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Modular composition via factorization

Joris van der Hoeven, Grégoire Lecerf
2018 Journal of Complexity  
Modular composition is the problem to compute the composition of two univariate polynomials modulo a third one.  ...  In this article, we explore particular cases of moduli over finite fields for which modular composition turns out to be cheaper than in the general case.  ...  MODULAR COMPOSITION VIA FACTORIZATION MODULAR COMPOSITION VIA FACTORIZATION  ... 
doi:10.1016/j.jco.2018.05.002 fatcat:dcqo5md4arbcrgwxw2ak634l3m

Fast Modular Composition in any Characteristic

Kiran S. Kedlaya, Christopher Umans
2008 2008 49th Annual IEEE Symposium on Foundations of Computer Science  
As in Umans (2008) , we reduce modular composition to certain instances of multipoint evaluation of multivariate polynomials.  ...  We give an algorithm for modular composition of degree n univariate polynomials over a finite field F q requiring n 1+o(1) log 1+o(1) q bit operations; this had earlier been achieved in characteristic  ...  COMPOSITION via the reduction.  ... 
doi:10.1109/focs.2008.13 dblp:conf/focs/KedlayaU08 fatcat:tfcb6jo4qncydci6sjrpvgitzu

Fast Polynomial Factorization and Modular Composition

Kiran S. Kedlaya, Christopher Umans
2011 SIAM journal on computing (Print)  
The improvements come from new algorithms for modular composition of degree n univariate polynomials, which is the asymptotic bottleneck in fast algorithms for factoring polynomials over finite fields.  ...  The best previous algorithms for modular composition use O(n (ω+1)/2 ) field operations, where ω is the exponent of matrix multiplication (Brent & Kung (1978) ), with a slight improvement in the exponent  ...  Unfortunately, this is not enough to yield an improved algorithm for MODULAR COMPOSITION via the above equivalence.  ... 
doi:10.1137/08073408x fatcat:vm32on54svfizhtnvgx6h7zfmm

Global architecture of metabolite distributions across species and its formation mechanisms

Kazuhiro Takemoto
2010 Biosystems (Amsterdam. Print)  
An earlier model represents that these structural properties in bipartite relationships are determined based on traits of elements and external factors.  ...  Living organisms produce metabolites of many types via their metabolisms. Especially, flavonoids, a kind of secondary metabolites, of plant species are interesting examples.  ...  However, we believe that elements' traits and external factors are important. Especially such factors might play crucial roles for the formation of local interaction patterns.  ... 
doi:10.1016/j.biosystems.2009.12.002 pmid:20004232 fatcat:gpeiclzlbnch5gdrfx4yjzeovi

Modular Modelling in Synthetic Biology: Light-Based Communication in E. coli

Donal Stewart, John Roger Wilson-Kanamori
2011 Electronical Notes in Theoretical Computer Science  
It also utilised newly developed spatial extensions to aid in the depiction of intercellular communication via light emitting and light sensing pathways, demonstrating the extensibility of the language  ...  A similar modularity in the modelling of such systems, however, has not been explored until much more recently.  ...  This Kappa statement produces a composite part in which the production of λ-cI is dependant on the availability of the transcription factor LovTAP.  ... 
doi:10.1016/j.entcs.2011.09.037 fatcat:rdzqv3nf4jdvhi7eqmngt2lqtu

Book reports

2005 Computers and Mathematics with Applications  
Application of the Euclidean Algorithm. 4.1 Modular arithmetic. 4.2 Modular inverses via Euclid. 4.3 Repeated squaring. 4.4 Modular inverses via Fermat. 4.5 Linear Diophantine equations. 4.6 Continued  ...  Fast linear algebra. 12.1 Strassen's matrix multiplication. 12.2 Application: fast modular composition of polynomials. 12.3 Linearly recurrent sequences. 12,4 Wiedemann's algorithm and black box linear  ... 
doi:10.1016/j.camwa.2005.02.001 fatcat:twqxvijfkrdx7gnr26gmsbuzvu

Modular approach applied to tailoring of bismuth-containing layered perovskites

D. O. Charkin, I. V. Kul'bakin, D. N. Moskvin
2005 Acta Crystallographica Section A Foundations of Crystallography  
For partially disordered crystals, the intensities of the non-family reflections are underestimated due to their diffusivity and the moduli of their structure factors are reduced by a common factor.  ...  The structure can be in most cases successfully refined if separate scale factors are assigned to either of the two kinds of reflections [3].  ...  Modular Approach Applied to Tailoring of Bismuth-Containing Layered Perovskites Dmitri O. Charkin a , Igor V. Kul'bakin a , Dmitri N.  ... 
doi:10.1107/s010876730509896x fatcat:3dbw5avshzdwbpullruqdmv5s4

Recurrent modules in modular structures

G. Ferraris
2005 Acta Crystallographica Section A Foundations of Crystallography  
A61, C23 Layered Compounds: from Modular Description to Rational Design Laurent Cario,  ...  For partially disordered crystals, the intensities of the non-family reflections are underestimated due to their diffusivity and the moduli of their structure factors are reduced by a common factor.  ...  Only recently it was understood that the problem could be overcome via more complicated mixed-layer structures involving additional new nonstoichiometric structural moduli (2D building blocks).  ... 
doi:10.1107/s0108767305098995 fatcat:y5mjzw27ybfedems23vdrydiq4

A Paradigm Shift in Tissue Engineering: From a Top–Down to a Bottom–Up Strategy

Theresa Schmidt, Yu Xiang, Xujin Bao, Tao Sun
2021 Processes  
This very limited clinical application of TE can be attributed to the constraints in manufacturing fully functional tissues via the traditional top–down approach, where very limited cell types are seeded  ...  the manufacture of fully functional tissues utilises a bottom–up approach to mimic developmental biology processes by implementing gradual tissue assembly alongside the growth of multiple cell types in modular  ...  Due to the use of micro-sized modular scaffolds and the reconstruction of vascular systems, mass transfer within the gradually expanded tissues is not a limiting factor.  ... 
doi:10.3390/pr9060935 fatcat:wtnxpomba5fgfdkvitwgk5hxe4

Bottom-Up Engineering of Biological Systems through Standard Bricks: A Modularity Study on Basic Parts and Devices

Lorenzo Pasotti, Nicolò Politi, Susanna Zucca, Maria Gabriella Cusella De Angelis, Paolo Magni, Mark Isalan
2012 PLoS ONE  
If modularity persists, identical transcriptional signals trigger identical GFP outputs.  ...  First, the activity of a set of promoters was quantified in Escherichia coli via different measurement systems (i.e., different plasmids, reporter genes, ribosome binding sites) relative to an in vivo  ...  studies should be conducted to investigate such factors.  ... 
doi:10.1371/journal.pone.0039407 pmid:22911685 pmcid:PMC3401228 fatcat:7ibfyxlotrfnlpyne6i7fftrga

Layered compounds: from modular description to rational design

L. Cario
2005 Acta Crystallographica Section A Foundations of Crystallography  
With these data we simultaneously determine, via a novel algorithm [3] , the orientation matrices of the crystallites which constitute the powder specimen.  ...  The cell parameters and chemical composition of the members linearly depend from those of the building modules.  ... 
doi:10.1107/s0108767305099009 fatcat:5lqv37ou5zhhpj5xhfhmlnee6i

Modular Utility Representation for Decision-Theoretic Planning [chapter]

Michael P. Wellman, Jon Doyle
1992 Artificial Intelligence Planning Systems  
Modularity, or separability in speci cation, is the key representational feature enabling this exibility.  ...  Decision-theoretic approaches require that representations of objectives possess a rm semantics in terms of utility functions, yet provide the exible compositionality needed for practical preference modeling  ...  Customized utility models can be constructed dynamically to re ect the relevant factors in a particular decision situation via bottom-up composition according to rules of multiattribute utility theory.  ... 
doi:10.1016/b978-0-08-049944-4.50033-1 fatcat:ko7letengrhn7a6g72lbbsoxre

Experience with modularity in an advanced teleconferencing service deployment

Eric Cheung, Thomas M. Smith
2009 2009 31st International Conference on Software Engineering - Companion Volume  
achieving software modularity.  ...  This paper discusses the factors that influenced our design decisions.  ...  Conclusion Many factors influence the choice of modularity scheme.  ... 
doi:10.1109/icse-companion.2009.5070962 dblp:conf/icse/CheungS09 fatcat:52lafwzij5crrd56al5uhpma6i

Molecular analyses identifies new domains and structural differences among Streptococcus pneumoniae immune evasion proteins PspC and Hic

Shanshan Du, Cláudia Vilhena, Samantha King, Alfredo Sahagún-Ruiz, Sven Hammerschmidt, Christine Skerka, Peter F. Zipfel
2021 Scientific Reports  
This knowledge improved pattern evaluation at the level of full-length proteins, allowed a sequence comparison at the domain level and identified domains with a modular composition.  ...  This novel strategy increased understanding of individual proteins variability and modular domain composition, enabled a structural and functional characterization at the domain level and furthermore revealed  ...  Our in-silico analysis identified a modular composition and further distinct proline-rich domains, which differ in length (57 to 286 aa), modular composition, and sequence. Fig. 7A ).  ... 
doi:10.1038/s41598-020-79362-3 pmid:33462258 fatcat:erd2umyn2nbcdc5ddrwyekzymy

Modular Analysis and Design of Biological Circuits

Theodore W. Grunberg, Domitilla Del Vecchio
2020 Current Opinion in Biotechnology  
Here, we summarize some of these studies and potential engineering solutions that have been proposed to enable modular composition of biological circuits.  ...  Modularity has been the subject of intense investigation in systems biology for more than two decades.  ...  Conflict of interest statement Nothing declared. composition (C) Modularity in systems biology (B) Modularity in engineering Figure 1 : 1 Modularity. (A) Modular composition.  ... 
doi:10.1016/j.copbio.2019.11.015 pmid:31877425 fatcat:jh4vhdjq7ffqleqzj756x2z4ue
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