Edit Profile (opens in new tab) Diao, Yuanan Co-Author Distance Author ID: diao.yuanan Published as: Diao, Yuanan; Diao, Y. Documents Indexed: 107 Publications since 1993, including 4 Additional arXiv Preprints Co-Authors: 53 Co-Authors with 97 Joint Publications 1,082 Co-Co-Authors all top 5 Co-Authors 9 single-authored 37 Ernst, Claus 18 Dai, Xingde 16 Arsuaga, Javier 16 Ziegler, Uta 12 Hinson, Kenneth 11 Hetyei, Gábor 9 Gu, Qing 7 Janse van Rensburg, Esaias J. 7 Li, Zhongyan 6 Han, Deguang 6 Montemayor, Anthony 5 Liu, Pengyu 5 Scharein, Robert G. 5 Stasiak, Andrzej 4 Rawdon, Eric J. 4 Vazquez, Mariel 3 Blackstone, T. 3 Dobay, Akos 3 Guo, Xunxiang 3 Sun, Yanqing 2 Borgo, B. 2 Cheng, Xiaosheng 2 Ishihara, Kai 2 Karadayi, Enver 2 Klingbeil, M. 2 Ray, Dawn 2 Saito, Masahico 2 Shimokawa, Koya 1 Ascigil, O. 1 Deng, Qingying 1 Denne, Elizabeth 1 Dubochet, Jacques 1 Finney, Michael Lee 1 High, D. 1 Huang, Wei 1 Ibrahim, L. 1 Kavuluru, V. 1 Kusner, Robert B. 1 Millett, Kenneth C. 1 Morton, Hugh R. 1 Nardo, J. C. 1 Pippenger, Nicholas J. 1 Polischuk, R. 1 Pór, Attila 1 Portillo, Javier I. 1 Reiter, Philipp 1 Saarinen, Sirpa 1 Sullivan, John Matthew 1 Sumners, De Witt L. 1 Sun, Shan 1 Thistlethwaite, Morwen B. 1 Xin, Jianguo 1 Yu, Xingxing all top 5 Serials 23 Journal of Knot Theory and its Ramifications 18 Journal of Physics A: Mathematical and Theoretical 4 Proceedings of the American Mathematical Society 4 Topology and its Applications 3 Mathematical Proceedings of the Cambridge Philosophical Society 3 Journal of Physics A: Mathematical and General 2 Journal of Mathematical Biology 2 Journal of Statistical Physics 2 Illinois Journal of Mathematics 2 Journal of Computational and Applied Mathematics 2 Acta Applicandae Mathematicae 2 Combinatorics, Probability and Computing 2 The Journal of Fourier Analysis and Applications 2 International Journal of Pure and Applied Mathematics 2 Computational and Mathematical Biophysics 1 Discrete Mathematics 1 Journal of Mathematical Analysis and Applications 1 Applied Mathematics and Computation 1 Journal of Functional Analysis 1 European Journal of Combinatorics 1 Kobe Journal of Mathematics 1 Graphs and Combinatorics 1 JCMCC. The Journal of Combinatorial Mathematics and Combinatorial Computing 1 SIAM Journal on Discrete Mathematics 1 Communications in Statistics. Theory and Methods 1 Experimental Mathematics 1 Geometry & Topology 1 JP Journal of Geometry and Topology 1 Journal of Applied Functional Analysis 1 International Journal of Contemporary Mathematical Sciences 1 Computational & Mathematical Methods in Medicine 1 Science China. Mathematics all top 5 Fields 71 Manifolds and cell complexes (57-XX) 23 Biology and other natural sciences (92-XX) 20 Harmonic analysis on Euclidean spaces (42-XX) 15 Probability theory and stochastic processes (60-XX) 10 Combinatorics (05-XX) 10 Statistical mechanics, structure of matter (82-XX) 8 Functional analysis (46-XX) 4 Computer science (68-XX) 3 Operator theory (47-XX) 3 Convex and discrete geometry (52-XX) 3 Differential geometry (53-XX) 2 General and overarching topics; collections (00-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Statistics (62-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Quantum theory (81-XX) 1 Astronomy and astrophysics (85-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 91 Publications have been cited 648 times in 285 Documents Cited by ▼ Year ▼ Frame wavelets in subspaces of \(L^2(\mathbb R^d)\). Zbl 1004.42025 Dai, X.; Diao, Y.; Gu, Q.; Han, D. 37 2002 Minimal knotted polygons on the cubic lattice. Zbl 0797.57004 Diao, Yuanan 31 1993 The knotting of equilateral polygons in \(\mathbb{R}^ 3\). Zbl 0846.57004 Diao, Yuanan 26 1995 On random knots. Zbl 0846.57003 Diao, Yuanan; Pippenger, Nicholas; Sumners, De Witt 25 1994 The existence of subspace wavelet sets. Zbl 1016.42020 Dai, X.; Diao, Y.; Gu, Q.; Han, D. 23 2003 Thickness of knots. Zbl 0924.57010 Diao, Y.; Ernst, C.; Janse van Rensburg, E. J. 22 1999 Subspaces with normalized tight frame wavelets in \(\mathbb{R}\). Zbl 1004.42024 Dai, Xingde; Diao, Yuanan; Gu, Qing 21 2002 The complexity of lattice knots. Zbl 0924.57007 Diao, Y.; Ernst, C. 19 1998 Frame wavelet sets in \(\mathbb{R}\). Zbl 0973.42029 Dai, X.; Diao, Y.; Gu, Q. 16 2001 Linking of uniform random polygons in confined spaces. Zbl 1123.57005 Arsuaga, J.; Blackstone, T.; Diao, Y.; Karadayi, E.; Saito, M. 15 2007 Bounds for the minimum step number of knots in the simple cubic lattice. Zbl 1185.82070 Scharein, R.; Ishihara, K.; Arsuaga, J.; Diao, Y.; Shimokawa, K.; Vazquez, M. 14 2009 Quadrisecants give new lower bounds for the ropelength of a knot. Zbl 1108.57004 Denne, Elizabeth; Diao, Yuanan; Sullivan, John M. 13 2006 The s-elementary frame wavelets are path connected. Zbl 1053.46054 Dai, X.; Diao, Y.; Gu, Q.; Han, D. 12 2004 Multipliers, phases and connectivity of MRA wavelets in \(L^{2}(\mathbb R^{2})\). Zbl 1197.42018 Li, Zhongyan; Dai, Xingde; Diao, Yuanan; Xin, Jianguo 12 2010 The lower bounds of the lengths of thick knots. Zbl 1028.57007 Diao, Yuanan 12 2003 Tutte polynomials of tensor products of signed graphs and their applications in knot theory. Zbl 1185.05083 Diao, Y.; Hetyei, G.; Hinson, K. 11 2009 Knot energies by ropes. Zbl 0889.57005 Diao, Y.; Ernst, C.; Janse van Rensburg, E. J. 11 1997 The number of smallest knots on the cubic lattice. Zbl 0834.57004 Diao, Yuanan 11 1994 The linear growth in the lengths of a family of thick knots. Zbl 1046.57006 Diao, Y.; Ernst, C.; Thistlethwaite, M. 11 2003 Frame wavelet sets in \({\mathbb{R}}^{d}\). Zbl 1021.42019 Dai, X.; Diao, Y.; Gu, Q.; Han, D. 11 2003 Hamiltonian knot projections and lengths of thick knots. Zbl 1040.57004 Diao, Yuanan; Ernst, Claus; Yu, Xingxing 11 2004 The additivity of crossing numbers. Zbl 1061.57009 Diao, Yuanan 10 2004 Nullification of knots and links. Zbl 1241.57005 Diao, Yuanan; Ernst, Claus; Montemayor, Anthony 10 2012 Upper bounds on linking numbers of thick lines. Zbl 0998.57013 Diao, Y.; Ernst, C.; Janse van Rensburg, E. J. 9 2002 Generating equilateral random polygons in confinement. II. Zbl 1320.60033 Diao, Y.; Ernst, C.; Montemayor, A.; Ziegler, U. 9 2012 The average crossing number of equilateral random polygons. Zbl 1052.57006 Diao, Y.; Dobay, A.; Kusner, R. B.; Millett, K.; Stasiak, A. 8 2003 Frame wavelets with frame set support in the frequency domain. Zbl 1063.42025 Dai, Xingde; Diao, Yuanan; Gu, Qing 7 2004 Generating equilateral random polygons in confinement. Zbl 1229.57004 Diao, Y.; Ernst, C.; Montemayor, A.; Ziegler, U. 7 2011 The path-connectivity of MRA wavelets in \(L^2(\mathbb R^d)\). Zbl 1238.42019 Li, Zhongyan; Dai, Xingde; Diao, Yuanan; Huang, Wei 7 2010 Jones polynomial of knots formed by repeated tangle replacement operations. Zbl 1207.57010 Diao, Y.; Ernst, C.; Ziegler, U. 7 2009 Wavelets with frame multiresolution analysis. Zbl 1030.42028 Dai, X.; Diao, Y.; Gu, Q.; Han, D. 7 2003 Generating equilateral random polygons in confinement. III. Zbl 1320.60034 Diao, Y.; Ernst, C.; Montemayor, A.; Ziegler, U. 7 2012 Global knotting in equilateral random polygons. Zbl 1001.57026 Diao, Y.; Nardo, J. C.; Sun, Y. 6 2001 Numerical upper bounds on ropelengths of large physical knots. Zbl 1092.57004 Diao, Y.; Ernst, C.; Kavuluru, V.; Ziegler, U. 6 2006 A fast ergodic algorithm for generating ensembles of equilateral random polygons. Zbl 1158.92019 Varela, R.; Hinson, K.; Arsuaga, J.; Diao, Y. 6 2009 On super-wavelets. Zbl 1079.42026 Gu, Q.; Dai, X.; Diao, Y. 6 2004 On the mean and variance of the writhe of random polygons. Zbl 1223.57011 Portillo, J.; Diao, Y.; Scharein, R.; Arsuaga, J.; Vazquez, M. 6 2011 Sampling large random knots in a confined space. Zbl 1133.57004 Arsuaga, J.; Blackstone, T.; Diao, Y.; Hinson, K.; Karadayi, E.; Saito, M. 6 2007 The path-connectivity of \(s\)-elementary tight frame wavelets. Zbl 1282.42034 Dai, Xingde; Diao, Yuanan 6 2007 The braid index of reduced alternating links. Zbl 1446.57002 Diao, Yuanan; Hetyei, Gábor; Liu, Pengyu 6 2020 The knot spectrum of confined random equilateral polygons. Zbl 1412.92086 Diao, Y.; Ernst, C.; Montemayor, A.; Rawdon, E.; Ziegler, U. 5 2014 Unsplittability of random links. Zbl 0838.57004 Diao, Yuanan 5 1994 Weyl-Heisenberg frame wavelets with basic supports. Zbl 1151.42315 Guo, Xunxiang; Diao, Yuanan; Dai, Xingde 5 2006 The effects of density on the topological structure of the mitochondrial DNA from trypanosomes. Zbl 1311.92145 Diao, Y.; Hinson, K.; Kaplan, R.; Vazquez, M.; Arsuaga, J. 5 2012 The linearity of the ropelengths of Conway algebraic knots in terms of their crossing numbers. Zbl 1261.57002 Diao, Yuanan; Ernst, Claus; Ziegler, Uta 5 2011 A partial ordering of knots and links through diagrammatic unknotting. Zbl 1200.57004 Diao, Yuanan; Ernst, Claus; Stasiak, Andrzej 5 2009 The mean squared writhe of alternating random knot diagrams. Zbl 1210.57005 Diao, Y.; Ernst, C.; Hinson, K.; Ziegler, U. 5 2010 Relative Tutte polynomials for coloured graphs and virtual knot theory. Zbl 1202.05064 Diao, Y.; Hetyei, G. 5 2010 The ropelengths of knots are almost linear in terms of their crossing numbers. Zbl 1441.57006 Diao, Yuanan; Ernst, Claus; Por, Attila; Ziegler, Uta 5 2019 Total curvature, ropelength and crossing number of thick knots. Zbl 1158.57007 Diao, Y.; Ernst, C. 5 2007 A diagrammatic approach for determining the braid index of alternating links. Zbl 1472.57003 Diao, Yuanan; Ernst, Claus; Hetyei, Gabor; Liu, Pengyu 5 2021 Generating random walks and polygons with stiffness in confinement. Zbl 1318.60051 Diao, Y.; Ernst, C.; Saarinen, S.; Ziegler, U. 4 2015 Properties of knot energies. Zbl 0932.57009 Diao, Y.; Ernst, C.; Janse van Rensburg, E. J. 4 1998 Percolation of linked circles. Zbl 0932.57011 Diao, Y.; Janse van Rensburg, E. J. 4 1998 In search of a good polygonal knot energy. Zbl 0889.57004 Diao, Y.; Ernst, C.; Janse van Rensburg, E. J. 4 1997 Generating large random knot projections. Zbl 1106.57005 Diao, Yuanan; Ernst, Claus; Ziegler, Uta 4 2005 On \(s\)-elementary super frame wavelets and their path-connectedness. Zbl 1226.42023 Diao, Yuanan; Li, Zhongyan 4 2011 DNA knotting in spooling like conformations in bacteriophages. Zbl 1160.92017 Arsuaga, J.; Diao, Y. 4 2008 The path-connectivity of \(s\)-elementary frame wavelets with frame MRA. Zbl 1175.42019 Dai, Xingde; Diao, Yuanan; Li, Zhongyan 4 2009 Realizable powers of ropelengths by non-trivial knot families. Zbl 1067.57002 Diao, Yuanan; Ernst, Claus 4 2004 Smooth quantile processes from right censored data and construction of simultaneous confidence bands. Zbl 1009.62536 Sun, Yanqing; Sun, Shan; Diao, Yuanan 3 2001 The minimum of knot energy functions. Zbl 0999.57011 Dai, Xingde; Diao, Yuanan 3 2000 Hamiltonian cycles and rope lengths of Conway algebraic knots. Zbl 1088.57005 Diao, Yuanan; Ernst, Claus 3 2006 The knot spectrum of random knot spaces. Zbl 1420.57019 Diao, Yuanan; Ernst, Claus; Ziegler, Uta; Rawdon, Eric J. 3 2018 The average inter-crossing number of equilateral random walks and polygons. Zbl 1100.82009 Diao, Y.; Dobay, A.; Stasiak, A. 3 2005 The growth of the mean average crossing number of equilateral polygons in confinement. Zbl 1182.92026 Arsuaga, J.; Borgo, B.; Diao, Y.; Scharein, R. 3 2009 Invariants of composite networks arising as a tensor product. Zbl 1221.05134 Diao, Y.; Hetyei, G.; Hinson, K. 3 2009 The effect of angle restriction on the topological characteristics of minicircle networks. Zbl 1235.82103 Arsuaga, J.; Diao, Y.; Hinson, K. 3 2012 Total curvature and total torsion of knotted random polygons in confinement. Zbl 1422.57019 Diao, Yuanan; Ernst, Claus; Rawdon, Eric J.; Ziegler, Uta 2 2018 Knots with minimal energies. Zbl 0945.57005 Diao, Y.; Ernst, C.; Janse van Rensburg, E. J. 2 1998 Relative frequencies of alternating and nonalternating prime knots and composite knots in random knot spaces. Zbl 1420.57018 Diao, Yuanan; Ernst, Claus; Rawdon, Eric J.; Ziegler, Uta 2 2018 The average crossing number of Gaussian random walks and polygons. Zbl 1104.57005 Diao, Yuanan; Ernst, Claus 2 2005 Braid index bounds ropelength from below. Zbl 1439.57009 Diao, Yuanan 2 2020 Knots with equal bridge index and braid index. Zbl 07478464 Diao, Yuanan; Ernst, Claus; Reiter, Philipp 2 2021 The growth of minicircle networks on regular lattices. Zbl 1234.92022 Diao, Y.; Hinson, K.; Arsuaga, J. 2 2012 Bounds for the minimum step number of knots confined to slabs in the simple cubic lattice. Zbl 1259.82142 Ishihara, K.; Scharein, R.; Diao, Y.; Arsuaga, J.; Vazquez, M.; Shimokawa, K. 2 2012 Intrinsic \(s\)-elementary Parseval frame multiwavelets in \(L^2(\mathbb R^d)\). Zbl 1192.42023 Li, Zhongyan; Dai, Xingde; Diao, Yuanan 2 2010 Invariants of rational links represented by reduced alternating diagrams. Zbl 07267542 Diao, Yuanan; Ernst, Claus; Hetyei, Gábor 2 2020 The crossing numbers of thick knots and links. Zbl 1014.57006 Diao, Yuanan; Ernst, Claus 1 2002 Properties of topological networks of flexible polygonal chains. Zbl 1412.92235 Arsuaga, J.; Diao, Y.; Klingbeil, M.; Rodriguez, V. 1 2014 Estimating properties of kinetoplast DNA by fragmentation reactions. Zbl 1422.92105 Ibrahim, L.; Liu, P.; Klingbeil, M.; Diao, Y.; Arsuaga, J. 1 2019 Scaling of the average crossing number in equilateral random walks, knots and proteins. Zbl 1092.92016 Dobay, Akos; Dubochet, Jacques; Stasiak, Andrzej; Diao, Yuanan 1 2005 Modeling of chromosome intermingling by partially overlapping uniform random polygons. Zbl 1303.92026 Blackstone, T.; Scharein, R.; Borgo, B.; Varela, R.; Diao, Y.; Arsuaga, J. 1 2011 Curvature of random walks and random polygons in confinement. Zbl 1277.82050 Diao, Y.; Ernst, C.; Montemayor, A.; Ziegler, U. 1 2013 The growth rate of some deficiency zero knot classes. Zbl 1083.57006 Diao, Yuanan; Ernst, Claus 1 2005 Configurations of DNA cages based on plane graphs and vertex junctions. Zbl 1519.92156 Cheng, Xiao-Sheng; Diao, Yuanan 1 2020 Writhe-like invariants of alternating links. Zbl 1464.57001 Diao, Yuanan; Pham, Van 1 2021 The HOMFLY polynomial of links in closed braid form. Zbl 1405.57022 Liu, Pengyu; Diao, Yuanan; Hetyei, Gábor 1 2019 Ropelengths of closed braids. Zbl 1129.57008 Diao, Yuanan; Ernst, Claus 1 2007 The average genus of oriented rational links with a given crossing number. Zbl 1518.57011 Ray, Dawn; Diao, Yuanan 1 2023 The number of oriented rational links with a given deficiency number. Zbl 1481.57009 Diao, Yuanan; Finney, Michael Lee; Ray, Dawn 1 2021 The average genus of oriented rational links with a given crossing number. Zbl 1518.57011 Ray, Dawn; Diao, Yuanan 1 2023 A diagrammatic approach for determining the braid index of alternating links. Zbl 1472.57003 Diao, Yuanan; Ernst, Claus; Hetyei, Gabor; Liu, Pengyu 5 2021 Knots with equal bridge index and braid index. Zbl 07478464 Diao, Yuanan; Ernst, Claus; Reiter, Philipp 2 2021 Writhe-like invariants of alternating links. Zbl 1464.57001 Diao, Yuanan; Pham, Van 1 2021 The number of oriented rational links with a given deficiency number. Zbl 1481.57009 Diao, Yuanan; Finney, Michael Lee; Ray, Dawn 1 2021 The braid index of reduced alternating links. Zbl 1446.57002 Diao, Yuanan; Hetyei, Gábor; Liu, Pengyu 6 2020 Braid index bounds ropelength from below. Zbl 1439.57009 Diao, Yuanan 2 2020 Invariants of rational links represented by reduced alternating diagrams. Zbl 07267542 Diao, Yuanan; Ernst, Claus; Hetyei, Gábor 2 2020 Configurations of DNA cages based on plane graphs and vertex junctions. Zbl 1519.92156 Cheng, Xiao-Sheng; Diao, Yuanan 1 2020 The ropelengths of knots are almost linear in terms of their crossing numbers. Zbl 1441.57006 Diao, Yuanan; Ernst, Claus; Por, Attila; Ziegler, Uta 5 2019 Estimating properties of kinetoplast DNA by fragmentation reactions. Zbl 1422.92105 Ibrahim, L.; Liu, P.; Klingbeil, M.; Diao, Y.; Arsuaga, J. 1 2019 The HOMFLY polynomial of links in closed braid form. Zbl 1405.57022 Liu, Pengyu; Diao, Yuanan; Hetyei, Gábor 1 2019 The knot spectrum of random knot spaces. Zbl 1420.57019 Diao, Yuanan; Ernst, Claus; Ziegler, Uta; Rawdon, Eric J. 3 2018 Total curvature and total torsion of knotted random polygons in confinement. Zbl 1422.57019 Diao, Yuanan; Ernst, Claus; Rawdon, Eric J.; Ziegler, Uta 2 2018 Relative frequencies of alternating and nonalternating prime knots and composite knots in random knot spaces. Zbl 1420.57018 Diao, Yuanan; Ernst, Claus; Rawdon, Eric J.; Ziegler, Uta 2 2018 Generating random walks and polygons with stiffness in confinement. Zbl 1318.60051 Diao, Y.; Ernst, C.; Saarinen, S.; Ziegler, U. 4 2015 The knot spectrum of confined random equilateral polygons. Zbl 1412.92086 Diao, Y.; Ernst, C.; Montemayor, A.; Rawdon, E.; Ziegler, U. 5 2014 Properties of topological networks of flexible polygonal chains. Zbl 1412.92235 Arsuaga, J.; Diao, Y.; Klingbeil, M.; Rodriguez, V. 1 2014 Curvature of random walks and random polygons in confinement. Zbl 1277.82050 Diao, Y.; Ernst, C.; Montemayor, A.; Ziegler, U. 1 2013 Nullification of knots and links. Zbl 1241.57005 Diao, Yuanan; Ernst, Claus; Montemayor, Anthony 10 2012 Generating equilateral random polygons in confinement. II. Zbl 1320.60033 Diao, Y.; Ernst, C.; Montemayor, A.; Ziegler, U. 9 2012 Generating equilateral random polygons in confinement. III. Zbl 1320.60034 Diao, Y.; Ernst, C.; Montemayor, A.; Ziegler, U. 7 2012 The effects of density on the topological structure of the mitochondrial DNA from trypanosomes. Zbl 1311.92145 Diao, Y.; Hinson, K.; Kaplan, R.; Vazquez, M.; Arsuaga, J. 5 2012 The effect of angle restriction on the topological characteristics of minicircle networks. Zbl 1235.82103 Arsuaga, J.; Diao, Y.; Hinson, K. 3 2012 The growth of minicircle networks on regular lattices. Zbl 1234.92022 Diao, Y.; Hinson, K.; Arsuaga, J. 2 2012 Bounds for the minimum step number of knots confined to slabs in the simple cubic lattice. Zbl 1259.82142 Ishihara, K.; Scharein, R.; Diao, Y.; Arsuaga, J.; Vazquez, M.; Shimokawa, K. 2 2012 Generating equilateral random polygons in confinement. Zbl 1229.57004 Diao, Y.; Ernst, C.; Montemayor, A.; Ziegler, U. 7 2011 On the mean and variance of the writhe of random polygons. Zbl 1223.57011 Portillo, J.; Diao, Y.; Scharein, R.; Arsuaga, J.; Vazquez, M. 6 2011 The linearity of the ropelengths of Conway algebraic knots in terms of their crossing numbers. Zbl 1261.57002 Diao, Yuanan; Ernst, Claus; Ziegler, Uta 5 2011 On \(s\)-elementary super frame wavelets and their path-connectedness. Zbl 1226.42023 Diao, Yuanan; Li, Zhongyan 4 2011 Modeling of chromosome intermingling by partially overlapping uniform random polygons. Zbl 1303.92026 Blackstone, T.; Scharein, R.; Borgo, B.; Varela, R.; Diao, Y.; Arsuaga, J. 1 2011 Multipliers, phases and connectivity of MRA wavelets in \(L^{2}(\mathbb R^{2})\). Zbl 1197.42018 Li, Zhongyan; Dai, Xingde; Diao, Yuanan; Xin, Jianguo 12 2010 The path-connectivity of MRA wavelets in \(L^2(\mathbb R^d)\). Zbl 1238.42019 Li, Zhongyan; Dai, Xingde; Diao, Yuanan; Huang, Wei 7 2010 The mean squared writhe of alternating random knot diagrams. Zbl 1210.57005 Diao, Y.; Ernst, C.; Hinson, K.; Ziegler, U. 5 2010 Relative Tutte polynomials for coloured graphs and virtual knot theory. Zbl 1202.05064 Diao, Y.; Hetyei, G. 5 2010 Intrinsic \(s\)-elementary Parseval frame multiwavelets in \(L^2(\mathbb R^d)\). Zbl 1192.42023 Li, Zhongyan; Dai, Xingde; Diao, Yuanan 2 2010 Bounds for the minimum step number of knots in the simple cubic lattice. Zbl 1185.82070 Scharein, R.; Ishihara, K.; Arsuaga, J.; Diao, Y.; Shimokawa, K.; Vazquez, M. 14 2009 Tutte polynomials of tensor products of signed graphs and their applications in knot theory. Zbl 1185.05083 Diao, Y.; Hetyei, G.; Hinson, K. 11 2009 Jones polynomial of knots formed by repeated tangle replacement operations. Zbl 1207.57010 Diao, Y.; Ernst, C.; Ziegler, U. 7 2009 A fast ergodic algorithm for generating ensembles of equilateral random polygons. Zbl 1158.92019 Varela, R.; Hinson, K.; Arsuaga, J.; Diao, Y. 6 2009 A partial ordering of knots and links through diagrammatic unknotting. Zbl 1200.57004 Diao, Yuanan; Ernst, Claus; Stasiak, Andrzej 5 2009 The path-connectivity of \(s\)-elementary frame wavelets with frame MRA. Zbl 1175.42019 Dai, Xingde; Diao, Yuanan; Li, Zhongyan 4 2009 The growth of the mean average crossing number of equilateral polygons in confinement. Zbl 1182.92026 Arsuaga, J.; Borgo, B.; Diao, Y.; Scharein, R. 3 2009 Invariants of composite networks arising as a tensor product. Zbl 1221.05134 Diao, Y.; Hetyei, G.; Hinson, K. 3 2009 DNA knotting in spooling like conformations in bacteriophages. Zbl 1160.92017 Arsuaga, J.; Diao, Y. 4 2008 Linking of uniform random polygons in confined spaces. Zbl 1123.57005 Arsuaga, J.; Blackstone, T.; Diao, Y.; Karadayi, E.; Saito, M. 15 2007 Sampling large random knots in a confined space. Zbl 1133.57004 Arsuaga, J.; Blackstone, T.; Diao, Y.; Hinson, K.; Karadayi, E.; Saito, M. 6 2007 The path-connectivity of \(s\)-elementary tight frame wavelets. Zbl 1282.42034 Dai, Xingde; Diao, Yuanan 6 2007 Total curvature, ropelength and crossing number of thick knots. Zbl 1158.57007 Diao, Y.; Ernst, C. 5 2007 Ropelengths of closed braids. Zbl 1129.57008 Diao, Yuanan; Ernst, Claus 1 2007 Quadrisecants give new lower bounds for the ropelength of a knot. Zbl 1108.57004 Denne, Elizabeth; Diao, Yuanan; Sullivan, John M. 13 2006 Numerical upper bounds on ropelengths of large physical knots. Zbl 1092.57004 Diao, Y.; Ernst, C.; Kavuluru, V.; Ziegler, U. 6 2006 Weyl-Heisenberg frame wavelets with basic supports. Zbl 1151.42315 Guo, Xunxiang; Diao, Yuanan; Dai, Xingde 5 2006 Hamiltonian cycles and rope lengths of Conway algebraic knots. Zbl 1088.57005 Diao, Yuanan; Ernst, Claus 3 2006 Generating large random knot projections. Zbl 1106.57005 Diao, Yuanan; Ernst, Claus; Ziegler, Uta 4 2005 The average inter-crossing number of equilateral random walks and polygons. Zbl 1100.82009 Diao, Y.; Dobay, A.; Stasiak, A. 3 2005 The average crossing number of Gaussian random walks and polygons. Zbl 1104.57005 Diao, Yuanan; Ernst, Claus 2 2005 Scaling of the average crossing number in equilateral random walks, knots and proteins. Zbl 1092.92016 Dobay, Akos; Dubochet, Jacques; Stasiak, Andrzej; Diao, Yuanan 1 2005 The growth rate of some deficiency zero knot classes. Zbl 1083.57006 Diao, Yuanan; Ernst, Claus 1 2005 The s-elementary frame wavelets are path connected. Zbl 1053.46054 Dai, X.; Diao, Y.; Gu, Q.; Han, D. 12 2004 Hamiltonian knot projections and lengths of thick knots. Zbl 1040.57004 Diao, Yuanan; Ernst, Claus; Yu, Xingxing 11 2004 The additivity of crossing numbers. Zbl 1061.57009 Diao, Yuanan 10 2004 Frame wavelets with frame set support in the frequency domain. Zbl 1063.42025 Dai, Xingde; Diao, Yuanan; Gu, Qing 7 2004 On super-wavelets. Zbl 1079.42026 Gu, Q.; Dai, X.; Diao, Y. 6 2004 Realizable powers of ropelengths by non-trivial knot families. Zbl 1067.57002 Diao, Yuanan; Ernst, Claus 4 2004 The existence of subspace wavelet sets. Zbl 1016.42020 Dai, X.; Diao, Y.; Gu, Q.; Han, D. 23 2003 The lower bounds of the lengths of thick knots. Zbl 1028.57007 Diao, Yuanan 12 2003 The linear growth in the lengths of a family of thick knots. Zbl 1046.57006 Diao, Y.; Ernst, C.; Thistlethwaite, M. 11 2003 Frame wavelet sets in \({\mathbb{R}}^{d}\). Zbl 1021.42019 Dai, X.; Diao, Y.; Gu, Q.; Han, D. 11 2003 The average crossing number of equilateral random polygons. Zbl 1052.57006 Diao, Y.; Dobay, A.; Kusner, R. B.; Millett, K.; Stasiak, A. 8 2003 Wavelets with frame multiresolution analysis. Zbl 1030.42028 Dai, X.; Diao, Y.; Gu, Q.; Han, D. 7 2003 Frame wavelets in subspaces of \(L^2(\mathbb R^d)\). Zbl 1004.42025 Dai, X.; Diao, Y.; Gu, Q.; Han, D. 37 2002 Subspaces with normalized tight frame wavelets in \(\mathbb{R}\). Zbl 1004.42024 Dai, Xingde; Diao, Yuanan; Gu, Qing 21 2002 Upper bounds on linking numbers of thick lines. Zbl 0998.57013 Diao, Y.; Ernst, C.; Janse van Rensburg, E. J. 9 2002 The crossing numbers of thick knots and links. Zbl 1014.57006 Diao, Yuanan; Ernst, Claus 1 2002 Frame wavelet sets in \(\mathbb{R}\). Zbl 0973.42029 Dai, X.; Diao, Y.; Gu, Q. 16 2001 Global knotting in equilateral random polygons. Zbl 1001.57026 Diao, Y.; Nardo, J. C.; Sun, Y. 6 2001 Smooth quantile processes from right censored data and construction of simultaneous confidence bands. Zbl 1009.62536 Sun, Yanqing; Sun, Shan; Diao, Yuanan 3 2001 The minimum of knot energy functions. Zbl 0999.57011 Dai, Xingde; Diao, Yuanan 3 2000 Thickness of knots. Zbl 0924.57010 Diao, Y.; Ernst, C.; Janse van Rensburg, E. J. 22 1999 The complexity of lattice knots. Zbl 0924.57007 Diao, Y.; Ernst, C. 19 1998 Properties of knot energies. Zbl 0932.57009 Diao, Y.; Ernst, C.; Janse van Rensburg, E. J. 4 1998 Percolation of linked circles. Zbl 0932.57011 Diao, Y.; Janse van Rensburg, E. J. 4 1998 Knots with minimal energies. Zbl 0945.57005 Diao, Y.; Ernst, C.; Janse van Rensburg, E. J. 2 1998 Knot energies by ropes. Zbl 0889.57005 Diao, Y.; Ernst, C.; Janse van Rensburg, E. J. 11 1997 In search of a good polygonal knot energy. Zbl 0889.57004 Diao, Y.; Ernst, C.; Janse van Rensburg, E. J. 4 1997 The knotting of equilateral polygons in \(\mathbb{R}^ 3\). Zbl 0846.57004 Diao, Yuanan 26 1995 On random knots. Zbl 0846.57003 Diao, Yuanan; Pippenger, Nicholas; Sumners, De Witt 25 1994 The number of smallest knots on the cubic lattice. Zbl 0834.57004 Diao, Yuanan 11 1994 Unsplittability of random links. Zbl 0838.57004 Diao, Yuanan 5 1994 Minimal knotted polygons on the cubic lattice. Zbl 0797.57004 Diao, Yuanan 31 1993 all cited Publications top 5 cited Publications all top 5 Cited by 320 Authors 48 Diao, Yuanan 26 Li, Yunzhang 21 Ernst, Claus 13 Han, Deguang 12 Li, Zhongyan 12 Rawdon, Eric J. 11 Dai, Xingde 11 Whittington, Stuart G. 9 Orlandini, Enzo 8 Oh, Seungsang 7 Arsuaga, Javier 7 Cantarella, Jason H. 7 Gu, Qing 6 Hetyei, Gábor 6 Panagiotou, Eleni 6 Ziegler, Uta 5 Even-Zohar, Chaim 5 Janse van Rensburg, Esaias J. 5 Jia, HuiFang 5 Kim, Hyoungjun 5 Millett, Kenneth C. 5 No, Sungjong 5 Simon, Jonathan K. 5 Vazquez, Mariel 5 Zhang, Jianping 4 Bribiesca, Ernesto 4 Cohen, Moshe 4 Denne, Elizabeth 4 Durumeric, Oguz C. 4 Gabardo, Jean-Pierre 4 Hinson, Kenneth 4 Huh, Youngsik 4 Liu, Pengyu 4 Montemayor, Anthony 4 Reiter, Philipp 4 Shonkwiler, Clayton 4 Soteros, Christine E. 4 Yadav, G. C. S. 4 Zhou, Fengying 3 Hass, Joel 3 Hong, Kyungpyo 3 Hu, Guoen 3 Jin, Xian’an 3 Kanenobu, Taizo 3 Liu, Zhanwei 3 Madras, Neal 3 Moriuchi, Hiromasa 3 Rechnitzer, Andrew Daniel 3 Shi, Xianliang 3 Sullivan, John Matthew 3 Sumners, De Witt L. 3 Wu, Guochang 3 Yu, Xiaojiang 3 Zhang, Yan 3 Zhao, Jing 2 Ahmad, Owais 2 Atapour, Mahshid 2 Bonato, Anthony 2 Buck, Gregory R. 2 Butler, Clark 2 Cazet, Nicholas 2 Chapman, Harrison 2 Chmutov, Sergei V. 2 Deguchi, Tetsuo 2 Dennis, Mark R. 2 Dwivedi, Amita 2 Ferrari, Franco 2 Guo, Xunxiang 2 Hinojosa, Gabriela 2 Huang, Wei 2 Ishihara, Kai 2 Klingbeil, M. 2 Klotz, Alexander R. 2 Kozai, Kenji 2 Krishnan, Sunder Ram 2 Larson, David Royal 2 Linial, Nathan 2 Mann, Casey E. 2 Mcloud-Mann, Jennifer C. 2 Micheletti, Cristian 2 Moore, Allison H. 2 Nowik, Tahl 2 Pór, Attila 2 Ramírez Alfonsín, Jorge Luis 2 Ray, Dawn 2 San Antolín, Angel 2 Scharein, Robert G. 2 Scholtes, Sebastian 2 Sheikh, Neyaz Ahmad 2 Soto-Bajo, Moisés 2 Sumetkijakan, Songkiat 2 Taylor, Alexander John 2 Tian, Yu 2 von der Mosel, Heiko 2 Yang, Deyun 2 Yoo, Hyungkee 2 Zhang, Fuji 2 Zhang, Wei 2 Zhao, Yani 2 Zhou, Xingwei ...and 220 more Authors all top 5 Cited in 92 Serials 59 Journal of Knot Theory and its Ramifications 21 Journal of Physics A: Mathematical and Theoretical 18 Topology and its Applications 10 Proceedings of the American Mathematical Society 8 Journal of Statistical Physics 7 International Journal of Wavelets, Multiresolution and Information Processing 6 Acta Applicandae Mathematicae 6 Experimental Mathematics 5 Applied and Computational Harmonic Analysis 5 Science China. 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Condensed Matter and Complex Systems 2 Involve 2 Journal of Pseudo-Differential Operators and Applications 1 Archive for Rational Mechanics and Analysis 1 Communications on Pure and Applied Mathematics 1 Israel Journal of Mathematics 1 Journal of Mathematical Analysis and Applications 1 Linear and Multilinear Algebra 1 Nuclear Physics. B 1 Physics Reports 1 Reviews of Modern Physics 1 Bulletin of Mathematical Biology 1 Journal of Geometry and Physics 1 Canadian Mathematical Bulletin 1 Commentarii Mathematici Helvetici 1 Gaṇita 1 Illinois Journal of Mathematics 1 Inventiones Mathematicae 1 Journal of Approximation Theory 1 Journal of Statistical Planning and Inference 1 Mathematische Annalen 1 Memoirs of the American Mathematical Society 1 Results in Mathematics 1 Chinese Annals of Mathematics. Series B 1 Annals of Global Analysis and Geometry 1 Acta Mathematicae Applicatae Sinica. English Series 1 Discrete & Computational Geometry 1 Applied Mathematics Letters 1 SIAM Journal on Discrete Mathematics 1 The Annals of Applied Probability 1 Computational Geometry 1 Differential Geometry and its Applications 1 The Journal of Geometric Analysis 1 Communications in Statistics. Theory and Methods 1 Linear Algebra and its Applications 1 Applied Mathematics. Series B (English Edition) 1 Russian Journal of Mathematical Physics 1 St. Petersburg Mathematical Journal 1 Doklady Mathematics 1 Abstract and Applied Analysis 1 Journal of Applied Statistics 1 Central European Journal of Mathematics 1 Complex Analysis and Operator Theory 1 Journal of Topology 1 Kyoto Journal of Mathematics 1 Symmetry 1 ISRN Algebra 1 Journal of Theoretical Biology 1 Problemy Analiza. Issues of Analysis 1 Journal of Mathematics 1 Molecular Based Mathematical Biology 1 Journal of Function Spaces 1 Arnold Mathematical Journal 1 Journal of Applied and Computational Topology 1 Algebraic Combinatorics all top 5 Cited in 33 Fields 154 Manifolds and cell complexes (57-XX) 88 Harmonic analysis on Euclidean spaces (42-XX) 41 Statistical mechanics, structure of matter (82-XX) 30 Combinatorics (05-XX) 27 Biology and other natural sciences (92-XX) 21 Differential geometry (53-XX) 21 Probability theory and stochastic processes (60-XX) 11 Functional analysis (46-XX) 9 Calculus of variations and optimal control; optimization (49-XX) 8 Convex and discrete geometry (52-XX) 7 Quantum theory (81-XX) 5 Operator theory (47-XX) 5 Global analysis, analysis on manifolds (58-XX) 5 Numerical analysis (65-XX) 5 Computer science (68-XX) 4 Geometry (51-XX) 4 Statistics (62-XX) 3 Group theory and generalizations (20-XX) 3 Approximations and expansions (41-XX) 3 Abstract harmonic analysis (43-XX) 3 Information and communication theory, circuits (94-XX) 2 Number theory (11-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Real functions (26-XX) 2 Partial differential equations (35-XX) 2 Mechanics of deformable solids (74-XX) 1 Mathematical logic and foundations (03-XX) 1 Associative rings and algebras (16-XX) 1 Special functions (33-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Algebraic topology (55-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX) Citations by Year