{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T15:20:16Z","timestamp":1767626416662,"version":"3.41.2"},"reference-count":56,"publisher":"AIP Publishing","issue":"10","funder":[{"DOI":"10.13039\/501100021171","name":"Basic and Applied Basic Research Foundation of Guangdong Province","doi-asserted-by":"publisher","award":["2024A1515011700"],"award-info":[{"award-number":["2024A1515011700"]}],"id":[{"id":"10.13039\/501100021171","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12171114"],"award-info":[{"award-number":["12171114"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12201133"],"award-info":[{"award-number":["12201133"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100021171","name":"Basic and Applied Basic Research Foundation of Guangdong Province","doi-asserted-by":"publisher","award":["2023A04J0365"],"award-info":[{"award-number":["2023A04J0365"]}],"id":[{"id":"10.13039\/501100021171","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Special fund for scientific research Talents of GPNU","award":["2021SDKYA029"],"award-info":[{"award-number":["2021SDKYA029"]}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2024,10,1]]},"abstract":"<jats:p>The scale-free trees are fundamental dynamics networks with extensive applications in material and engineering fields owing to their high reliability and low power consumption characteristics. Controlling and optimizing transport (search) efficiency on scale-free trees has attracted much attention. In this paper, we first introduce degree-dependent weighted tree by assigning each edge (x,y) a weight wxy=(dxdy)\u03b8, with dx and dy being the degree of nodes x and y, and \u03b8 being a controllable parameter. Then, we design a parameterized biased random walk strategy with the transition probability depending on the local information (the degree of neighboring nodes) and a parameter \u03b8. Finally, we evaluate analytically the global mean first-passage time, which is an important indicator for measuring the transport (search) efficiency on the underlying networks, and find the interval for parameter \u03b8 where transport (search) efficiency can be improved on a class of scale-free trees. We also analyze the (transfinite) walk dimension for our biased random walk on the scale-free trees and find one can obtain arbitrary transfinite walk dimension in an interval by properly tuning the biased parameter \u03b8. The results obtained here would shed light on controlling and optimizing transport (search) efficiency on objects with scale-free tree structures.<\/jats:p>","DOI":"10.1063\/5.0223595","type":"journal-article","created":{"date-parts":[[2024,10,21]],"date-time":"2024-10-21T17:16:34Z","timestamp":1729530994000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":1,"title":["Controlling and optimizing the transport (search) efficiency with local information on a class of scale-free trees"],"prefix":"10.1063","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-2182-4836","authenticated-orcid":false,"given":"Long","family":"Gao","sequence":"first","affiliation":[{"name":"School of Mathematical and Information Science, Guangzhou University 1 , Guangzhou 510006,","place":["China"]},{"name":"Guangdong Provincial Key Laboratory co-sponsored by province and city of Information Security Technology, Guangzhou University 2 , Guangzhou 510006,","place":["China"]},{"name":"Guangzhou Center for Applied Mathematics, Guangzhou University 3 , Guangzhou 510006,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8839-7070","authenticated-orcid":false,"given":"Junhao","family":"Peng","sequence":"additional","affiliation":[{"name":"School of Mathematical and Information Science, Guangzhou University 1 , Guangzhou 510006,","place":["China"]},{"name":"Guangdong Provincial Key Laboratory co-sponsored by province and city of Information Security Technology, Guangzhou University 2 , Guangzhou 510006,","place":["China"]},{"name":"Guangzhou Center for Applied Mathematics, Guangzhou University 3 , Guangzhou 510006,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7634-4705","authenticated-orcid":false,"given":"Chunming","family":"Tang","sequence":"additional","affiliation":[{"name":"School of Mathematical and Information Science, Guangzhou University 1 , Guangzhou 510006,","place":["China"]},{"name":"Guangdong Provincial Key Laboratory co-sponsored by province and city of Information Security Technology, Guangzhou University 2 , Guangzhou 510006,","place":["China"]},{"name":"Guangzhou Center for Applied Mathematics, Guangzhou University 3 , Guangzhou 510006,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qiuxia","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Systems Science, Guangdong Polytechnic Normal University 4 , Guangzhou 510665,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"317","published-online":{"date-parts":[[2024,10,21]]},"reference":[{"key":"2024102117162708800_c1","doi-asserted-by":"publisher","first-page":"509\u2013512","DOI":"10.1126\/science.286.5439.509","volume":"286","year":"1999","journal-title":"Science"},{"key":"2024102117162708800_c2","doi-asserted-by":"publisher","first-page":"516","DOI":"10.1239\/jap\/1371648958","volume":"50","year":"2013","journal-title":"J. Appl. Probab."},{"key":"2024102117162708800_c3"},{"key":"2024102117162708800_c4","doi-asserted-by":"publisher","first-page":"199\u2013214","DOI":"10.1016\/0012-365X(90)90361-K","volume":"86","year":"1990","journal-title":"Discrete Math."},{"key":"2024102117162708800_c5","doi-asserted-by":"publisher","first-page":"046126","DOI":"10.1103\/PhysRevE.70.046126","volume":"70","year":"2004","journal-title":"Phys. Rev. E"},{"key":"2024102117162708800_c6","first-page":"1\u201327","volume":"51","year":"1995","journal-title":"Theory Probab. Math. Stat."},{"key":"2024102117162708800_c7","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1088\/1367-2630\/9\/6\/175","volume":"9","year":"2007","journal-title":"New J. Phys."},{"key":"2024102117162708800_c8","doi-asserted-by":"publisher","first-page":"075102","DOI":"10.1088\/1751-8113\/44\/7\/075102","volume":"44","year":"2011","journal-title":"J. Phys. A"},{"key":"2024102117162708800_c9","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/49\/27\/275101","volume":"49","year":"2016","journal-title":"J. Phys. A"},{"key":"2024102117162708800_c10","doi-asserted-by":"publisher","first-page":"3114\u20133118","DOI":"10.1016\/j.physleta.2011.06.053","volume":"375","year":"2016","journal-title":"Phys. Lett. A"},{"key":"2024102117162708800_c11","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1038\/nature06201","volume":"450","year":"2007","journal-title":"Nature"},{"volume-title":"A Guide to First-Passage Processes","year":"2007","key":"2024102117162708800_c12"},{"key":"2024102117162708800_c13"},{"key":"2024102117162708800_c14","doi-asserted-by":"publisher","first-page":"225\u2013284","DOI":"10.1016\/j.physrep.2014.02.003","volume":"539","year":"2014","journal-title":"Phys. Rep."},{"volume-title":"Dynamical Processes on Complex Networks","year":"2008","key":"2024102117162708800_c15"},{"volume-title":"First-Passage Phenomena and Their Applications","year":"2014","key":"2024102117162708800_c16"},{"volume-title":"Diffusion and Reactions in Fractals and Disordered Systems","year":"2000","key":"2024102117162708800_c17"},{"key":"2024102117162708800_c18","doi-asserted-by":"publisher","first-page":"041111","DOI":"10.1103\/PhysRevE.78.041111","volume":"78","year":"2008","journal-title":"Phys. Rev. E"},{"key":"2024102117162708800_c19","doi-asserted-by":"publisher","first-page":"911","DOI":"10.1038\/44831","volume":"401","year":"1999","journal-title":"Nature"},{"key":"2024102117162708800_c20","doi-asserted-by":"publisher","first-page":"1944","DOI":"10.1039\/c1nj20142e","volume":"35","year":"2011","journal-title":"New J. Chem."},{"key":"2024102117162708800_c21"},{"key":"2024102117162708800_c22","doi-asserted-by":"publisher","first-page":"19072","DOI":"10.1073\/pnas.0801926105","volume":"105","year":"2008","journal-title":"Proc. Natl. Acad. Sci. U.S.A."},{"key":"2024102117162708800_c23","doi-asserted-by":"publisher","first-page":"1098","DOI":"10.1038\/nature06518","volume":"451","year":"2008","journal-title":"Nature"},{"key":"2024102117162708800_c24","doi-asserted-by":"publisher","first-page":"138102","DOI":"10.1103\/PhysRevLett.103.138102","volume":"103","year":"2009","journal-title":"Phys. Rev. Lett."},{"key":"2024102117162708800_c25","doi-asserted-by":"publisher","first-page":"065104","DOI":"10.1103\/PhysRevE.80.065104","volume":"80","year":"2009","journal-title":"Phys. Rev. E"},{"key":"2024102117162708800_c26","doi-asserted-by":"publisher","first-page":"118701","DOI":"10.1103\/PhysRevLett.92.118701","volume":"92","year":"2004","journal-title":"Phys. Rev. Lett."},{"key":"2024102117162708800_c27","doi-asserted-by":"publisher","first-page":"031125","DOI":"10.1103\/PhysRevE.80.031125","volume":"80","year":"2009","journal-title":"Phys. Rev. E"},{"key":"2024102117162708800_c28","doi-asserted-by":"publisher","first-page":"026113","DOI":"10.1103\/PhysRevE.85.026113","volume":"85","year":"2012","journal-title":"Phys. Rev. E"},{"key":"2024102117162708800_c29","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1140\/epjb\/e2011-10863-1","volume":"80","year":"2011","journal-title":"Eur. Phys. J. B"},{"key":"2024102117162708800_c30","doi-asserted-by":"publisher","first-page":"P08013","DOI":"10.1088\/1742-5468\/2011\/08\/P08013","year":"2011","journal-title":"J. Stat. Mech."},{"key":"2024102117162708800_c31","doi-asserted-by":"publisher","first-page":"094905","DOI":"10.1063\/1.4793309","volume":"138","year":"2013","journal-title":"J. Chem Phys."},{"key":"2024102117162708800_c32","doi-asserted-by":"publisher","first-page":"P04032","DOI":"10.1088\/1742-5468\/2014\/04\/P04032","volume":"2014","year":"2014","journal-title":"J. Stat. Mech."},{"key":"2024102117162708800_c33","doi-asserted-by":"publisher","first-page":"40004","DOI":"10.1209\/0295-5075\/133\/40004","volume":"133","year":"2021","journal-title":"Europhys. Lett."},{"key":"2024102117162708800_c34","doi-asserted-by":"publisher","first-page":"021127","DOI":"10.1103\/PhysRevE.79.021127","volume":"79","year":"2009","journal-title":"Phys. Rev. E"},{"key":"2024102117162708800_c35","doi-asserted-by":"publisher","first-page":"073118","DOI":"10.1063\/1.4927085","volume":"25","year":"2015","journal-title":"Chaos"},{"key":"2024102117162708800_c36","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.mbs.2018.10.004","volume":"306","year":"2018","journal-title":"Math. Biosci."},{"key":"2024102117162708800_c37","doi-asserted-by":"publisher","first-page":"234104","DOI":"10.1063\/1.4883335","volume":"140","year":"2014","journal-title":"J. Chem Phys."},{"key":"2024102117162708800_c38","doi-asserted-by":"publisher","first-page":"063027","DOI":"10.1088\/1367-2630\/14\/6\/063027","volume":"14","year":"2012","journal-title":"New J. Phys."},{"key":"2024102117162708800_c39","doi-asserted-by":"publisher","first-page":"022133","DOI":"10.1103\/PhysRevE.93.022133","volume":"93","year":"2016","journal-title":"Phys. Rev. E"},{"key":"2024102117162708800_c40","doi-asserted-by":"publisher","first-page":"062140","DOI":"10.1103\/PhysRevE.87.062140","volume":"87","year":"2013","journal-title":"Phys. Rev. E"},{"key":"2024102117162708800_c41","doi-asserted-by":"publisher","first-page":"103207","DOI":"10.1088\/1742-5468\/ab38c0","volume":"2019","year":"2019","journal-title":"J. Stat. Mech."},{"key":"2024102117162708800_c42","doi-asserted-by":"publisher","first-page":"043209","DOI":"10.1088\/1742-5468\/ab7af0","volume":"2020","year":"2020","journal-title":"J. Stat. Mech."},{"key":"2024102117162708800_c43","doi-asserted-by":"publisher","first-page":"1950028","DOI":"10.1142\/S0218348X19500282","volume":"27","year":"2019","journal-title":"Fractals"},{"key":"2024102117162708800_c44","doi-asserted-by":"publisher","first-page":"113115","DOI":"10.1063\/1.5045829","volume":"28","year":"2018","journal-title":"Chaos"},{"key":"2024102117162708800_c45","doi-asserted-by":"publisher","first-page":"063405","DOI":"10.1088\/1742-5468\/ac02cb","volume":"2021","year":"2021","journal-title":"J. Stat. Mech."},{"key":"2024102117162708800_c46","doi-asserted-by":"publisher","first-page":"184","DOI":"10.3390\/fractalfract5040184","volume":"2021","year":"2021","journal-title":"Fractal Fract."},{"key":"2024102117162708800_c47","doi-asserted-by":"publisher","first-page":"046135","DOI":"10.1103\/PhysRevE.64.046135","volume":"64","year":"2001","journal-title":"Phys. Rev. E"},{"key":"2024102117162708800_c48"},{"key":"2024102117162708800_c49","doi-asserted-by":"publisher","first-page":"3825","DOI":"10.1016\/j.comnet.2012.10.007","volume":"56","year":"2014","journal-title":"Comput. Netw."},{"key":"2024102117162708800_c50","doi-asserted-by":"publisher","first-page":"065102","DOI":"10.1103\/PhysRevE.78.065102","volume":"78","year":"2008","journal-title":"Phys. Rev. E"},{"key":"2024102117162708800_c51"},{"key":"2024102117162708800_c52","doi-asserted-by":"publisher","first-page":"065101","DOI":"10.1103\/PhysRevE.65.056101","volume":"65","year":"2002","journal-title":"Phys. Rev. E"},{"key":"2024102117162708800_c53","first-page":"312\u2013340","volume":"6","year":"1996","journal-title":"Comput. Complex."},{"key":"2024102117162708800_c54","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1007\/BF01046996","volume":"4","year":"1991","journal-title":"J. Theor. Probab."},{"key":"2024102117162708800_c55","doi-asserted-by":"publisher","first-page":"1308","DOI":"10.1109\/TNSE.2022.3140213","volume":"9","year":"2022","journal-title":"IEEE Trans. Netw. Sci. Eng."},{"key":"2024102117162708800_c56","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1038\/nphys266","volume":"2","year":"2006","journal-title":"Nat. Phys."}],"container-title":["Chaos: An Interdisciplinary Journal of Nonlinear Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/cha\/article-pdf\/doi\/10.1063\/5.0223595\/20215208\/103136_1_5.0223595.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/cha\/article-pdf\/doi\/10.1063\/5.0223595\/20215208\/103136_1_5.0223595.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,21]],"date-time":"2024-10-21T17:16:38Z","timestamp":1729530998000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/cha\/article\/34\/10\/103136\/3317519\/Controlling-and-optimizing-the-transport-search"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,1]]},"references-count":56,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2024,10,1]]}},"URL":"https:\/\/doi.org\/10.1063\/5.0223595","relation":{},"ISSN":["1054-1500","1089-7682"],"issn-type":[{"type":"print","value":"1054-1500"},{"type":"electronic","value":"1089-7682"}],"subject":[],"published-other":{"date-parts":[[2024,10]]},"published":{"date-parts":[[2024,10,1]]},"article-number":"103136"}}