[{"oa_version":"Preprint","abstract":[{"lang":"eng","text":"In pipes, turbulence sets in despite the linear stability of the laminar Hagen–Poiseuille flow. The Reynolds number ( ) for which turbulence first appears in a given experiment – the ‘natural transition point’ – depends on imperfections of the set-up, or, more precisely, on the magnitude of finite amplitude perturbations. At onset, turbulence typically only occupies a certain fraction of the flow, and this fraction equally is found to differ from experiment to experiment. Despite these findings, Reynolds proposed that after sufficiently long times, flows may settle to steady conditions: below a critical velocity, flows should (regardless of initial conditions) always return to laminar, while above this velocity, eddying motion should persist. As will be shown, even in pipes several thousand diameters long, the spatio-temporal intermittent flow patterns observed at the end of the pipe strongly depend on the initial conditions, and there is no indication that different flow patterns would eventually settle to a (statistical) steady state. Exploiting the fact that turbulent puffs do not age (i.e. they are memoryless), we continuously recreate the puff sequence exiting the pipe at the pipe entrance, and in doing so introduce periodic boundary conditions for the puff pattern. This procedure allows us to study the evolution of the flow patterns for arbitrary long times, and we find that after times in excess of advective time units, indeed a statistical steady state is reached. Although the resulting flows remain spatio-temporally intermittent, puff splitting and decay rates eventually reach a balance, so that the turbulent fraction fluctuates around a well-defined level which only depends on . In accordance with Reynolds’ proposition, we find that at lower (here 2020), flows eventually always resume to laminar, while for higher ( ), turbulence persists. The critical point for pipe flow hence falls in the interval of $2020 , which is in very good agreement with the recently proposed value of . The latter estimate was based on single-puff statistics and entirely neglected puff interactions. Unlike in typical contact processes where such interactions strongly affect the percolation threshold, in pipe flow, the critical point is only marginally influenced. Interactions, on the other hand, are responsible for the approach to the statistical steady state. As shown, they strongly affect the resulting flow patterns, where they cause ‘puff clustering’, and these regions of large puff densities are observed to travel across the puff pattern in a wave-like fashion."}],"intvolume":" 839","month":"03","main_file_link":[{"url":"https://arxiv.org/abs/1709.06372","open_access":"1"}],"scopus_import":"1","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0022-1120"],"eissn":["1469-7645"]},"ec_funded":1,"volume":839,"_id":"5996","status":"public","article_type":"original","type":"journal_article","date_updated":"2023-09-19T14:37:49Z","department":[{"_id":"BjHo"}],"acknowledgement":" We also thank Philipp Maier and the IST Austria workshop for theirdedicated technical support","oa":1,"publisher":"Cambridge University Press","quality_controlled":"1","publication":"Journal of Fluid Mechanics","day":"25","year":"2018","isi":1,"date_created":"2019-02-14T12:50:50Z","doi":"10.1017/jfm.2017.923","date_published":"2018-03-25T00:00:00Z","page":"76-94","project":[{"name":"Decoding the complexity of turbulence at its origin","grant_number":"306589","_id":"25152F3A-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"chicago":"Vasudevan, Mukund, and Björn Hof. “The Critical Point of the Transition to Turbulence in Pipe Flow.” Journal of Fluid Mechanics. Cambridge University Press, 2018. https://doi.org/10.1017/jfm.2017.923.","ista":"Vasudevan M, Hof B. 2018. The critical point of the transition to turbulence in pipe flow. Journal of Fluid Mechanics. 839, 76–94.","mla":"Vasudevan, Mukund, and Björn Hof. “The Critical Point of the Transition to Turbulence in Pipe Flow.” Journal of Fluid Mechanics, vol. 839, Cambridge University Press, 2018, pp. 76–94, doi:10.1017/jfm.2017.923.","ieee":"M. Vasudevan and B. Hof, “The critical point of the transition to turbulence in pipe flow,” Journal of Fluid Mechanics, vol. 839. Cambridge University Press, pp. 76–94, 2018.","short":"M. Vasudevan, B. Hof, Journal of Fluid Mechanics 839 (2018) 76–94.","ama":"Vasudevan M, Hof B. The critical point of the transition to turbulence in pipe flow. Journal of Fluid Mechanics. 2018;839:76-94. doi:10.1017/jfm.2017.923","apa":"Vasudevan, M., & Hof, B. (2018). The critical point of the transition to turbulence in pipe flow. Journal of Fluid Mechanics. Cambridge University Press. https://doi.org/10.1017/jfm.2017.923"},"title":"The critical point of the transition to turbulence in pipe flow","article_processing_charge":"No","external_id":{"arxiv":["1709.06372"],"isi":["000437858300003"]},"author":[{"first_name":"Mukund","id":"3C5A959A-F248-11E8-B48F-1D18A9856A87","last_name":"Vasudevan","full_name":"Vasudevan, Mukund"},{"orcid":"0000-0003-2057-2754","full_name":"Hof, Björn","last_name":"Hof","id":"3A374330-F248-11E8-B48F-1D18A9856A87","first_name":"Björn"}]},{"article_number":"7","project":[{"_id":"2584A770-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Modern Graph Algorithmic Techniques in Formal Verification","grant_number":"P 23499-N23"},{"grant_number":"S 11407_N23","name":"Rigorous Systems Engineering","call_identifier":"FWF","_id":"25832EC2-B435-11E9-9278-68D0E5697425"},{"_id":"2581B60A-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Quantitative Graph Games: Theory and Applications","grant_number":"279307"},{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"citation":{"ista":"Chatterjee K, Fu H, Novotný P, Hasheminezhad R. 2018. Algorithmic analysis of qualitative and quantitative termination problems for affine probabilistic programs. ACM Transactions on Programming Languages and Systems. 40(2), 7.","chicago":"Chatterjee, Krishnendu, Hongfei Fu, Petr Novotný, and Rouzbeh Hasheminezhad. “Algorithmic Analysis of Qualitative and Quantitative Termination Problems for Affine Probabilistic Programs.” ACM Transactions on Programming Languages and Systems. Association for Computing Machinery (ACM), 2018. https://doi.org/10.1145/3174800.","ama":"Chatterjee K, Fu H, Novotný P, Hasheminezhad R. Algorithmic analysis of qualitative and quantitative termination problems for affine probabilistic programs. ACM Transactions on Programming Languages and Systems. 2018;40(2). doi:10.1145/3174800","apa":"Chatterjee, K., Fu, H., Novotný, P., & Hasheminezhad, R. (2018). Algorithmic analysis of qualitative and quantitative termination problems for affine probabilistic programs. ACM Transactions on Programming Languages and Systems. Association for Computing Machinery (ACM). https://doi.org/10.1145/3174800","ieee":"K. Chatterjee, H. Fu, P. Novotný, and R. Hasheminezhad, “Algorithmic analysis of qualitative and quantitative termination problems for affine probabilistic programs,” ACM Transactions on Programming Languages and Systems, vol. 40, no. 2. Association for Computing Machinery (ACM), 2018.","short":"K. Chatterjee, H. Fu, P. Novotný, R. Hasheminezhad, ACM Transactions on Programming Languages and Systems 40 (2018).","mla":"Chatterjee, Krishnendu, et al. “Algorithmic Analysis of Qualitative and Quantitative Termination Problems for Affine Probabilistic Programs.” ACM Transactions on Programming Languages and Systems, vol. 40, no. 2, 7, Association for Computing Machinery (ACM), 2018, doi:10.1145/3174800."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","article_processing_charge":"No","external_id":{"isi":["000434634500003"],"arxiv":["1510.08517"]},"author":[{"id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","first_name":"Krishnendu","last_name":"Chatterjee","full_name":"Chatterjee, Krishnendu","orcid":"0000-0002-4561-241X"},{"last_name":"Fu","full_name":"Fu, Hongfei","id":"3AAD03D6-F248-11E8-B48F-1D18A9856A87","first_name":"Hongfei"},{"first_name":"Petr","id":"3CC3B868-F248-11E8-B48F-1D18A9856A87","full_name":"Novotný, Petr","last_name":"Novotný"},{"first_name":"Rouzbeh","last_name":"Hasheminezhad","full_name":"Hasheminezhad, Rouzbeh"}],"title":"Algorithmic analysis of qualitative and quantitative termination problems for affine probabilistic programs","oa":1,"quality_controlled":"1","publisher":"Association for Computing Machinery (ACM)","year":"2018","isi":1,"publication":"ACM Transactions on Programming Languages and Systems","day":"01","date_created":"2019-02-14T12:29:10Z","date_published":"2018-06-01T00:00:00Z","doi":"10.1145/3174800","_id":"5993","type":"journal_article","status":"public","date_updated":"2023-09-19T14:38:42Z","department":[{"_id":"KrCh"}],"abstract":[{"text":"In this article, we consider the termination problem of probabilistic programs with real-valued variables. Thequestions concerned are: qualitative ones that ask (i) whether the program terminates with probability 1(almost-sure termination) and (ii) whether the expected termination time is finite (finite termination); andquantitative ones that ask (i) to approximate the expected termination time (expectation problem) and (ii) tocompute a boundBsuch that the probability not to terminate afterBsteps decreases exponentially (con-centration problem). To solve these questions, we utilize the notion of ranking supermartingales, which isa powerful approach for proving termination of probabilistic programs. In detail, we focus on algorithmicsynthesis of linear ranking-supermartingales over affine probabilistic programs (Apps) with both angelic anddemonic non-determinism. An important subclass of Apps is LRApp which is defined as the class of all Appsover which a linear ranking-supermartingale exists.Our main contributions are as follows. Firstly, we show that the membership problem of LRApp (i) canbe decided in polynomial time for Apps with at most demonic non-determinism, and (ii) isNP-hard and inPSPACEfor Apps with angelic non-determinism. Moreover, theNP-hardness result holds already for Appswithout probability and demonic non-determinism. Secondly, we show that the concentration problem overLRApp can be solved in the same complexity as for the membership problem of LRApp. Finally, we show thatthe expectation problem over LRApp can be solved in2EXPTIMEand isPSPACE-hard even for Apps withoutprobability and non-determinism (i.e., deterministic programs). Our experimental results demonstrate theeffectiveness of our approach to answer the qualitative and quantitative questions over Apps with at mostdemonic non-determinism.","lang":"eng"}],"oa_version":"Submitted Version","main_file_link":[{"url":"https://arxiv.org/abs/1510.08517","open_access":"1"}],"scopus_import":"1","intvolume":" 40","month":"06","publication_status":"published","publication_identifier":{"issn":["0164-0925"]},"language":[{"iso":"eng"}],"ec_funded":1,"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"1438"}]},"volume":40,"issue":"2"},{"status":"public","type":"journal_article","_id":"5999","department":[{"_id":"TaHa"}],"date_updated":"2023-09-19T14:37:19Z","intvolume":" 116","month":"05","main_file_link":[{"url":"https://arxiv.org/abs/1407.7994","open_access":"1"}],"scopus_import":"1","oa_version":"Preprint","abstract":[{"lang":"eng","text":"We introduce for each quiver Q and each algebraic oriented cohomology theory A, the cohomological Hall algebra (CoHA) of Q, as the A-homology of the moduli of representations of the preprojective algebra of Q. This generalizes the K-theoretic Hall algebra of commuting varieties defined by Schiffmann-Vasserot. When A is the Morava K-theory, we show evidence that this algebra is a candidate for Lusztig's reformulated conjecture on modular representations of algebraic groups.\r\nWe construct an action of the preprojective CoHA on the A-homology of Nakajima quiver varieties. We compare this with the action of the Borel subalgebra of Yangian when A is the intersection theory. We also give a shuffle algebra description of this CoHA in terms of the underlying formal group law of A. As applications, we obtain a shuffle description of the Yangian. "}],"issue":"5","volume":116,"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0024-6115"]},"title":"The cohomological Hall algebra of a preprojective algebra","article_processing_charge":"No","external_id":{"isi":["000431506400001"],"arxiv":["1407.7994"]},"author":[{"first_name":"Yaping","full_name":"Yang, Yaping","last_name":"Yang"},{"first_name":"Gufang","id":"2BC2AC5E-F248-11E8-B48F-1D18A9856A87","last_name":"Zhao","full_name":"Zhao, Gufang"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"ieee":"Y. Yang and G. Zhao, “The cohomological Hall algebra of a preprojective algebra,” Proceedings of the London Mathematical Society, vol. 116, no. 5. Oxford University Press, pp. 1029–1074, 2018.","short":"Y. Yang, G. Zhao, Proceedings of the London Mathematical Society 116 (2018) 1029–1074.","apa":"Yang, Y., & Zhao, G. (2018). The cohomological Hall algebra of a preprojective algebra. Proceedings of the London Mathematical Society. Oxford University Press. https://doi.org/10.1112/plms.12111","ama":"Yang Y, Zhao G. The cohomological Hall algebra of a preprojective algebra. Proceedings of the London Mathematical Society. 2018;116(5):1029-1074. doi:10.1112/plms.12111","mla":"Yang, Yaping, and Gufang Zhao. “The Cohomological Hall Algebra of a Preprojective Algebra.” Proceedings of the London Mathematical Society, vol. 116, no. 5, Oxford University Press, 2018, pp. 1029–74, doi:10.1112/plms.12111.","ista":"Yang Y, Zhao G. 2018. The cohomological Hall algebra of a preprojective algebra. Proceedings of the London Mathematical Society. 116(5), 1029–1074.","chicago":"Yang, Yaping, and Gufang Zhao. “The Cohomological Hall Algebra of a Preprojective Algebra.” Proceedings of the London Mathematical Society. Oxford University Press, 2018. https://doi.org/10.1112/plms.12111."},"oa":1,"publisher":"Oxford University Press","quality_controlled":"1","date_created":"2019-02-14T13:14:22Z","date_published":"2018-05-01T00:00:00Z","doi":"10.1112/plms.12111","page":"1029-1074","publication":"Proceedings of the London Mathematical Society","day":"01","year":"2018","isi":1},{"_id":"5989","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode","image":"/images/cc_by_nc.png","name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)","short":"CC BY-NC (4.0)"},"type":"journal_article","ddc":["570"],"date_updated":"2023-09-19T14:39:08Z","department":[{"_id":"BeVi"}],"file_date_updated":"2020-07-14T12:47:15Z","oa_version":"Published Version","abstract":[{"text":"Schistosomes are the causative agents of schistosomiasis, a neglected tropical disease affecting over 230 million people worldwide.Additionally to their major impact on human health, they are also models of choice in evolutionary biology. These parasitic flatwormsare unique among the common hermaphroditic trematodes as they have separate sexes. This so-called “evolutionary scandal”displays a female heterogametic genetic sex-determination system (ZZ males and ZW females), as well as a pronounced adult sexualdimorphism. These phenotypic differences are determined by a shared set of genes in both sexes, potentially leading to intralocussexual conflicts. To resolve these conflicts in sexually selected traits, molecular mechanisms such as sex-biased gene expression couldoccur, but parent-of-origin gene expression also provides an alternative. In this work we investigated the latter mechanism, that is,genes expressed preferentially from either the maternal or the paternal allele, inSchistosoma mansonispecies. To this end, tran-scriptomes from male and female hybrid adults obtained by strain crosses were sequenced. Strain-specific single nucleotide poly-morphism (SNP) markers allowed us to discriminate the parental origin, while reciprocal crosses helped to differentiate parentalexpression from strain-specific expression. We identified genes containing SNPs expressed in a parent-of-origin manner consistentwith paternal and maternal imprints. Although the majority of the SNPs was identified in mitochondrial and Z-specific loci, theremaining SNPs found in male and female transcriptomes were situated in genes that have the potential to explain sexual differencesin schistosome parasites. Furthermore, we identified and validated four new Z-specific scaffolds.","lang":"eng"}],"intvolume":" 10","month":"03","scopus_import":"1","language":[{"iso":"eng"}],"file":[{"relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_id":"5991","checksum":"736a459cb77de5824354466bb0331caf","creator":"dernst","file_size":529755,"date_updated":"2020-07-14T12:47:15Z","file_name":"2018_GBE_Kincaid_Smith.pdf","date_created":"2019-02-14T12:20:01Z"}],"publication_status":"published","publication_identifier":{"issn":["1759-6653"]},"license":"https://creativecommons.org/licenses/by-nc/4.0/","volume":10,"issue":"3","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"mla":"Kincaid-Smith, Julien, et al. “Parent-of-Origin-Dependent Gene Expression in Male and Female Schistosome Parasites.” Genome Biology and Evolution, vol. 10, no. 3, Oxford University Press, 2018, pp. 840–56, doi:10.1093/gbe/evy037.","ama":"Kincaid-Smith J, Picard MAL, Cosseau C, et al. Parent-of-Origin-Dependent Gene Expression in Male and Female Schistosome Parasites. Genome Biology and Evolution. 2018;10(3):840-856. doi:10.1093/gbe/evy037","apa":"Kincaid-Smith, J., Picard, M. A. L., Cosseau, C., Boissier, J., Severac, D., Grunau, C., & Toulza, E. (2018). Parent-of-Origin-Dependent Gene Expression in Male and Female Schistosome Parasites. Genome Biology and Evolution. Oxford University Press. https://doi.org/10.1093/gbe/evy037","short":"J. Kincaid-Smith, M.A.L. Picard, C. Cosseau, J. Boissier, D. Severac, C. Grunau, E. Toulza, Genome Biology and Evolution 10 (2018) 840–856.","ieee":"J. Kincaid-Smith et al., “Parent-of-Origin-Dependent Gene Expression in Male and Female Schistosome Parasites,” Genome Biology and Evolution, vol. 10, no. 3. Oxford University Press, pp. 840–856, 2018.","chicago":"Kincaid-Smith, Julien, Marion A L Picard, Céline Cosseau, Jérôme Boissier, Dany Severac, Christoph Grunau, and Eve Toulza. “Parent-of-Origin-Dependent Gene Expression in Male and Female Schistosome Parasites.” Genome Biology and Evolution. Oxford University Press, 2018. https://doi.org/10.1093/gbe/evy037.","ista":"Kincaid-Smith J, Picard MAL, Cosseau C, Boissier J, Severac D, Grunau C, Toulza E. 2018. Parent-of-Origin-Dependent Gene Expression in Male and Female Schistosome Parasites. Genome Biology and Evolution. 10(3), 840–856."},"title":"Parent-of-Origin-Dependent Gene Expression in Male and Female Schistosome Parasites","article_processing_charge":"No","external_id":{"isi":["000429483700013"]},"author":[{"first_name":"Julien","full_name":"Kincaid-Smith, Julien","last_name":"Kincaid-Smith"},{"id":"2C921A7A-F248-11E8-B48F-1D18A9856A87","first_name":"Marion A L","last_name":"Picard","orcid":"0000-0002-8101-2518","full_name":"Picard, Marion A L"},{"last_name":"Cosseau","full_name":"Cosseau, Céline","first_name":"Céline"},{"first_name":"Jérôme","last_name":"Boissier","full_name":"Boissier, Jérôme"},{"last_name":"Severac","full_name":"Severac, Dany","first_name":"Dany"},{"first_name":"Christoph","full_name":"Grunau, Christoph","last_name":"Grunau"},{"first_name":"Eve","last_name":"Toulza","full_name":"Toulza, Eve"}],"oa":1,"quality_controlled":"1","publisher":"Oxford University Press","publication":"Genome Biology and Evolution","day":"01","year":"2018","has_accepted_license":"1","isi":1,"date_created":"2019-02-14T12:13:52Z","doi":"10.1093/gbe/evy037","date_published":"2018-03-01T00:00:00Z","page":"840-856"},{"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","date_updated":"2023-09-19T14:41:51Z","citation":{"ista":"Stojanov A, Smith TM, Alistarh D-A, Puschel M. 2018. Fast quantized arithmetic on x86: Trading compute for data movement. 2018 IEEE International Workshop on Signal Processing Systems. SiPS: Workshop on Signal Processing Systems vol. 2018–October, 8598402.","chicago":"Stojanov, Alen, Tyler Michael Smith, Dan-Adrian Alistarh, and Markus Puschel. “Fast Quantized Arithmetic on X86: Trading Compute for Data Movement.” In 2018 IEEE International Workshop on Signal Processing Systems, Vol. 2018–October. IEEE, 2018. https://doi.org/10.1109/SiPS.2018.8598402.","ieee":"A. Stojanov, T. M. Smith, D.-A. Alistarh, and M. Puschel, “Fast quantized arithmetic on x86: Trading compute for data movement,” in 2018 IEEE International Workshop on Signal Processing Systems, Cape Town, South Africa, 2018, vol. 2018–October.","short":"A. Stojanov, T.M. Smith, D.-A. Alistarh, M. Puschel, in:, 2018 IEEE International Workshop on Signal Processing Systems, IEEE, 2018.","ama":"Stojanov A, Smith TM, Alistarh D-A, Puschel M. Fast quantized arithmetic on x86: Trading compute for data movement. In: 2018 IEEE International Workshop on Signal Processing Systems. Vol 2018-October. IEEE; 2018. doi:10.1109/SiPS.2018.8598402","apa":"Stojanov, A., Smith, T. M., Alistarh, D.-A., & Puschel, M. (2018). Fast quantized arithmetic on x86: Trading compute for data movement. In 2018 IEEE International Workshop on Signal Processing Systems (Vol. 2018–October). Cape Town, South Africa: IEEE. https://doi.org/10.1109/SiPS.2018.8598402","mla":"Stojanov, Alen, et al. “Fast Quantized Arithmetic on X86: Trading Compute for Data Movement.” 2018 IEEE International Workshop on Signal Processing Systems, vol. 2018–October, 8598402, IEEE, 2018, doi:10.1109/SiPS.2018.8598402."},"title":"Fast quantized arithmetic on x86: Trading compute for data movement","department":[{"_id":"DaAl"}],"author":[{"first_name":"Alen","full_name":"Stojanov, Alen","last_name":"Stojanov"},{"first_name":"Tyler Michael","full_name":"Smith, Tyler Michael","last_name":"Smith"},{"last_name":"Alistarh","orcid":"0000-0003-3650-940X","full_name":"Alistarh, Dan-Adrian","id":"4A899BFC-F248-11E8-B48F-1D18A9856A87","first_name":"Dan-Adrian"},{"full_name":"Puschel, Markus","last_name":"Puschel","first_name":"Markus"}],"external_id":{"isi":["000465106800060"]},"article_processing_charge":"No","article_number":"8598402","_id":"6031","status":"public","type":"conference","conference":{"start_date":"2018-10-21","location":"Cape Town, South Africa","end_date":"2018-10-24","name":"SiPS: Workshop on Signal Processing Systems"},"day":"31","publication":"2018 IEEE International Workshop on Signal Processing Systems","language":[{"iso":"eng"}],"isi":1,"publication_status":"published","year":"2018","volume":"2018-October","doi":"10.1109/SiPS.2018.8598402","date_published":"2018-12-31T00:00:00Z","date_created":"2019-02-17T22:59:25Z","oa_version":"None","abstract":[{"text":"We introduce Clover, a new library for efficient computation using low-precision data, providing mathematical routines required by fundamental methods in optimization and sparse recovery. Our library faithfully implements variants of stochastic quantization that guarantee convergence at low precision, and supports data formats from 4-bit quantized to 32-bit IEEE-754 on current Intel processors. In particular, we show that 4-bit can be implemented efficiently using Intel AVX despite the lack of native support for this data format. Experimental results with dot product, matrix-vector multiplication (MVM), gradient descent (GD), and iterative hard thresholding (IHT) demonstrate that the attainable speedups are in many cases close to linear with respect to the reduction of precision due to reduced data movement. Finally, for GD and IHT, we show examples of absolute speedup achieved by 4-bit versus 32-bit, by iterating until a given target error is achieved.","lang":"eng"}],"month":"12","scopus_import":"1","quality_controlled":"1","publisher":"IEEE"}]