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Table representation of search results timeline featuring number of search results per year.

Year Number of Results
1886 1
1887 1
1891 1
1892 1
1897 1
1899 1
1906 1
1916 1
1922 1
1925 2
1926 1
1928 3
1929 4
1930 2
1931 3
1932 2
1934 4
1935 4
1937 4
1938 3
1939 4
1940 1
1942 3
1943 1
1945 3
1946 1
1947 2
1948 1
1949 6
1950 3
1952 8
1953 3
1954 6
1955 8
1956 8
1957 4
1958 1
1959 3
1960 2
1961 4
1962 3
1963 12
1964 2
1965 2
1966 13
1967 9
1968 8
1969 15
1970 11
1971 12
1972 14
1973 12
1974 17
1975 24
1976 30
1977 32
1978 31
1979 36
1980 47
1981 51
1982 42
1983 49
1984 48
1985 57
1986 63
1987 73
1988 69
1989 91
1990 80
1991 95
1992 97
1993 106
1994 106
1995 86
1996 83
1997 92
1998 99
1999 100
2000 150
2001 143
2002 135
2003 179
2004 175
2005 181
2006 199
2007 230
2008 235
2009 241
2010 259
2011 311
2012 317
2013 349
2014 446
2015 409
2016 436
2017 445
2018 482
2019 469
2020 535
2021 565
2022 625
2023 619
2024 195

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9,420 results

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Page 1
Algebra, Geometry and Topology of ERK Kinetics.
Marsh L, Dufresne E, Byrne HM, Harrington HA. Marsh L, et al. Bull Math Biol. 2022 Oct 23;84(12):137. doi: 10.1007/s11538-022-01088-2. Bull Math Biol. 2022. PMID: 36273372 Free PMC article.
The experimental dataset is a time-course of ERK measurements in different phosphorylation states following activation of either wild-type MEK or MEK mutations associated with cancer or developmental defects. We demonstrate how methods from computational algebraic geometry …
The experimental dataset is a time-course of ERK measurements in different phosphorylation states following activation of either wild-type M …
Algebra dissociates from arithmetic in the brain semantic network.
Cheng D, Li M, Cui J, Wang L, Wang N, Ouyang L, Wang X, Bai X, Zhou X. Cheng D, et al. Behav Brain Funct. 2022 Jan 7;18(1):1. doi: 10.1186/s12993-022-00186-4. Behav Brain Funct. 2022. PMID: 34996499 Free PMC article.
BACKGROUND: Mathematical expressions mainly include arithmetic (such as 8 - (1 + 3)) and algebra (such as a - (b + c)). Previous studies have shown that both algebraic processing and arithmetic involved the bilateral parietal brain regions. Although previous studies …
BACKGROUND: Mathematical expressions mainly include arithmetic (such as 8 - (1 + 3)) and algebra (such as a - (b + c)). Previous stud …
Persistent Tor-algebra for protein-protein interaction analysis.
Liu X, Feng H, Lü Z, Xia K. Liu X, et al. Brief Bioinform. 2023 Mar 19;24(2):bbad046. doi: 10.1093/bib/bbad046. Brief Bioinform. 2023. PMID: 36790858
Even with the gigantic amount of PPI models from graphs, networks, geometry and topology, it remains as a great challenge to design functional models that efficiently characterize the complicated multiphysical information within PPIs. Here we propose persistent Tor-algebra …
Even with the gigantic amount of PPI models from graphs, networks, geometry and topology, it remains as a great challenge to design function …
Algebra of diffeomorphism-invariant observables in Jackiw-Teitelboim gravity.
Harlow D, Wu JQ. Harlow D, et al. J High Energy Phys. 2022;2022(5):97. doi: 10.1007/JHEP05(2022)097. Epub 2022 May 16. J High Energy Phys. 2022. PMID: 35602930 Free PMC article.
In this paper we use the covariant Peierls bracket to compute the algebra of a sizable number of diffeomorphism-invariant observables in classical Jackiw-Teitelboim gravity coupled to fairly arbitrary matter. We then show that many recent results, including the constructio …
In this paper we use the covariant Peierls bracket to compute the algebra of a sizable number of diffeomorphism-invariant observables …
The linear framework: using graph theory to reveal the algebra and thermodynamics of biomolecular systems.
Nam KM, Martinez-Corral R, Gunawardena J. Nam KM, et al. Interface Focus. 2022 Jun 10;12(4):20220013. doi: 10.1098/rsfs.2022.0013. eCollection 2022 Aug 6. Interface Focus. 2022. PMID: 35860006 Free PMC article. Review.
The key advantage of the framework has been that steady states are determined as rational algebraic functions of the labels by the Matrix-Tree theorems of graph theory. ...
The key advantage of the framework has been that steady states are determined as rational algebraic functions of the labels by the Ma …
Tensor-tensor algebra for optimal representation and compression of multiway data.
Kilmer ME, Horesh L, Avron H, Newman E. Kilmer ME, et al. Proc Natl Acad Sci U S A. 2021 Jul 13;118(28):e2015851118. doi: 10.1073/pnas.2015851118. Proc Natl Acad Sci U S A. 2021. PMID: 34234014 Free PMC article.
Since such optimality properties can be proven in both matrix and tensor-based algebras, a fundamental question arises: Does the tensor construct subsume the matrix construct in terms of representation efficiency? ...
Since such optimality properties can be proven in both matrix and tensor-based algebras, a fundamental question arises: Does the tens …
Pseudo-loop conditions.
Gillibert P, Jonušas J, Pinsker M. Gillibert P, et al. Bull Lond Math Soc. 2019 Oct;51(5):917-936. doi: 10.1112/blms.12286. Epub 2019 Sep 12. Bull Lond Math Soc. 2019. PMID: 32051650 Free PMC article.
About a decade ago, it was realised that the satisfaction of a given identity (or equation) of the form f(x1, , xn) f(y1, , yn) in an algebra is equivalent to the algebra forcing a loop into any graph on which it acts and which contains a certain finite subgraph ass …
About a decade ago, it was realised that the satisfaction of a given identity (or equation) of the form f(x1, , xn) f(y1, , yn) in an alg …
Predicting Middle School Profiles of Algebra Performance Using Fraction Knowledge.
Barbieri CA, Young LK, Newton KJ, Booth JL. Barbieri CA, et al. Child Dev. 2021 Sep;92(5):1984-2005. doi: 10.1111/cdev.13568. Epub 2021 Apr 30. Child Dev. 2021. PMID: 33929044
Fraction knowledge and algebraic skill are closely linked. Algebra is a gatekeeper for advanced courses (Booth & Newton, 2012; Brown & Quinn, 2007). ...Notably, fraction number line estimation did not predict algebra performance on any of the four mea …
Fraction knowledge and algebraic skill are closely linked. Algebra is a gatekeeper for advanced courses (Booth & Newton, 2 …
Determining Feynman Integrals with Only Input from Linear Algebra.
Liu ZF, Ma YQ. Liu ZF, et al. Phys Rev Lett. 2022 Nov 23;129(22):222001. doi: 10.1103/PhysRevLett.129.222001. Phys Rev Lett. 2022. PMID: 36493441
Therefore, FI computation is conceptually changed to a linear algebraic problem. Examples up to five loops are given to verify this observation. ...
Therefore, FI computation is conceptually changed to a linear algebraic problem. Examples up to five loops are given to verify this o …
Destructive relativity.
Przybylska M, Szumiński W, Maciejewski AJ. Przybylska M, et al. Chaos. 2023 Jun 1;33(6):063156. doi: 10.1063/5.0140633. Chaos. 2023. PMID: 37368038
If Hamilton equations are integrable in the Liouville sense, then eigenvalues of the scaled Hessian matrix gamma-1V"(d) at any non-zero solution d of the algebraic system V'(d)=gammad must be integer numbers of appropriate form depending on k. ...The obtained integrability …
If Hamilton equations are integrable in the Liouville sense, then eigenvalues of the scaled Hessian matrix gamma-1V"(d) at any non-zero solu …
9,420 results