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We invite you to attend colloquium of Laboratoire Dieudonné, Université Côte d'Azur, France on December 12, 2022 at 12:00 CET https://math.unice.fr/~sangam/colloquium/seminar.php =============================================================================== where Prof. Dmitry Zaitsev (http://daze.ho.ua) provides a talk "Composition of clans to speed-up solving sparse linear systems on parallel and distributed architecture". Join Zoom Meeting https://univ-cotedazur.zoom.us/j/83822470756?pwd=OU0vRnJpamtRei9RT2FtMmd5L2xjUT09 Meeting ID: 838 2247 0756 Passcode: 109907 =============================================================================== Dmitry Zaitsev is ICL (https://icl.utk.edu/) an alumni who worked in Jack Dongarra - laureat of 2021 Turing Award - laboratory on Fulbright scholarship in 2017, joint papers published, joint software ParAd issued. @ICL_UTK recommends attending the colloquium on its Twitter news tape https://twitter.com/ICL_UTK/status/1597991346777661451 As a part of colloquium, an invitation for further collective developing the clan composition theory in frames of international research projects will be announced, preliminarily based on the following research plan: https://docs.google.com/document/d/1XDe8LlNCvqfna8FlWcFzd3Z4OnBE0OdjnZMWe2cFmL0/edit?usp=share_link Resume of colloquium: ------------------------------- Solving linear Diophantine systems of equations is applied in discrete-event systems, model checking, formal languages and automata, logic programming, cryptography, networking, signal processing, and chemistry. For modeling discrete systems with Petri nets, a solution in non-negative integer numbers is required, which represents an intractable problem. For this reason, solving such kinds of tasks with significant speedup is highly appreciated. We introduce a nearness relation on a set of system’s equations, which transitive closure gives a clan relation. A sparse system is decomposed into a set of its clans. Solving a subsystem for each clan and then the clan composition system gives a speed-up of computations. We design a new solver of linear Diophantine systems, based on the simultaneous and parallel-sequential composition of the system clans, that runs on parallel architectures using a two level parallelization concept based on MPI and OpenMP. A decomposable system is usually represented by a sparse matrix; a minimal clan size of the decomposition restricts the granulation of the technique. A dynamic task-dispatching subsystem is developed for distributing systems on nodes in the process of compositional solution. Computational speedups are obtained on a series of test examples, e.g., illustrating that the best value constitutes up to 45 times speedup obtained on 5 nodes with 20 cores each. For load balancing, aggregation of the minimal clans has been implemented, that yields an additional speed-up. Solving sparse systems over fields of real numbers, using SVD decomposition to obtain basis solutions for clans, also reveals considerable speed-up on real-life tasks from the MatrixMarket depository. Basic references: ----------------------- Dmitry A. Zaitsev, Tatiana R. Shmeleva, Piotr Luszczek. Aggregation of clans to speed-up solving linear systems on parallel architectures, International Journal of Parallel, Emergent and Distributed Systems, 37(2), 2022, 198-219. http://dx.doi.org/10.1080/17445760.2021.2004412 Dmitry Zaitsev, Stanimire Tomov, Jack Dongarra. Solving Linear Diophantine Systems on Parallel Architectures, IEEE Transactions on Parallel and Distributed Systems, 30(5), 2019, 1158-1169. http://dx.doi.org/10.1109/TPDS.2018.2873354 Zaitsev D.A. Sequential composition of linear systems' clans, Information Sciences, 363, 2016, 292-307. http://dx.doi.org/10.1016/j.ins.2016.02.016 *********************************************************************************************************************** -- Yours truly, Dmitry Zaitsev Dr.Sci., Professor, Senior Member of ACM and IEEE http://daze.ho.ua https://twitter.com/ICL_UTK/status/1597991346777661451 https://youtu.be/Cy6xRTpP0d8 <https://l.facebook.com/l.php?u=https%3A%2F%2Fyoutu.be%2FCy6xRTpP0d8%3Ffbclid%3DIwAR190xifVopkYBgqdRVbb0Ey1OyzH-ZlO3AkCzqsLQswNpe-UH0Pqsmu3jU&h=AT3_54deSf0jS1vNHCTAzj4aJb_p9vfEM-JYHILicq5r9P04P0_YlNa7Ybas339LU0cAZEMqgeAFNG9VnKJmVQZeABUqTVFI8oQnqi0bsTn2yDdPBj8gUfwSWaCv&__tn__=-UK-R&c[0]=AT2N6IU-uHvB0_2o_s7Jl5vqW7lI5WraVAEJ8ZnbfRy2PKaOHb7MCEJPWBEJCwsxX2H2XX12Vy_o4BT3aYwTRF_5s_p2KZj60hu3aZmPUkwSYPINOaxn7dODIhbYdMOzllpcDlmxnriUW6dMGvlGdEv4oA> -- Yours truly, Dmitry Zaitsev Dr.Sci., Professor, Senior Member of ACM and IEEE http://daze.ho.ua https://twitter.com/ICL_UTK/status/1597991346777661451 https://youtu.be/Cy6xRTpP0d8 <https://l.facebook.com/l.php?u=https%3A%2F%2Fyoutu.be%2FCy6xRTpP0d8%3Ffbclid%3DIwAR190xifVopkYBgqdRVbb0Ey1OyzH-ZlO3AkCzqsLQswNpe-UH0Pqsmu3jU&h=AT3_54deSf0jS1vNHCTAzj4aJb_p9vfEM-JYHILicq5r9P04P0_YlNa7Ybas339LU0cAZEMqgeAFNG9VnKJmVQZeABUqTVFI8oQnqi0bsTn2yDdPBj8gUfwSWaCv&__tn__=-UK-R&c[0]=AT2N6IU-uHvB0_2o_s7Jl5vqW7lI5WraVAEJ8ZnbfRy2PKaOHb7MCEJPWBEJCwsxX2H2XX12Vy_o4BT3aYwTRF_5s_p2KZj60hu3aZmPUkwSYPINOaxn7dODIhbYdMOzllpcDlmxnriUW6dMGvlGdEv4oA> -- Yours truly, Dmitry Zaitsev Dr.Sci., Professor, Senior Member of ACM and IEEE http://daze.ho.ua https://twitter.com/ICL_UTK/status/1597991346777661451 https://youtu.be/Cy6xRTpP0d8 <https://l.facebook.com/l.php?u=https%3A%2F%2Fyoutu.be%2FCy6xRTpP0d8%3Ffbclid%3DIwAR190xifVopkYBgqdRVbb0Ey1OyzH-ZlO3AkCzqsLQswNpe-UH0Pqsmu3jU&h=AT3_54deSf0jS1vNHCTAzj4aJb_p9vfEM-JYHILicq5r9P04P0_YlNa7Ybas339LU0cAZEMqgeAFNG9VnKJmVQZeABUqTVFI8oQnqi0bsTn2yDdPBj8gUfwSWaCv&__tn__=-UK-R&c[0]=AT2N6IU-uHvB0_2o_s7Jl5vqW7lI5WraVAEJ8ZnbfRy2PKaOHb7MCEJPWBEJCwsxX2H2XX12Vy_o4BT3aYwTRF_5s_p2KZj60hu3aZmPUkwSYPINOaxn7dODIhbYdMOzllpcDlmxnriUW6dMGvlGdEv4oA> -- Yours truly, Dmitry Zaitsev Dr.Sci., Professor, Senior Member of ACM and IEEE http://daze.ho.ua https://twitter.com/ICL_UTK/status/1597991346777661451 https://youtu.be/Cy6xRTpP0d8 <https://l.facebook.com/l.php?u=https%3A%2F%2Fyoutu.be%2FCy6xRTpP0d8%3Ffbclid%3DIwAR190xifVopkYBgqdRVbb0Ey1OyzH-ZlO3AkCzqsLQswNpe-UH0Pqsmu3jU&h=AT3_54deSf0jS1vNHCTAzj4aJb_p9vfEM-JYHILicq5r9P04P0_YlNa7Ybas339LU0cAZEMqgeAFNG9VnKJmVQZeABUqTVFI8oQnqi0bsTn2yDdPBj8gUfwSWaCv&__tn__=-UK-R&c[0]=AT2N6IU-uHvB0_2o_s7Jl5vqW7lI5WraVAEJ8ZnbfRy2PKaOHb7MCEJPWBEJCwsxX2H2XX12Vy_o4BT3aYwTRF_5s_p2KZj60hu3aZmPUkwSYPINOaxn7dODIhbYdMOzllpcDlmxnriUW6dMGvlGdEv4oA> -- Yours truly, Dmitry Zaitsev Dr.Sci., Professor, Senior Member of ACM and IEEE http://daze.ho.ua https://twitter.com/ICL_UTK/status/1597991346777661451 https://youtu.be/Cy6xRTpP0d8 <https://l.facebook.com/l.php?u=https%3A%2F%2Fyoutu.be%2FCy6xRTpP0d8%3Ffbclid%3DIwAR190xifVopkYBgqdRVbb0Ey1OyzH-ZlO3AkCzqsLQswNpe-UH0Pqsmu3jU&h=AT3_54deSf0jS1vNHCTAzj4aJb_p9vfEM-JYHILicq5r9P04P0_YlNa7Ybas339LU0cAZEMqgeAFNG9VnKJmVQZeABUqTVFI8oQnqi0bsTn2yDdPBj8gUfwSWaCv&__tn__=-UK-R&c[0]=AT2N6IU-uHvB0_2o_s7Jl5vqW7lI5WraVAEJ8ZnbfRy2PKaOHb7MCEJPWBEJCwsxX2H2XX12Vy_o4BT3aYwTRF_5s_p2KZj60hu3aZmPUkwSYPINOaxn7dODIhbYdMOzllpcDlmxnriUW6dMGvlGdEv4oA>
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