysis shows that the algorithm is effective for a crude inner tolerance and is not particularly sensitive to the choice of the parameters involved. Numerical examples featuring matrices of dimensions up to approximately $10^7$ confirm the analytical results and demonstrate the accelerated convergence of the algorithm compared to the power method.
Cite as

Andrew P. Gray, Chen Greif, and Tracy Lau. An Inner/Outer Stationary Iteration for Computing PageRank. In Web Information Retrieval and Linear Algebra Algorithms. Dagstuhl Seminar Proceedings, Volume 7071, pp. 1-8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{gray_et_al:DagSemProc.07071.5,
  author =	{Gray, Andrew P. and Greif, Chen and Lau, Tracy},
  title =	{{An Inner/Outer Stationary Iteration for Computing PageRank}},
  booktitle =	{Web Information Retrieval and Linear Algebra Algorithms},
  pages =	{1--8},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7071},
  editor =	{Andreas Frommer and Michael W. Mahoney and Daniel B. Szyld},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07071.5},
  URN =		{urn:nbn:de:0030-drops-10628},
  doi =		{10.4230/DagSemProc.07071.5},
  annote =	{Keywords: PageRank, power method, stationary method, inner/outer iterations, damping factor}
}
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