Colin Barquist. Biological Scaling Laws and Universality PHZ 7429

Transcription

1 Colin Barquist Biological Scaling Laws and Universality PHZ 7429

2 <latexit sha1_base64="humg1ix6zok959u2tgpi6+r+uds=">aaab6nicbvdlsgnbeoynrxhfuy9ebopgkeykei9blx7jiw9ilja76u2gzm4um7ncwpijxjwo4tuv8ubfoen2oikfduvvn91dqsk4nq777rtw1jc2t4rbpz3dvf2d8ufrs8epythksyhvj6aabzfynnwi7cqkarqibafjm5nffkkleswfzsrbp6jdyupoqlhsw31f9msvt+roqvajl5mk5gj0y1+9qczsckvhgmrd9dze+blvhjob01iv1zhqnqzd7foqaytaz+antsmzvqykjjutachc/t2r0ujrsrtyzoiakv72zuj/xjc14zwfczmkbivblaptquxmzn+tavfijjhyqpni9lbcrlrrzmw6jruct/zykmldvd236t1dvurxerxfoiftoacpalchw2haexgm4rle4c0rzovz7nwswgtopnmmf+b8/garoi21</latexit> <latexit sha1_base64="humg1ix6zok959u2tgpi6+r+uds=">aaab6nicbvdlsgnbeoynrxhfuy9ebopgkeykei9blx7jiw9ilja76u2gzm4um7ncwpijxjwo4tuv8ubfoen2oikfduvvn91dqsk4nq777rtw1jc2t4rbpz3dvf2d8ufrs8epythksyhvj6aabzfynnwi7cqkarqibafjm5nffkkleswfzsrbp6jdyupoqlhsw31f9msvt+roqvajl5mk5gj0y1+9qczsckvhgmrd9dze+blvhjob01iv1zhqnqzd7foqaytaz+antsmzvqykjjutachc/t2r0ujrsrtyzoiakv72zuj/xjc14zwfczmkbivblaptquxmzn+tavfijjhyqpni9lbcrlrrzmw6jruct/zykmldvd236t1dvurxerxfoiftoacpalchw2haexgm4rle4c0rzovz7nwswgtopnmmf+b8/garoi21</latexit> <latexit sha1_base64="humg1ix6zok959u2tgpi6+r+uds=">aaab6nicbvdlsgnbeoynrxhfuy9ebopgkeykei9blx7jiw9ilja76u2gzm4um7ncwpijxjwo4tuv8ubfoen2oikfduvvn91dqsk4nq777rtw1jc2t4rbpz3dvf2d8ufrs8epythksyhvj6aabzfynnwi7cqkarqibafjm5nffkkleswfzsrbp6jdyupoqlhsw31f9msvt+roqvajl5mk5gj0y1+9qczsckvhgmrd9dze+blvhjob01iv1zhqnqzd7foqaytaz+antsmzvqykjjutachc/t2r0ujrsrtyzoiakv72zuj/xjc14zwfczmkbivblaptquxmzn+tavfijjhyqpni9lbcrlrrzmw6jruct/zykmldvd236t1dvurxerxfoiftoacpalchw2haexgm4rle4c0rzovz7nwswgtopnmmf+b8/garoi21</latexit> <latexit sha1_base64="humg1ix6zok959u2tgpi6+r+uds=">aaab6nicbvdlsgnbeoynrxhfuy9ebopgkeykei9blx7jiw9ilja76u2gzm4um7ncwpijxjwo4tuv8ubfoen2oikfduvvn91dqsk4nq777rtw1jc2t4rbpz3dvf2d8ufrs8epythksyhvj6aabzfynnwi7cqkarqibafjm5nffkkleswfzsrbp6jdyupoqlhsw31f9msvt+roqvajl5mk5gj0y1+9qczsckvhgmrd9dze+blvhjob01iv1zhqnqzd7foqaytaz+antsmzvqykjjutachc/t2r0ujrsrtyzoiakv72zuj/xjc14zwfczmkbivblaptquxmzn+tavfijjhyqpni9lbcrlrrzmw6jruct/zykmldvd236t1dvurxerxfoiftoacpalchw2haexgm4rle4c0rzovz7nwswgtopnmmf+b8/garoi21</latexit> <latexit sha1_base64="dmnmk2yxyytv+zn0rwxywo/yulg=">aaab6hicbvbns8naej3ur1q/qh69lbbbu0le0itq9okxbfsbbsib7ardu9me3y1qqn+bfw+kepunefpfug1z0nyha4/3zpizfysca+o6305hbx1jc6u4xdrz3ds/kb8etxsckoznfotydqkquxcjtconwe6ikeabwhywvpv57sdumsfywuws9cm6ldzkjbornw765ypbdecgq8tlsqvy1pvlr94gzmme0jbbte56bml8jcrdmcbpqzdqtcgb0yf2lzu0qu1n80on5mwqaxlgypy0zk7+nshoppukcmxnrm1il3sz8t+vm5rw2s+4tfkdki0whakgjiazr8mak2rgtcyhthf7k2ejqigznpusdcfbfnmvtc6qnlv1gpev2m0erxfo4btowymrqme91kejdbce4rxenefnxxl3phatbsefoyy/cd5/aiznjme=</latexit> <latexit sha1_base64="dmnmk2yxyytv+zn0rwxywo/yulg=">aaab6hicbvbns8naej3ur1q/qh69lbbbu0le0itq9okxbfsbbsib7ardu9me3y1qqn+bfw+kepunefpfug1z0nyha4/3zpizfysca+o6305hbx1jc6u4xdrz3ds/kb8etxsckoznfotydqkquxcjtconwe6ikeabwhywvpv57sdumsfywuws9cm6ldzkjbornw765ypbdecgq8tlsqvy1pvlr94gzmme0jbbte56bml8jcrdmcbpqzdqtcgb0yf2lzu0qu1n80on5mwqaxlgypy0zk7+nshoppukcmxnrm1il3sz8t+vm5rw2s+4tfkdki0whakgjiazr8mak2rgtcyhthf7k2ejqigznpusdcfbfnmvtc6qnlv1gpev2m0erxfo4btowymrqme91kejdbce4rxenefnxxl3phatbsefoyy/cd5/aiznjme=</latexit> <latexit sha1_base64="dmnmk2yxyytv+zn0rwxywo/yulg=">aaab6hicbvbns8naej3ur1q/qh69lbbbu0le0itq9okxbfsbbsib7ardu9me3y1qqn+bfw+kepunefpfug1z0nyha4/3zpizfysca+o6305hbx1jc6u4xdrz3ds/kb8etxsckoznfotydqkquxcjtconwe6ikeabwhywvpv57sdumsfywuws9cm6ldzkjbornw765ypbdecgq8tlsqvy1pvlr94gzmme0jbbte56bml8jcrdmcbpqzdqtcgb0yf2lzu0qu1n80on5mwqaxlgypy0zk7+nshoppukcmxnrm1il3sz8t+vm5rw2s+4tfkdki0whakgjiazr8mak2rgtcyhthf7k2ejqigznpusdcfbfnmvtc6qnlv1gpev2m0erxfo4btowymrqme91kejdbce4rxenefnxxl3phatbsefoyy/cd5/aiznjme=</latexit> Overview Scaling and Universality in Condensed Matter Observations of Scaling in Biological systems R l Theory: Resource Distribution Network Theory: Scaling Hypothesis Universality in Ontogenetic Growth Curves Provocative Conclusion =<latexit sha1_base64="dmnmk2yxyytv+zn0rwxywo/yulg=">aaab6hicbvbns8naej3ur1q/qh69lbbbu0le0itq9okxbfsbbsib7ardu9me3y1qqn+bfw+kepunefpfug1z0nyha4/3zpizfysca+o6305hbx1jc6u4xdrz3ds/kb8etxsckoznfotydqkquxcjtconwe6ikeabwhywvpv57sdumsfywuws9cm6ldzkjbornw765ypbdecgq8tlsqvy1pvlr94gzmme0jbbte56bml8jcrdmcbpqzdqtcgb0yf2lzu0qu1n80on5mwqaxlgypy0zk7+nshoppukcmxnrm1il3sz8t+vm5rw2s+4tfkdki0whakgjiazr8mak2rgtcyhthf7k2ejqigznpusdcfbfnmvtc6qnlv1gpev2m0erxfo4btowymrqme91kejdbce4rxenefnxxl3phatbsefoyy/cd5/aiznjme=</latexit> Mammalian size limits Lifespans: can we live forever?

3 Scaling and Universality Magnetization vs T. CrBr 3, EuO, YIG, Pd 3 Fe, and Ni H. E. Stanley Rev. Mod. Phys. 71 (1999)

4 Scaling In Biological Systems

5 Resource Distribution Networks

6 <latexit sha1_base64="dhcns2ne4rajapzher5uij+kqkm=">aaacchicbvdlssnafj3uv62vqesxdhzbegoigm6eohuxfewd2ham05t2yotbzeqoius3/oobf4q49rpc+tdo2iy0emcym+fcy517viqzqszry6gslc4tr1rxa2vrg5tb5vzor8aponcmmy9fzymsoiugrzji0esekndj0pwc68lv3ooqli7u1cqbjysjipmmequl19wfekcig+bllnwsolbzk+lo9xvmmhwryu2b/xk7jhvuouwan4nhtnmqiku5kbjvw4lymiiuoxzy2icvkbaakbh0ny1icnljpovk+farq+zhqp9i4an6symjozst0novivfjoe8v4n9ep1x+hzoxkekvrhq2ye85vjeuusfdjoaqptgeumh0xzede0go0tnvdaj2/mp/see0yvsn+/as3rwq46iipxsajpcnzlet3aawaiokhtatekgvxqpxblwz77psilh27kjfmd6+acaqmig=</latexit> <latexit sha1_base64="dhcns2ne4rajapzher5uij+kqkm=">aaacchicbvdlssnafj3uv62vqesxdhzbegoigm6eohuxfewd2ham05t2yotbzeqoius3/oobf4q49rpc+tdo2iy0emcym+fcy517viqzqszry6gslc4tr1rxa2vrg5tb5vzor8aponcmmy9fzymsoiugrzji0esekndj0pwc68lv3ooqli7u1cqbjysjipmmequl19wfekcig+bllnwsolbzk+lo9xvmmhwryu2b/xk7jhvuouwan4nhtnmqiku5kbjvw4lymiiuoxzy2icvkbaakbh0ny1icnljpovk+farq+zhqp9i4an6symjozst0novivfjoe8v4n9ep1x+hzoxkekvrhq2ye85vjeuusfdjoaqptgeumh0xzede0go0tnvdaj2/mp/see0yvsn+/as3rwq46iipxsajpcnzlet3aawaiokhtatekgvxqpxblwz77psilh27kjfmd6+acaqmig=</latexit> <latexit sha1_base64="dhcns2ne4rajapzher5uij+kqkm=">aaacchicbvdlssnafj3uv62vqesxdhzbegoigm6eohuxfewd2ham05t2yotbzeqoius3/oobf4q49rpc+tdo2iy0emcym+fcy517viqzqszry6gslc4tr1rxa2vrg5tb5vzor8aponcmmy9fzymsoiugrzji0esekndj0pwc68lv3ooqli7u1cqbjysjipmmequl19wfekcig+bllnwsolbzk+lo9xvmmhwryu2b/xk7jhvuouwan4nhtnmqiku5kbjvw4lymiiuoxzy2icvkbaakbh0ny1icnljpovk+farq+zhqp9i4an6symjozst0novivfjoe8v4n9ep1x+hzoxkekvrhq2ye85vjeuusfdjoaqptgeumh0xzede0go0tnvdaj2/mp/see0yvsn+/as3rwq46iipxsajpcnzlet3aawaiokhtatekgvxqpxblwz77psilh27kjfmd6+acaqmig=</latexit> <latexit sha1_base64="dhcns2ne4rajapzher5uij+kqkm=">aaacchicbvdlssnafj3uv62vqesxdhzbegoigm6eohuxfewd2ham05t2yotbzeqoius3/oobf4q49rpc+tdo2iy0emcym+fcy517viqzqszry6gslc4tr1rxa2vrg5tb5vzor8aponcmmy9fzymsoiugrzji0esekndj0pwc68lv3ooqli7u1cqbjysjipmmequl19wfekcig+bllnwsolbzk+lo9xvmmhwryu2b/xk7jhvuouwan4nhtnmqiku5kbjvw4lymiiuoxzy2icvkbaakbh0ny1icnljpovk+farq+zhqp9i4an6symjozst0novivfjoe8v4n9ep1x+hzoxkekvrhq2ye85vjeuusfdjoaqptgeumh0xzede0go0tnvdaj2/mp/see0yvsn+/as3rwq46iipxsajpcnzlet3aawaiokhtatekgvxqpxblwz77psilh27kjfmd6+acaqmig=</latexit> <latexit sha1_base64="vxooztjuzifqpduylmnajjnkrhu=">aaaccnicbvbns8mwge7n15xfvy9eokmqhnmkobdh6mxjbpcbwylplm6hsvqsvbilzy/+fs8efphql/dmvzhdetdpayfpnud9efm+qcko0o7zzvuwfpewv6qrtbx1jc0te3uno+juytlgmytll0ckmcpiw1pnsc+rbpgakw4qxrd+955irwnxpycj8tgacrpsjlsrfht/mekciz+cl5d5wxts5iffnzt3adl1p+fmaf8styr1ukll25+dyyxttotgdcnvd51eexmsmmjg8togvsrboeij0jduie6ul01xyeghuyywjku5qsop+rmjq1ypcq9mjud6roa9qvzp66c6vpaykpjue4fng8kuqr3dihc4pjjgzsagicyp+sveyyqr1ia9mgnbnv/5l+mcnlyn4d6e1ztxzrxvsacowbfwwtloghvqam2awqn4ai/g1xq0nq03631wwrhknl3wc9bhn04mmv4=</latexit> <latexit sha1_base64="vxooztjuzifqpduylmnajjnkrhu=">aaaccnicbvbns8mwge7n15xfvy9eokmqhnmkobdh6mxjbpcbwylplm6hsvqsvbilzy/+fs8efphql/dmvzhdetdpayfpnud9efm+qcko0o7zzvuwfpewv6qrtbx1jc0te3uno+juytlgmytll0ckmcpiw1pnsc+rbpgakw4qxrd+955irwnxpycj8tgacrpsjlsrfht/mekciz+cl5d5wxts5iffnzt3adl1p+fmaf8styr1ukll25+dyyxttotgdcnvd51eexmsmmjg8togvsrboeij0jduie6ul01xyeghuyywjku5qsop+rmjq1ypcq9mjud6roa9qvzp66c6vpaykpjue4fng8kuqr3dihc4pjjgzsagicyp+sveyyqr1ia9mgnbnv/5l+mcnlyn4d6e1ztxzrxvsacowbfwwtloghvqam2awqn4ai/g1xq0nq03631wwrhknl3wc9bhn04mmv4=</latexit> <latexit sha1_base64="vxooztjuzifqpduylmnajjnkrhu=">aaaccnicbvbns8mwge7n15xfvy9eokmqhnmkobdh6mxjbpcbwylplm6hsvqsvbilzy/+fs8efphql/dmvzhdetdpayfpnud9efm+qcko0o7zzvuwfpewv6qrtbx1jc0te3uno+juytlgmytll0ckmcpiw1pnsc+rbpgakw4qxrd+955irwnxpycj8tgacrpsjlsrfht/mekciz+cl5d5wxts5iffnzt3adl1p+fmaf8styr1ukll25+dyyxttotgdcnvd51eexmsmmjg8togvsrboeij0jduie6ul01xyeghuyywjku5qsop+rmjq1ypcq9mjud6roa9qvzp66c6vpaykpjue4fng8kuqr3dihc4pjjgzsagicyp+sveyyqr1ia9mgnbnv/5l+mcnlyn4d6e1ztxzrxvsacowbfwwtloghvqam2awqn4ai/g1xq0nq03631wwrhknl3wc9bhn04mmv4=</latexit> <latexit sha1_base64="vxooztjuzifqpduylmnajjnkrhu=">aaaccnicbvbns8mwge7n15xfvy9eokmqhnmkobdh6mxjbpcbwylplm6hsvqsvbilzy/+fs8efphql/dmvzhdetdpayfpnud9efm+qcko0o7zzvuwfpewv6qrtbx1jc0te3uno+juytlgmytll0ckmcpiw1pnsc+rbpgakw4qxrd+955irwnxpycj8tgacrpsjlsrfht/mekciz+cl5d5wxts5iffnzt3adl1p+fmaf8styr1ukll25+dyyxttotgdcnvd51eexmsmmjg8togvsrboeij0jduie6ul01xyeghuyywjku5qsop+rmjq1ypcq9mjud6roa9qvzp66c6vpaykpjue4fng8kuqr3dihc4pjjgzsagicyp+sveyyqr1ia9mgnbnv/5l+mcnlyn4d6e1ztxzrxvsacowbfwwtloghvqam2awqn4ai/g1xq0nq03631wwrhknl3wc9bhn04mmv4=</latexit> <latexit sha1_base64="rwsokmp8tuiw+99znnsxvciemke=">aaab9hicbvbnswmxej2tx7v+vt16crbbu9kvqy+lxrwifewhtgvjptk2njvejfsopb/diwdfvppjvplvtns9aoudgcd7m8zmixrnxvr+t5dbw9/y3mpvf3z29/ypiodhdsnttwidsc51k8kgcizo3tllautpipoi02y0vjn5zrhvhknxymekhgnucxyzgq2twirqkc2vlejuexeljb/sz4fwszcremsodytfnz4kaukfjrwb0w58zcmj1pyrtqeftmqowmsi+7ttqmajnefkfvquntmlh2kpxqml5urviqlojbknketmsb2yzw8m/ue1uxtfhxmmvgqpiitfccqre3kwaooxtynly0cw0czdisgaa0ysy6ngqgiwx14ljyty4jed+8tspzrfkyctoivzcoakknalnagdgsd4hld480bei/fufsxac142cwx/4h3+ao3okyo=</latexit> <latexit sha1_base64="rwsokmp8tuiw+99znnsxvciemke=">aaab9hicbvbnswmxej2tx7v+vt16crbbu9kvqy+lxrwifewhtgvjptk2njvejfsopb/diwdfvppjvplvtns9aoudgcd7m8zmixrnxvr+t5dbw9/y3mpvf3z29/ypiodhdsnttwidsc51k8kgcizo3tllautpipoi02y0vjn5zrhvhknxymekhgnucxyzgq2twirqkc2vlejuexeljb/sz4fwszcremsodytfnz4kaukfjrwb0w58zcmj1pyrtqeftmqowmsi+7ttqmajnefkfvquntmlh2kpxqml5urviqlojbknketmsb2yzw8m/ue1uxtfhxmmvgqpiitfccqre3kwaooxtynly0cw0czdisgaa0ysy6ngqgiwx14ljyty4jed+8tspzrfkyctoivzcoakknalnagdgsd4hld480bei/fufsxac142cwx/4h3+ao3okyo=</latexit> <latexit sha1_base64="rwsokmp8tuiw+99znnsxvciemke=">aaab9hicbvbnswmxej2tx7v+vt16crbbu9kvqy+lxrwifewhtgvjptk2njvejfsopb/diwdfvppjvplvtns9aoudgcd7m8zmixrnxvr+t5dbw9/y3mpvf3z29/ypiodhdsnttwidsc51k8kgcizo3tllautpipoi02y0vjn5zrhvhknxymekhgnucxyzgq2twirqkc2vlejuexeljb/sz4fwszcremsodytfnz4kaukfjrwb0w58zcmj1pyrtqeftmqowmsi+7ttqmajnefkfvquntmlh2kpxqml5urviqlojbknketmsb2yzw8m/ue1uxtfhxmmvgqpiitfccqre3kwaooxtynly0cw0czdisgaa0ysy6ngqgiwx14ljyty4jed+8tspzrfkyctoivzcoakknalnagdgsd4hld480bei/fufsxac142cwx/4h3+ao3okyo=</latexit> <latexit sha1_base64="rwsokmp8tuiw+99znnsxvciemke=">aaab9hicbvbnswmxej2tx7v+vt16crbbu9kvqy+lxrwifewhtgvjptk2njvejfsopb/diwdfvppjvplvtns9aoudgcd7m8zmixrnxvr+t5dbw9/y3mpvf3z29/ypiodhdsnttwidsc51k8kgcizo3tllautpipoi02y0vjn5zrhvhknxymekhgnucxyzgq2twirqkc2vlejuexeljb/sz4fwszcremsodytfnz4kaukfjrwb0w58zcmj1pyrtqeftmqowmsi+7ttqmajnefkfvquntmlh2kpxqml5urviqlojbknketmsb2yzw8m/ue1uxtfhxmmvgqpiitfccqre3kwaooxtynly0cw0czdisgaa0ysy6ngqgiwx14ljyty4jed+8tspzrfkyctoivzcoakknalnagdgsd4hld480bei/fufsxac142cwx/4h3+ao3okyo=</latexit> Resource Distribution Network Examples: Circulatory System Respiratory System Plant Vascular System Requirements: Space Filling, i.e. every cell needs oxygen. Invariant terminal units: capillaries, mitochondria, respiratory complexes Energy required for transportation of resources is minimized. More energy for survival/reproduction + natural selection ensure this. k = r k+1 /r k = k = l k+1 /l k = n k = n <latexit sha1_base64="emwxcnikffwxlvt3g0spe0ylgm8=">aaab7nicbvbns8naej3ur1q/qh69lbbbu0le0itq9okxgv2anptndtmu2wzc7kqoot/ciwdfvpp7vplv3ly5aoudgcd7m8zmc1ipdlrut1naw9/y3cpvv3z29/ypqodhbznkmvews2siuwe1xarfwyhq8m6qoy0dyttbddfzo09cg5gor5yk3i/psilqmipw6qhbrg6iglrrbt2dg6wsrya1knacvl/6w4rlmvfijdwm57kp+jnvkjjk00o/mzyllkij3rnu0zgbp5+foyvnvhmsmng2fjk5+nsip7exkziwnthfsvn2zuj/xi/d8nrphuoz5iotfowzjjiq2e9kkdrnkcewukafvzwwmdwuou2oykpwll9eje2luufwvyflwuo2ikmmj3ak5+dbfttghprqagyrpmmrvdmp8+k8ox+l1pjtzbzdhzifp1isjum=</latexit> <latexit sha1_base64="emwxcnikffwxlvt3g0spe0ylgm8=">aaab7nicbvbns8naej3ur1q/qh69lbbbu0le0itq9okxgv2anptndtmu2wzc7kqoot/ciwdfvpp7vplv3ly5aoudgcd7m8zmc1ipdlrut1naw9/y3cpvv3z29/ypqodhbznkmvews2siuwe1xarfwyhq8m6qoy0dyttbddfzo09cg5gor5yk3i/psilqmipw6qhbrg6iglrrbt2dg6wsrya1knacvl/6w4rlmvfijdwm57kp+jnvkjjk00o/mzyllkij3rnu0zgbp5+foyvnvhmsmng2fjk5+nsip7exkziwnthfsvn2zuj/xi/d8nrphuoz5iotfowzjjiq2e9kkdrnkcewukafvzwwmdwuou2oykpwll9eje2luufwvyflwuo2ikmmj3ak5+dbfttghprqagyrpmmrvdmp8+k8ox+l1pjtzbzdhzifp1isjum=</latexit> <latexit sha1_base64="emwxcnikffwxlvt3g0spe0ylgm8=">aaab7nicbvbns8naej3ur1q/qh69lbbbu0le0itq9okxgv2anptndtmu2wzc7kqoot/ciwdfvpp7vplv3ly5aoudgcd7m8zmc1ipdlrut1naw9/y3cpvv3z29/ypqodhbznkmvews2siuwe1xarfwyhq8m6qoy0dyttbddfzo09cg5gor5yk3i/psilqmipw6qhbrg6iglrrbt2dg6wsrya1knacvl/6w4rlmvfijdwm57kp+jnvkjjk00o/mzyllkij3rnu0zgbp5+foyvnvhmsmng2fjk5+nsip7exkziwnthfsvn2zuj/xi/d8nrphuoz5iotfowzjjiq2e9kkdrnkcewukafvzwwmdwuou2oykpwll9eje2luufwvyflwuo2ikmmj3ak5+dbfttghprqagyrpmmrvdmp8+k8ox+l1pjtzbzdhzifp1isjum=</latexit> <latexit sha1_base64="emwxcnikffwxlvt3g0spe0ylgm8=">aaab7nicbvbns8naej3ur1q/qh69lbbbu0le0itq9okxgv2anptndtmu2wzc7kqoot/ciwdfvpp7vplv3ly5aoudgcd7m8zmc1ipdlrut1naw9/y3cpvv3z29/ypqodhbznkmvews2siuwe1xarfwyhq8m6qoy0dyttbddfzo09cg5gor5yk3i/psilqmipw6qhbrg6iglrrbt2dg6wsrya1knacvl/6w4rlmvfijdwm57kp+jnvkjjk00o/mzyllkij3rnu0zgbp5+foyvnvhmsmng2fjk5+nsip7exkziwnthfsvn2zuj/xi/d8nrphuoz5iotfowzjjiq2e9kkdrnkcewukafvzwwmdwuou2oykpwll9eje2luufwvyflwuo2ikmmj3ak5+dbfttghprqagyrpmmrvdmp8+k8ox+l1pjtzbzdhzifp1isjum=</latexit> B / M a

7 Scaling Relations Q 0 = Nk Q k = Nc rc2 u c N c = nn <latexit sha1_base64="f8lsrttuc5wtvbv6q81/518i6ym=">aaab8hicbvbnswmxej2tx7v+vt16crbbu9kvqs9c0yunusf+sluwbjptq5pskmsfsvrxepggifd/jjf/jdl2d9r6yodx3gwz84kym21c99sprkyurw8un0tb2zu7e+x9g5aoekvok0q8up0aa8qzpe3ddkedwfesak7bwfgm89tpvgkwyxsziakv8fcykbfsrprq7xn0herjvv+uufv3brrmvjxuieejx/7qdsksccon4vjrrufgxk+xmoxwoi31ek1jtmz4sluwsiyo9tpzwvn0ypubcinlsxo0u39ppfhoprgb7rtyjpsil4n/ed3ehjd+ymscgcrjffgycgqilh2pbkxryvjeekwus7cimsike2mzktkqvmwxl0nrroq5ve/uvfk7zumowhecwyl4cae1uiugnigaggd4htdhos/ou/mxby04+cwh/ihz+qnnoy97</latexit> <latexit sha1_base64="7xiyvhs8jnbidwaonqnwlskp1kw=">aaachhicbvdlsgmxfm34rpu16tjnsaiuykwvdcmu3bisfuwdouoqstntaozbckcow3yig3/fjqtf3lgq/bvtdhbaeibw7jn3jrnhtwrxyfnfxtlyyuraemmjvlm1vbnr7u23vzxkylo0frhs+kqxwspwag6cdrpjsogl1vfh1xo/88ck4nf0b+oeusezrdzglicwpppu6ceqnt0rx5f41hvhoh7naoqdhgpp0fsadnwiszt3qgdwrko1bv4kdkeqqeddmz/1rtqnwqruekv6tpwamxejnaqwl51usytqermwnqyrczlys+lyot7wsh8hsdqnajxvf09kjfrqhpq6myqwvpperpzp66uqxlgzj5iuwerndwwpwbdjsvk4zywjimaaecq5/iumqyijbz1nwydgz6+8snq1qm1v7ezzpx5vxffch+ginsabnam6uken1eiupajn9irejcfjxxg3pmats0yxc4d+wpj6ats0odu=</latexit> Nc / Q 0 / B / M a <latexit sha1_base64="eumag7utgbfxgreyh94vzn/xe6k=">aaacfhicbvblswmxgmzwv62vvy9egkuqhlirgh5lvxhrwrapanclm6ztadyjsvyos3+ef/+kfw+kepxgzx9j2i6irqobyeb7ksxeklftpo/lys0tr6yu5dclg5tb2zvu7l5di0rhuseccdwkkcamcli31ddskoqgogkkgq0vj37znihnbb81i0mcgpu57vgmjjvc9+qmxlajlzbgwe5xmlqweumfpfldru9q6ba9kjcfxcr+roogqzv0p+2noikjn5ghrdu+j02qimuozmrc6csasishqe/alniuex2k01bjegsvluwjzq83ckr+3khrrpuojuxkjmxaz3st8t+vnzjerzbslhndoj491esytcendceuvqqbnrieyuxtxyeeiiwwst0wban+forf0jgt+v7jr50vy5wsjjw4aifggpjghjtbfaicosdgatybf/dqpdrpzpvzphvnodnopvgd5+mbrrcd8g==</latexit> a log(m/m0 ) N= log(n) <latexit sha1_base64="juz7nns/hh3hlpngo2xgyhvzssm=">aaaccxicbvdlssnafj34rpuvdelmsajtpiyi6eyounftqwaf0iqwmu7aoznjmjkijwtrxl9x40irt/6bo//gazqfth64coace5l7jx8zkpvlfrtlyyura+uljflm1vborrm335frijbp44hfoucjsrjlpk2oyqqxc4jcn5gup76e+t0hiisn+l2axmqn0zdtggkktosz8bzeqicqckfiydgw2jxpelyts/mhr2wewbhqvg64soycvecblmd+oymijyhhcjmkzd+2yuwmscikgcnktijjjpaydulfu45cit00vysdx1ozwcasuricufp7ikwhljpq150huim5703f/7x+ooiln6u8ththepzrkdcoijinbq6oifixisyic6p3hxiedcxkh1fwidjzjy+szmndtur23vmlcvxeuqkh4ahugq3oqqpcgbzoawwewtn4bw/gk/fivbsfs9ylo5g5ah9gfp4abtiyow==</latexit> M / Vb = <latexit sha1_base64="bg6aw1s7cvxxe1mbnfkeoevrnwu=">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</latexit> a= <latexit sha1_base64="z9lksotu6timijejem30ssnb4qe=">aaacenicbzdlsgmxfiyz9vbrrerstbai7ciyuwtdceu3livyc3rqoznm2takmyqzoqx9bje+ihsxirh15c63mb0stpwhwmd/zuhk/ehmmtau++1kvlbx1jeym7mt7z3dvfz+qunhisk0tiieqvyamnimad0ww2krvhrewgkzgf5p6s0hqjsl5j0zxbqjoc9zyagya3xzjccx+bt7oqks+jzqf2vppao/d0kah1ad95xsujsvugv3krwm3hwkak5an//l9yksccon4ab123nj00lbguy4hef8rnmyybd6tg1rgqc6k05pgumt6/rwgcn7pmft9/decklrkqhspwaz0iu1iflfrz2y8kktmhknhkoywxqmhjsit/lbpayomxxkayhi9q+ydmcmy2ykoruct3jymjqqzc8te7dnhervpi4soklhqig8di6q6abvub0r9iie0st6c56cf+fd+zi1zpz5zch6i+fzbyjsnis=</latexit> N X k rk2 lk nk / ( log(n) log( 2 ) 2 ) N

8 Determining gamma and beta Beta is determined by minimizing the impedance for a network of pipes with pulsatile flow. 2 rk+1 Nk+1 = <latexit sha1_base64="qvmx7rvz2qnnkbg/qdifle5vjmg=">aaacdnicbzdlsgmxfibp1futt1gxbokliahlpgi6eypuxekfe4f2hdjppg2tuzbkhdl0cdz4km5ckolwttvfxrqdufsphpx8/zkk5/cszqsyrc+jsls8srpwxc9tbg5t75i7ey0zp4lqjol5ldoelpszidyvu5x2ekfx6hha9ollid++p0kyolpvo4q6ir5ezgcek41cs9jlgbj3ntclju3x9exc5+ghaxi4ztmqwtnci8lorrnyarjmz68fkzskksics9m1ruq5grakeu7hpv4qayjjgae0q2weqyqdblrogfu06sm/fvpeck3p74kmh1koqk93hlgn5bw3gf953vt5z07goirvnckzh/yuixwjstaozwqlio+0weqw/vdehlhgonscjr2cpb/yomjvqrzvtw9oyvwlpi4ihmahhienp1chk2haewg8wbo8wkvxadwbb8b7rlvg5dp78kemj2/itpqs</latexit> Gamma is determined by requiring that each branch of the network services the whole volume of the network 3 lk Nk 2 rk Nk rk+1 /rk = (Nk /Nk+1 ) <latexit sha1_base64="oq/+f9bopo0qnw2j5ydjowyngtw=">aaacbnicbzdlssnafizpvnz6i7ouybaiglasfxqjfn24kgr2am0mk+mkhtk5mdmrsujkja/ixouibn0gd76n0zqlbf1h4jv/nmpm+b2em6ks69uym19yxfourzrx19y3ns2t7aamu0fog8q8fm0ps8pzrbukku7biaa49dhtechvun56oekyolptw4q6ie5hzgcek2255h53g/stdomg6ajxnwuo7ff+z8k1k1bvyovmws6gaoxqrvnv7cukdwmkcmdsdmwruu6ghwke01g5m0qayblgpu1ojhbipzpla4zqgxz6yi+fppfcuft7isohlmpq050hvgm5xrub/9u6qflpnyxfsaporcyp+slhkkbjtfcpcuouh2rardd9v0qgwgcidhjlhyi9vfisni+rtlw1b08rtcsijhlswj4cgg1nuinrqemdcdzcm7zcm/fkvbjvxsekdc4oznbgj4zphw+flva=</latexit> 1/2 = 3 lk+1 Nk+1 lk+1 /lk = (Nk /Nk+1 ) <latexit sha1_base64="be9hzpmcrf9ivqxrzrlmxujneem=">aaacdhicbvdlsgmxfm34rpvvdekmwisk0e5u0i1qdooqvlapamchk2bamjkhsuyow3yag3/fjqtf3pob7vwbm+0stpvayogcc0nucslopdlnb2nhcwl5zbwwvlzf2nzalu3stmuyc0jbjosh6dpyus4c2ljmcdqnbmw+w2nh8a4zv/nahwrhckfgebv8payyywhwwrjlzw4n3jfka9mdwktyadhertevj+4tvdtndcqsmhpaeyjyugy5mnbpqz8iseztqbgopewhm1jwgovihno02i8ljtdx8jd2na2wt6wvtjzj4afwbtanht6bghp190scfsnhvqotplyjoetl4n9el1buhzwwiiovdcj0itfmuiuwawyomkbe8bemmaim/wrjcatmlo6vqetasyvpk/zjfzlvdhtwrl/ldrtapjgafydaoaidg9aeludai3ggr+dnedjejhfjyxpdmpkzpfahxucpheozwg==</latexit> <latexit sha1_base64="fjwj+gvzz+g6sdbohd6ti9kbtem=">aaacdhicbvdlsgmxfm34rpvvdekmwisk0e6kobuh6mzvqwaf0i5djs20ytipkoxqhvkan/6kgxekupud3pk3ztpzaoubkmm555lc40scswwa38bs8srq2npho7i5tb2zw9rb78gwfos2schd0xowpjwftk2y4rqxcyp9h9ou411nfvebcsnc4e5nimr5ebqwlxgstgsxysjovfou1ri7hzew0rs9wnmmntwnqfzpdcqsmlparyjyugy5wnbpazamseztqbgopewjm1jwgovihno0oigljtdx8ij2nq2wt6wvtjdj4bfwhtanht6bglp190scfsknvqotplzjoe9l4n9ep1buhzwwiiovdcjsitfmuiuwawyomabe8ykmmaim/wrjgatmlo6vqeta8ysvkk69iswquj0rn67yogrgebybckdghdtadwibnidgetydv/bmpbkvxrvxmysugfnmafgd4/mhllazzq==</latexit> <latexit sha1_base64="vykvpifsrp58lbhazlqtez0unj8=">aaab+xicbvdlsgnbejz1genr1aoxwsb4me4gqs9c0ivhcoybsqyzk95kyozsmtmbcev+xishrbz6j978gyepgyywnbrv3xr3bykubj3v21lzxvvf2mxt5bd3dvf23ypdmoltzahkyxnrrsamskggigilnbinlaok1ipb3csvd0ebeathhcxqjlhpivbwhlbqug4ragt0hqqn7ny/ki07bserelpqzelpsyhmuem4x61uznmifhljjgn6xoltjgkuxmi430onjiwpwa+aliowgwln08vh9nqqxrrg2pzcolv/t2qsmmyubbyzytg3i95e/m9rphhetzohkhrb8dmimjuuyzqjgxafbo5yzanjwthbke8zztjaspi2bh/x5wvskxv9r+g/xbbkt/m4cusynjaz4pmruib3pekqhjmhesav5m3jnbfn3fmyta4485kj8gfo5w+cjpjd</latexit> =n 1/2 <latexit sha1_base64="ytgu1m0vhcz+n9szvlpjegho7ow=">aaab+nicbvdlsgnbejz1genro0cvg0hwytxvqs9c0ivhcoybyrp6j7pjkjnzzwzwcws+xyshrbz6jd78gyepgyywnbrv3xr3hqln2njet7owuls8sppby69vbg5tu4wdmo5trwivxdxwjra05uzsqmgg00aikiiq03ryvx759qeqnivlnrkknbdqlsxibiyv2m6h1quhaf9iez8d+cenw7zb9ereghie+fnsrfnu2u5xqxotvfbpcaetm76xmcadzrjhdjhvpzomqprqpu1ljqiqg2x8+hafwkwdo1jzkgap1d8tgqitbyk0nqjmt896i/e/r5ma6climexsqywzlipsjk2mrzngdlougd6wbihi9lzmeqcagjtw3obgz748t2onjd8r+bdnxflvni4c2kp76bd56byv0q2qocoi6be9o1f05jw5l8678zfpxxcmm7vod5zph0tikru=</latexit> =n 1/3 1/3

9 <latexit sha1_base64="z9lksotu6timijejem30ssnb4qe=">aaacenicbzdlsgmxfiyz9vbrrerstbai7ciyuwtdceu3livyc3rqoznm2takmyqzoqx9bje+ihsxirh15c63mb0stpwhwmd/zuhk/ehmmtau++1kvlbx1jeym7mt7z3dvfz+qunhisk0tiieqvyamnimad0ww2krvhrewgkzgf5p6s0hqjsl5j0zxbqjoc9zyagya3xzjccx+bt7oqks+jzqf2vppao/d0kah1ad95xsujsvugv3krwm3hwkak5an//l9yksccon4ab123nj00lbguy4hef8rnmyybd6tg1rgqc6k05pgumt6/rwgcn7pmft9/decklrkqhspwaz0iu1iflfrz2y8kktmhknhkoywxqmhjsit/lbpayomxxkayhi9q+ydmcmy2ykoruct3jymjqqzc8te7dnhervpi4soklhqig8di6q6abvub0r9iie0st6c56cf+fd+zi1zpz5zch6i+fzbyjsnis=</latexit> <latexit sha1_base64="z9lksotu6timijejem30ssnb4qe=">aaacenicbzdlsgmxfiyz9vbrrerstbai7ciyuwtdceu3livyc3rqoznm2takmyqzoqx9bje+ihsxirh15c63mb0stpwhwmd/zuhk/ehmmtau++1kvlbx1jeym7mt7z3dvfz+qunhisk0tiieqvyamnimad0ww2krvhrewgkzgf5p6s0hqjsl5j0zxbqjoc9zyagya3xzjccx+bt7oqks+jzqf2vppao/d0kah1ad95xsujsvugv3krwm3hwkak5an//l9yksccon4ab123nj00lbguy4hef8rnmyybd6tg1rgqc6k05pgumt6/rwgcn7pmft9/decklrkqhspwaz0iu1iflfrz2y8kktmhknhkoywxqmhjsit/lbpayomxxkayhi9q+ydmcmy2ykoruct3jymjqqzc8te7dnhervpi4soklhqig8di6q6abvub0r9iie0st6c56cf+fd+zi1zpz5zch6i+fzbyjsnis=</latexit> <latexit sha1_base64="z9lksotu6timijejem30ssnb4qe=">aaacenicbzdlsgmxfiyz9vbrrerstbai7ciyuwtdceu3livyc3rqoznm2takmyqzoqx9bje+ihsxirh15c63mb0stpwhwmd/zuhk/ehmmtau++1kvlbx1jeym7mt7z3dvfz+qunhisk0tiieqvyamnimad0ww2krvhrewgkzgf5p6s0hqjsl5j0zxbqjoc9zyagya3xzjccx+bt7oqks+jzqf2vppao/d0kah1ad95xsujsvugv3krwm3hwkak5an//l9yksccon4ab123nj00lbguy4hef8rnmyybd6tg1rgqc6k05pgumt6/rwgcn7pmft9/decklrkqhspwaz0iu1iflfrz2y8kktmhknhkoywxqmhjsit/lbpayomxxkayhi9q+ydmcmy2ykoruct3jymjqqzc8te7dnhervpi4soklhqig8di6q6abvub0r9iie0st6c56cf+fd+zi1zpz5zch6i+fzbyjsnis=</latexit> <latexit sha1_base64="z9lksotu6timijejem30ssnb4qe=">aaacenicbzdlsgmxfiyz9vbrrerstbai7ciyuwtdceu3livyc3rqoznm2takmyqzoqx9bje+ihsxirh15c63mb0stpwhwmd/zuhk/ehmmtau++1kvlbx1jeym7mt7z3dvfz+qunhisk0tiieqvyamnimad0ww2krvhrewgkzgf5p6s0hqjsl5j0zxbqjoc9zyagya3xzjccx+bt7oqks+jzqf2vppao/d0kah1ad95xsujsvugv3krwm3hwkak5an//l9yksccon4ab123nj00lbguy4hef8rnmyybd6tg1rgqc6k05pgumt6/rwgcn7pmft9/decklrkqhspwaz0iu1iflfrz2y8kktmhknhkoywxqmhjsit/lbpayomxxkayhi9q+ydmcmy2ykoruct3jymjqqzc8te7dnhervpi4soklhqig8di6q6abvub0r9iie0st6c56cf+fd+zi1zpz5zch6i+fzbyjsnis=</latexit> <latexit sha1_base64="f9zlyvevzjmyne1+imvkaq6a3kk=">aaab7xicbvbnswmxej2tx7v+vt16crbbu93vgl6eohepfewhtevjptk2npsssvyos/+dfw+kepx/eppfmg33ok0pbh7vztazl4g508z1v53cyura+kzxs7s1vbo7v94/agmzkekbrhkpoghwldnbm4yztjuxojgkog0h49vmbz9rpzkud2ysuz/cq8fcrrcxugtdo4uzwr9ccavudgizedmpqi5gv/zvg0isrfqywrhwxc+njz9izrjhdfrqjzrgmizxkhytftii2k9n107rivugkjtkljbopv6eshgk9sqkbgeezugvepn4n9dnthjlp0zeiagczbefcudgoux1ngckesmnlmciml0vkrfwmbgbummg4c2+vexa51xprxr3tur9jo+jcedwdkfgwsxu4q4a0aqcj/amr/dmsoffexc+5q0fj585hd9wpn8ajfsnyq==</latexit> <latexit sha1_base64="f9zlyvevzjmyne1+imvkaq6a3kk=">aaab7xicbvbnswmxej2tx7v+vt16crbbu93vgl6eohepfewhtevjptk2npsssvyos/+dfw+kepx/eppfmg33ok0pbh7vztazl4g508z1v53cyura+kzxs7s1vbo7v94/agmzkekbrhkpoghwldnbm4yztjuxojgkog0h49vmbz9rpzkud2ysuz/cq8fcrrcxugtdo4uzwr9ccavudgizedmpqi5gv/zvg0isrfqywrhwxc+njz9izrjhdfrqjzrgmizxkhytftii2k9n107rivugkjtkljbopv6eshgk9sqkbgeezugvepn4n9dnthjlp0zeiagczbefcudgoux1ngckesmnlmciml0vkrfwmbgbummg4c2+vexa51xprxr3tur9jo+jcedwdkfgwsxu4q4a0aqcj/amr/dmsoffexc+5q0fj585hd9wpn8ajfsnyq==</latexit> <latexit sha1_base64="f9zlyvevzjmyne1+imvkaq6a3kk=">aaab7xicbvbnswmxej2tx7v+vt16crbbu93vgl6eohepfewhtevjptk2npsssvyos/+dfw+kepx/eppfmg33ok0pbh7vztazl4g508z1v53cyura+kzxs7s1vbo7v94/agmzkekbrhkpoghwldnbm4yztjuxojgkog0h49vmbz9rpzkud2ysuz/cq8fcrrcxugtdo4uzwr9ccavudgizedmpqi5gv/zvg0isrfqywrhwxc+njz9izrjhdfrqjzrgmizxkhytftii2k9n107rivugkjtkljbopv6eshgk9sqkbgeezugvepn4n9dnthjlp0zeiagczbefcudgoux1ngckesmnlmciml0vkrfwmbgbummg4c2+vexa51xprxr3tur9jo+jcedwdkfgwsxu4q4a0aqcj/amr/dmsoffexc+5q0fj585hd9wpn8ajfsnyq==</latexit> <latexit sha1_base64="f9zlyvevzjmyne1+imvkaq6a3kk=">aaab7xicbvbnswmxej2tx7v+vt16crbbu93vgl6eohepfewhtevjptk2npsssvyos/+dfw+kepx/eppfmg33ok0pbh7vztazl4g508z1v53cyura+kzxs7s1vbo7v94/agmzkekbrhkpoghwldnbm4yztjuxojgkog0h49vmbz9rpzkud2ysuz/cq8fcrrcxugtdo4uzwr9ccavudgizedmpqi5gv/zvg0isrfqywrhwxc+njz9izrjhdfrqjzrgmizxkhytftii2k9n107rivugkjtkljbopv6eshgk9sqkbgeezugvepn4n9dnthjlp0zeiagczbefcudgoux1ngckesmnlmciml0vkrfwmbgbummg4c2+vexa51xprxr3tur9jo+jcedwdkfgwsxu4q4a0aqcj/amr/dmsoffexc+5q0fj585hd9wpn8ajfsnyq==</latexit> Scaling Predictions a = log(n) log( 2 ) =3/4

10 Flaws and Resolutions Original calculation for beta assumed area preserving branching for impedance matched pulsatile flow Flow through small blood vessels is heavily damped and becomes DC. This changes requirements on scaling to minimize impedance. Recover scaling exponents as long as largest few tiers of network have same scaling parameters as before. Essentially redefinition of terminal unit. Fixes problem of large velocity in capillaries.

11 Scaling Hypothesis Assumptions: Natural selection maximizes fitness by maximizing metabolic rate. More energy for survival and reproduction Metabolic rate is proportional to effective surface area a across which nutrients can flow There is some invariant length: capillary, mitochondria, cytochrome oxidase. a(l0, l1,..., ln ) = 2+ a v(l0, l1,..., ln ) = 3+ v l(l0, l1,..., ln ) = 1+ l <latexit sha1_base64="5d0/m8wx3qrex76jc/c48c09c54=">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</latexit> <latexit sha1_base64="jdfjs2voary5vwg4ru1lf+obifi=">aaaconicbvdlsgmxfm3uv62vqks3wsk0wmyzfxqjfn24bme+odmomtrtqzozickuytdvcunxuhphxouibv0a03ywtfva4nxz7+hmhj9ivcrlejuyk6tr6xvzzdzw9s7uxn7/ochdwgbsxyelrcthkjdksv1rxugregqfpinnf3a36tehrega8gc1iogbob6nxyqr0pkxrw2lzlpkdtowdolms8umac7vvarvyfo+jhendokkzdo6hmop9yz16nejlxn5gmvau8blyqekafjuvfyl0wlxhbcumenstm0rum6chkkykxhoiswjeb6ghmlrylfapjtmtx/de610ydcu+nefp+q8i0gblkpa15mbun252jui//xasepeuwnluawix7nf3zhbfcjjjrbdbcgkjtrbwfd9v4j7sccsdno5hyk9epiyazybtmxatctc5taniwuowdeoahtcgqq4b1vqbxg8gtfwat6nz+pd+dk+z6mzi/ucgj8wfn4b0c6p1a==</latexit> <latexit sha1_base64="sgl7rnp1/j+wjywgat4y6esldxm=">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</latexit> a(l0, l1,..., ln ) = l12 (l0 /l1,...ln /l1 ) <latexit sha1_base64="l6nchwfkrtn8wf8krs+fyyagy1o=">aaachhicbvbns8mwge79npor6tflcagbjnpoqs/c0ivhce4dtlrsln3c0rqkqtdkfogx/4oxd4p48sd4b0y3hntzgzanz/o+vhkfp2zuktv+npawv1bx1gsbxc2t7z1dc2+/janeynleeytex0esmmpju1hfsccwbiu+i21/dj357qciji34nrrhxa3rgnoayqs05jmnqmw8u8o8p2pzlr55bv5c/byvwv5jsdp3jhe1mdgkz5zsy54clhinjywqo+gzn71+hjoqciuzkrlr2lfyuyquxyxmir1ekhjherqqrqychus66xs5ctzwsh8gkdchkzhvf3ekkjryhpq6mkrqkoe9tpzp6yyquhbtyuneey5ng4keqrxblcnyp4jgxcaaicyo/iveqyqqvjrpog7bmv95kbrqlmnbzu1zqx6vx1eah+ailiedzked3iagaaimhsezeavvxppxyrwbh7psjspvoqb/yhz9al38nna=</latexit> li! li <latexit sha1_base64="/vtupobeylrgxz7jzgbqv9qgcsi=">aaacbhicbvdlssnafl3xwesr6rkbwsk4kokiuiy6cvnbpqajytkztemnkzazuurowo2/4safim79chf+jdm2c209mha45x7u3bnmncnton/wyura+szmzau6vbo7t28fhhzumktc2ytlqeyfwfhobg1rpjntzzlijos0g46up373nkrfungnxxn1ezwqlgyeaymfdo0hdhmsdyyas5k+ii+bcisr0qo77jscgdaycutshxktwp7yoptkcrwackxu33uy7rdyaky4nvs9xnemkxee0l6haidu+cxsiak6muqe4lsajzsaqb8tbu6ugiehmuywhqpfbyr+5/vzhv/6brnzrqkg80vxzpfo0bqrfdfjiezjqzcrzpwvksgwmgjtw9wu4c6evew6zw3xabi35/xmvvlhbwpwdkfgwgu04qza0aycj/amr/bmpvkv1rv1mr9dscrmefyb9fkdwxgx4w==</latexit> a(l0, l1,..., ln ) = <latexit sha1_base64="fj2ww5fxugphc0alyodhlwzs6ga=">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</latexit> a <latexit sha1_base64="glhkxiie3uhvqtipifoonkilteu=">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</latexit> (l0 /l1,...ln /l1 ) = (l0 / l1,...ln /l1 ) (l0 / l1,...ln /l1 ) v/m a(l0 /l1,...ln /l1 ) <latexit sha1_base64="nrjdkfqawa2oglwhvmk1foqn10i=">aaab8nicbvdlsgmxfm3uv62vqks3wsk4kjmi6lloxo1qwt5goprmmmldm0li7htk0m9w40irt36no//gtj2fvg8edufcs+45srbcgu9/eaw19y3nrfj2zwd3b/+genjutiozllwoesp0y2kz4jk1gingxw0yswpbovh4du53jsxyruqjtdwlujkupogugjpcce5pozqofn+v1vy6vwd+s4kc1fcbzr/62rsomqvmahxe2jdwnuq5mccpylnkl7nmezomqxy6kknkbjqvtp7hm6cmckkmexlwqv25kzpu2mkau8muwmiuenpxpy/milmoci51bkzs5udjjrclom+pb9wwcmlqckggu1sxhrfdkliwkq6eydxyx9k+qad+pxi4rdvuijrk6asdonmuocvuqheoivqiiowe0at69cb79t689+voyst2jteveb/fyy2q6w==</latexit> a/m v(l0 /l1,...ln /l1 ) l(l0 /l1,...ln /l1 ) 2 2 l1 2+ a 3+ a + l <latexit sha1_base64="gur7f0lm+c/yrynhcni6utr08os=">aaackhicbvblswmxgmzwv62vvy9egkuqhljbbb1z9ojfqgaf0f1lns22odlssljcwfbnepgvebfrpfd/iwm7h9o6ejjmzefytsayvdpxxlzhzxvtfao4wdra3tnds/cpmipojcynhlnytgokckocndtvjlsfjcgkggkfw9uj33omutgyp+qrih6e+pygfcntpk59jaanzcx0do+fui+uckdveay9ihrljogy9hz+ou+xlovazafitagxizutmshr79ofxi/gsus4xgwp1xedof0usu0xi1njsxqrca9rn3qm5sgiyk+ni2bwxcg9gmbshk7hvj2fsfgk1cgktdjceqawvyn4n9djdhjlp5slrboozw+fcyomlklrseclwzqndefyuvnxiafilkvntyvtgru48jjpviuuu3eflsq1m7yoijgcx+auuoas1madqimgwoafvifp8gw9wu/wtzwerqtwpnmi/sd6+qve8ayg</latexit> B/a/M <latexit sha1_base64="dmn+i3j/zinvr60vc5piecpayce=">aaacc3icbvdlsgmxfm3uv62vuzduqovgqsxoqzelbtwifewdompjpjk2njmmsuyow+zd+ctuxcji1h9w59+ytino64ha4zx7utkniblv2ng+rmlk6tr6rngztlw9s7tn7x+0lugkji0smjddacnckcctttuj3vgsfawmdilx5dtv3bopqoc3ehitp0jdtkokktzs3y43vfikwaui4a+7vku9uckcnmvplcv6dswpojpazelmpajynpv2pzcqoiki15ghpxque2s/rvjtzehw8hjfyothaeh6hniueewnsywzpdbkaizcmsc1nkm/n1iuktwjajmzit1si95u/m/rjtq88fpk40qtjuehworbe3hadbxqsbbme0mqltt8feirmjvou1/jloaurl4m7doq61tdm1ql3sjrkiijuaynwaxnoa6uqbo0aayp4am8gffr0xq23qz3+wjbyncowr9yh9/mqjr0</latexit> 3 4

12 Results from Scaling Hypothesis

13 Results of Scaling Hypothesis

14 Ontogenetic Growth and Universality

15 Ontogenetic Growth and Universality Energy either goes to maintaining cells or creating new ones. B= X c <latexit sha1_base64="m3udyq3gem/fj6td5o48sscw9gy=">aaachhicbvdlssnafj34rpvvdelmsaicubivdcouiubkktghjcfmjpn26otbzi1qqj7ejb/ixouiblwi/o3tx0jbd1w4c869zl3htwvxyjrfxsli0vlkammtvl6xubvd2dltqystllvoihlz9yligsesbrwe66askcgxromprkz+54fjxzp4hoypcypsi3nikqetezxtbr7ejsoij2jhsbdsw4829omyx3vucswheaclig+gcctv9ch1klwzzo6b54k1jvu0rdorfdpbqroixuafucq2zbtcnejgvlci7gskpyqosi/zmsykysrnx8cv+faraq4tqssgpfz/t+qkumoy+bozitbxs95i/m+zmwgv3jzhaqysppopwkxgspaokrxwysiiosaesq53xbrpdccg8yzrekzzk+dj+6rmmtxr7qxab0zjkkf9dicokixour3doczqiyoe0tn6rw/gk/fivbsfk9yfyzqzh/7a+pobr6gg7g==</latexit> dnc N c B c + Ec dt <latexit sha1_base64="q1scymjchiohilxr6u79j0tsmoq=">aaacbnicbvdlssnafj3uv62vqesrbovgxppoqtdc0y3lcvybbsytyaqdojmjmxohhkzc+ctuxcji1m9w5984bbpq1gmxdufcy733+dgjsjvot1vywfxaximultbwnza37o2dpoosiukdryysbr8pwqggdu01i+1yesr9rlr+8hrstx6ivdqsd3oue4+jvqahxugbqwfvd0ojcbrwla10bi8h4vfp2uk1g8fq5z277fsccea8cxnsbjnqpfurg0q44urozjbshdejtzciqslmjct1e0vihieotzqgcssj8tljgxk8neoaw0iaehpo1n8tkejkjbhvojnsazxrjcx/ve6iwwsvpsjonbf4uihmgnqrhgccayoj1mxkcmksmlshhictizbjluwi7uzl86r5wngdintbldeu8jikya8cgcpggnnqazegdhoag0fwdf7bm/vkvvjv1se0twdlm7vgd6zph35rl9e=</latexit> dm 3/4 = am dt B = B0 m3/4 <latexit sha1_base64="9iqereu0aeohmvqwn/s/wrt0em4=">aaab+hicbvbns8naej3ur1o/gvxozbeinmqibb0ipv48vraf0maw2w7apztn2n0infsxepggifd/ijf/jds2b60+ghi8n8pmvcdhtgnh+bikk6tr6xvfzdlw9s5u2d7bb6s4lys2smxj2q2wopwj2tjmc9pnjmvrwgkngf/p/m4dlyrf4k5peupfechyyajwrvltcgndoybvoog+oz+ttx274lsdodbf4uakajmavv3zh8qkjajqhgoleq6tac/dujpc6btutxvnmbnjie0zknbelzfnd5+iy6mmubhlu0kjufpzisorupmomj0r1io17m3e/7xeqsnll2mistuvzleotdnsmzqlgazmuql5xbbmjdo3ijlcehntsiqzenzll/+s9lnvdaruba1sb+rxfoeqjuaexliaotxae1paiiuneifx69f6tt6s90vrwcpnduaxri9v5jarsg==</latexit> b = Bc /Ec <latexit sha1_base64="qyxbul+99bvlvmxmqny4+n5sewg=">aaab8nicbvbns8naej3ur1q/qh69lbbbu01e0itqkolhcvyd0ha22027dlmbdjdccf0zxjwo4tvf481/47bnqaspbh7vztazl0o508z1v5zsyura+kz5s7k1vbo7v90/6gizkulbrhkpehhwldnb24yztnupojijoo1g45uz332ksjmphswkpugch4lfjgbjjt9c16gzkrpbkitvmlt350b/iveqghrohdxp/kcslkhcei619j03nugolwge02mln2mayjlgq+pbknbcdzdpt56ie6smucyvlwhqxp05kene60ks2c4em5fe9mbif56fmfgqyjlim0mfwsykm46mrlp/0yapsgyfwikjyvzwrezyywjsshubgrf88l/soa97bt27v6g1mkuczticyzgfdy6haxfqgjyqkpael/dqgofzexpef60lp5g5hf9wpr4byf6qaq==</latexit> M = (a/b)4 = (B0 mc /Bc )4 <latexit sha1_base64="bophkz3dqc2k0mqrwcdji7vzvxu=">aaacbxicbzdlsgmxfiyzxmu9jbrurbaiddposee3qqkbn0ife4f2hdjppg1nmkosecrqjrtfxy0lrdz6du58gzntf9r6q+djp+dwcv4gzlrpx/m2lpzxvtfwcxv5za3tnv17b7+pokri0sari2q7qiowkkhdu81io5ye8ycrvjc8yuqtbyivjcsdhsxe46gvaegx0sby7ambeamlqbyc3lcyqvko93g55mnj+hbbktktwuvwz1aam9v9+6vbi3dcidcyiau6rhnrl0vsu8zion9nfikrhqi+6rguibplpzmrxvdeod0yrti8oehe/t2riq7uiaemkym9upo1zpyv1kl0eoglvmsjjgjpf4ujgzqcwsswryxbmo0micyp+sveayqr1ia4vanbnt95ezpnjdcpubevqru2iymhdsexkaixnimquaz10aaypijn8arercfrxxq3pqats9zs5gd8kfx5a9oxlpu=</latexit> 1 <latexit sha1_base64="id5hysc9bjwps6zmp/tmqrygqa8=">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</latexit> m 1/4 M = 1 m 1/4 0 M e at/4m 1/4 bm a = B0 mc /Ec <latexit sha1_base64="mspbbbytlxuirfe1ani2opgbpvk=">aaab9xicbvbnswmxej2tx7v+vt16crbbu90vqs9cqqgek9gpanclm2bb0cs7jfmllp0fxjwo4tx/4s1/y9ruqaspbh7vztazl0w408z1v5zc0vlk6lpxvbsxubw9u97da+k4vyq2scxj1qmxppxj2jtmcnpjfmui5lqdjq6mfvubks1iewfgcfufhkgwmyknle4xukt1wbubobkosfcuufv3bvsxedmpqi5gup7s9woscion4vjrrucmxs+wmoxwoin1uk0ttez4qluwsiyo9rpz1rn0zju+imjlsxo0u39ozfhoprah7rtydpwinxx/87qpis78jmkknvss+aio5cjeabob6jnfiefjszbrzn6kybartiwnqmrd8bzf/ktap1xprxq3z5vapy+jcadwcmfgwtnu4aya0aqccp7gbv6dr+fzexpe560fj5/zh19wpr4bv6krgg==</latexit>

16 <latexit sha1_base64="ah5agulbhaissx9sx8qrybwk/08=">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</latexit> <latexit sha1_base64="ah5agulbhaissx9sx8qrybwk/08=">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</latexit> <latexit sha1_base64="ah5agulbhaissx9sx8qrybwk/08=">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</latexit> <latexit sha1_base64="ah5agulbhaissx9sx8qrybwk/08=">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</latexit> <latexit sha1_base64="i/otau7tq4jflhpxooh6maochjw=">aaab+3icbvbns8naen34wetxrecvi0xw1czs0itq9ojfqga/oi1ls920szebsdsrs8hf8ejbea/+ew/+g7dtdtr6yodx3gwz8/xyca2o822trk6tb2wwtorbo7t7+/zbqawjrfhwpjgivmcnmgkuwrm4cnajfsohl1jbh19p/fyju5ph8h4mmfncmpq84jsakfp2qqckwzeyqlv2+5c61vrwt8toxzkblxm3j2wuo9g3v3qdicyhk0af0brrojf4kvhaqwbzszdofhm6jkpwnvsskgkvnd2e4rojdhaqkvms8ez9pzgsuotj6jvokmbil3pt8t+vm0bw4avcxgkwseelgkrgipa0cdzgileqe0mivdzciumikelbxfu0ibilly+t1lnfdsruxa1cv8rjkkajdixokyvour3doazqioqe0dn6rw9wzr1y79bhvhxfymco0r9ynz+/ujlx</latexit> <latexit sha1_base64="i/otau7tq4jflhpxooh6maochjw=">aaab+3icbvbns8naen34wetxrecvi0xw1czs0itq9ojfqga/oi1ls920szebsdsrs8hf8ejbea/+ew/+g7dtdtr6yodx3gwz8/xyca2o822trk6tb2wwtorbo7t7+/zbqawjrfhwpjgivmcnmgkuwrm4cnajfsohl1jbh19p/fyju5ph8h4mmfncmpq84jsakfp2qqckwzeyqlv2+5c61vrwt8toxzkblxm3j2wuo9g3v3qdicyhk0af0brrojf4kvhaqwbzszdofhm6jkpwnvsskgkvnd2e4rojdhaqkvms8ez9pzgsuotj6jvokmbil3pt8t+vm0bw4avcxgkwseelgkrgipa0cdzgileqe0mivdzciumikelbxfu0ibilly+t1lnfdsruxa1cv8rjkkajdixokyvour3doazqioqe0dn6rw9wzr1y79bhvhxfymco0r9ynz+/ujlx</latexit> <latexit sha1_base64="i/otau7tq4jflhpxooh6maochjw=">aaab+3icbvbns8naen34wetxrecvi0xw1czs0itq9ojfqga/oi1ls920szebsdsrs8hf8ejbea/+ew/+g7dtdtr6yodx3gwz8/xyca2o822trk6tb2wwtorbo7t7+/zbqawjrfhwpjgivmcnmgkuwrm4cnajfsohl1jbh19p/fyju5ph8h4mmfncmpq84jsakfp2qqckwzeyqlv2+5c61vrwt8toxzkblxm3j2wuo9g3v3qdicyhk0af0brrojf4kvhaqwbzszdofhm6jkpwnvsskgkvnd2e4rojdhaqkvms8ez9pzgsuotj6jvokmbil3pt8t+vm0bw4avcxgkwseelgkrgipa0cdzgileqe0mivdzciumikelbxfu0ibilly+t1lnfdsruxa1cv8rjkkajdixokyvour3doazqioqe0dn6rw9wzr1y79bhvhxfymco0r9ynz+/ujlx</latexit> <latexit sha1_base64="i/otau7tq4jflhpxooh6maochjw=">aaab+3icbvbns8naen34wetxrecvi0xw1czs0itq9ojfqga/oi1ls920szebsdsrs8hf8ejbea/+ew/+g7dtdtr6yodx3gwz8/xyca2o822trk6tb2wwtorbo7t7+/zbqawjrfhwpjgivmcnmgkuwrm4cnajfsohl1jbh19p/fyju5ph8h4mmfncmpq84jsakfp2qqckwzeyqlv2+5c61vrwt8toxzkblxm3j2wuo9g3v3qdicyhk0af0brrojf4kvhaqwbzszdofhm6jkpwnvsskgkvnd2e4rojdhaqkvms8ez9pzgsuotj6jvokmbil3pt8t+vm0bw4avcxgkwseelgkrgipa0cdzgileqe0mivdzciumikelbxfu0ibilly+t1lnfdsruxa1cv8rjkkajdixokyvour3doazqioqe0dn6rw9wzr1y79bhvhxfymco0r9ynz+/ujlx</latexit> Ontogenetic Growth and Universality r = m M 1/4 log apple 1 m0 M 1/4 = at/4m 1/4

17 Is there a size limit? Rl = <latexit sha1_base64="dmnmk2yxyytv+zn0rwxywo/yulg=">aaab6hicbvbns8naej3ur1q/qh69lbbbu0le0itq9okxbfsbbsib7ardu9me3y1qqn+bfw+kepunefpfug1z0nyha4/3zpizfysca+o6305hbx1jc6u4xdrz3ds/kb8etxsckoznfotydqkquxcjtconwe6ikeabwhywvpv57sdumsfywuws9cm6ldzkjbornw765ypbdecgq8tlsqvy1pvlr94gzmme0jbbte56bml8jcrdmcbpqzdqtcgb0yf2lzu0qu1n80on5mwqaxlgypy0zk7+nshoppukcmxnrm1il3sz8t+vm5rw2s+4tfkdki0whakgjiazr8mak2rgtcyhthf7k2ejqigznpusdcfbfnmvtc6qnlv1gpev2m0erxfo4btowymrqme91kejdbce4rxenefnxxl3phatbsefoyy/cd5/aiznjme=</latexit> <latexit <latexit sha1_base64="humg1ix6zok959u2tgpi6+r+uds=">aaab6nicbvdlsgnbeoynrxhfuy9ebopgkeykei9blx7jiw9ilja76u2gzm4um7ncwpijxjwo4tuv8ubfoen2oikfduvvn91dqsk4nq777rtw1jc2t4rbpz3dvf2d8ufrs8epythksyhvj6aabzfynnwi7cqkarqibafjm5nffkkleswfzsrbp6jdyupoqlhsw31f9msvt+roqvajl5mk5gj0y1+9qczsckvhgmrd9dze+blvhjob01iv1zhqnqzd7foqaytaz+antsmzvqykjjutachc/t2r0ujrsrtyzoiakv72zuj/xjc14zwfczmkbivblaptquxmzn+tavfijjhyqpni9lbcrlrrzmw6jruct/zykmldvd236t1dvurxerxfoiftoacpalchw2haexgm4rle4c0rzovz7nwswgtopnmmf+b8/garoi21</latexit> Nc / M 3/4 <latexit sha1_base64="rjtz6khomouj9nv45otsskccac0=">aaab/hicbvdlsgmxfm3uv62v0s7dbivgqs5oqzdfn26ucvyb7thk0kwbmklckhggof6kgxekupvd3pk3po+fvg9cojxzl/fee0lgtfg8l6ewtlyyulzcl21sbm3vult7ls1shuktcyzuj0kammpj01ddsecqgpkikxy0upz47qeinbx8zmssbakacbptjiyvqrd8e2lyk0pii+d1fx56xbuhbswrelpav8sfkwqyoxg6n72+wglcumemad31pwmchcldmspjui/vrci8qgpstzsjhoggnx4/hodw6cnykfvcwkn6cyjhidzzetnobjmhxvqm4n9enzxxezbtllndoj4tilmg7aotjgcfkoinyyxbwff7k8rdpba2nq+sdcfffpkvaz1ufa/q39yq9yt5hewwdw7aefdbgaidk9aatybbbp7ac3h1hp1n5815n7uwnplmgfyc8/enzmkt8g==</latexit> 3 dc Nc <latexit sha1_base64="rgbtnwwyl5iqjepwfcc/dhozdpo=">aaab+3icbvdlsgmxfm3uv62vss7dbivgqsyoomuig1dswt6ghydmjtogzpkqzmqy9ffcufdert/izr8xbwehrqcuhm65l3vvissj2njet1nawv1b3yhvvra2d3b33p1qw4tmydlcggnvjzamjhlsmtqw0pwkodripbonrqd+55eotqw/n2njghqnoe0orszkovunq/xwdhti2jdkscngo3rrxt2bas4tvya1ukazul/9woasjdxghrtu+z40qy6uozirsawfasirhqeb6vnkuup0km9un8bjq8qwecown3cm/p7iuar1oi1sz4rmuc96u/e/r5ez5dlikzezirzpfyuzg/bfarawpopgw8awikyovrxiiviigxtxxybgl768tnqndd+r+3fntczveuczhiijcaj8caea4ay0qqtg8asewst4cyboi/pufmxbs04xcwd+wpn8aff/k7w=</latexit> /V dc / M 1/12 <latexit sha1_base64="ahr9uzl+twoy4qszhinjvhzdwgu=">aaab/xicbvdlsgmxfm3uv62v8bfzeyycqzopgi6lbtwifewd2nhizdjtagyskoxqh+kvuhghifv/w51/y/pyaoubc4dz7uxee0ljmtae9+0ulpzxvtek66wnza3thxd3r6lfpghtemgfaodyu85s2jdmcnqwiuik5lqvdq7gfuubks1eemegkvoj7quszgqbkwxuqrqq2jvkscpgzx2otlf1flhlr+jnabcjmpeymkeeuf/dsjasoakhhgvdqz40fo6vyyttuambasoxgeae7via4orqp59cp4lhvolgljst1mcj+nsix4nwwys0nqk2ft3vjcx/ve5m4gs/z6nmde3jdfgccwg/hucbi6yomxxocsak2vsh6wofibgblwwiap7lrdksvpbxqbdn5drlli4ioarh4aqgca5q4bruqqmq8aiewst4c56cf+fd+zi2fpzzzd74a+fzb/jnld8=</latexit> dc <latexit sha1_base64="qskjmjfcq/bzx93d4oh13djejjq=">aaab6nicbvbns8naej3ur1q/qh69lbbbu0le0gpri8ek9gpaudabsbt0swm7g6ge/gqvhhtx6i/y5r9x2+agrq8ghu/nmdmvsaxxxnw/ndla+sbmvnm7sro7t39qptxq6yrtdfsseynqblsj4bjbhhub3vqhjqobnwb8o/m7t6g0t+sjmatox3qoecqznvz6cadsuk25dxcoskq8gtsgqhnq/eqhcctiliyjqnxpc1pj51qzzgrok/1my0rzma6xz6mkmwo/n586jwdwcumukfvskln6eyknsdatolcdmtujveznxp+8xmaiaz/nms0msrzyfgwcmitm/iyhv8immfhcmel2vsjgvffmbdovg4k3/piqav/upbfu3v/wgjdfhgu4gvm4bw+uoaf30iqwmbjcm7zcmyocf+fd+vi0lpxi5hj+wpn8atkajb4=</latexit>? <latexit sha1_base64="vm44zil6bf7waa6ljkwwch0pvoi=">aaab6hicbvbns8naej3ur1q/qh69lbbbu0le0jtflx5bsb/qhrlzttq1m03y3qgl9bd48aciv3+sn/+n2zyhbx0w8hhvhpl5qsk4nq777rtw1jc2t4rbpz3dvf2d8ufrs8epythksyhvj6aabzfynnwi7cqkarqibafju5nffkkleswfzcrbp6jdyupoqlfs46zfrrhvdw6ysrycvcbhvv/+6g1ilkyodrnu667njsbpqdkcczyweqnghlixhwlxukkj1h42p3rkzqwyiggsbeld5urviyxgwk+iwhzg1iz0sjct//o6qqmv/yzljduo2wjrmapiyjl7mgy4qmbexblkfle3ejaiijjjsynzelzll1dj66lquvwvcvmp3ezxfoeetuecplicgtxdhzraaoezxuhnexrenhfny9facpkzy/gd5/mhj9wmww==</latexit> <latexit

18 <latexit sha1_base64="dzekknlqd8m1mexbeu9kbhxx8f8=">aaab/xicbvdlsgnbejz1genrfdy8dabbu7iroh5dviggrmglkjxmtjrjkjnddwzwievwv7x4umsr/+hnv3gs7eetcxqkqm66u/yim6ud59tawfxaxlnnrgxxnza3tu2d3zoky0mhskmeyozpfhawqfuzzaerssdc51d3b5djv/4aurewqohhbj4gvyb1gsxasg17v1iq3ocwyglusevcnehrqq9t55y8mwgej25kcihfuw1/ttohjquemnkivnn1iu0lrgpgoyyyrvhbroia9kbpaeaekc+zxd/cr0bp4g4otquat9tfewkrsg2fbzof0x01643f/7xmrlsxxskcknyq0omibsyxdve4ctxheqjmq0milczcimmfsek1csxrqnbnx54ntzo86+td29ncsztgkueh6badixedoyk6qmvurrq9omf0it6sj+vferc+pq0lvjqzh/7a+vwbwgotnq==</latexit> <latexit sha1_base64="dzekknlqd8m1mexbeu9kbhxx8f8=">aaab/xicbvdlsgnbejz1genrfdy8dabbu7iroh5dviggrmglkjxmtjrjkjnddwzwievwv7x4umsr/+hnv3gs7eetcxqkqm66u/yim6ud59tawfxaxlnnrgxxnza3tu2d3zoky0mhskmeyozpfhawqfuzzaerssdc51d3b5djv/4aurewqohhbj4gvyb1gsxasg17v1iq3ocwyglusevcnehrqq9t55y8mwgej25kcihfuw1/ttohjquemnkivnn1iu0lrgpgoyyyrvhbroia9kbpaeaekc+zxd/cr0bp4g4otquat9tfewkrsg2fbzof0x01643f/7xmrlsxxskcknyq0omibsyxdve4ctxheqjmq0milczcimmfsek1csxrqnbnx54ntzo86+td29ncsztgkueh6badixedoyk6qmvurrq9omf0it6sj+vferc+pq0lvjqzh/7a+vwbwgotnq==</latexit> <latexit sha1_base64="dzekknlqd8m1mexbeu9kbhxx8f8=">aaab/xicbvdlsgnbejz1genrfdy8dabbu7iroh5dviggrmglkjxmtjrjkjnddwzwievwv7x4umsr/+hnv3gs7eetcxqkqm66u/yim6ud59tawfxaxlnnrgxxnza3tu2d3zoky0mhskmeyozpfhawqfuzzaerssdc51d3b5djv/4aurewqohhbj4gvyb1gsxasg17v1iq3ocwyglusevcnehrqq9t55y8mwgej25kcihfuw1/ttohjquemnkivnn1iu0lrgpgoyyyrvhbroia9kbpaeaekc+zxd/cr0bp4g4otquat9tfewkrsg2fbzof0x01643f/7xmrlsxxskcknyq0omibsyxdve4ctxheqjmq0milczcimmfsek1csxrqnbnx54ntzo86+td29ncsztgkueh6badixedoyk6qmvurrq9omf0it6sj+vferc+pq0lvjqzh/7a+vwbwgotnq==</latexit> <latexit sha1_base64="dzekknlqd8m1mexbeu9kbhxx8f8=">aaab/xicbvdlsgnbejz1genrfdy8dabbu7iroh5dviggrmglkjxmtjrjkjnddwzwievwv7x4umsr/+hnv3gs7eetcxqkqm66u/yim6ud59tawfxaxlnnrgxxnza3tu2d3zoky0mhskmeyozpfhawqfuzzaerssdc51d3b5djv/4aurewqohhbj4gvyb1gsxasg17v1iq3ocwyglusevcnehrqq9t55y8mwgej25kcihfuw1/ttohjquemnkivnn1iu0lrgpgoyyyrvhbroia9kbpaeaekc+zxd/cr0bp4g4otquat9tfewkrsg2fbzof0x01643f/7xmrlsxxskcknyq0omibsyxdve4ctxheqjmq0milczcimmfsek1csxrqnbnx54ntzo86+td29ncsztgkueh6badixedoyk6qmvurrq9omf0it6sj+vferc+pq0lvjqzh/7a+vwbwgotnq==</latexit> <latexit sha1_base64="efla1oaterty+jscmfjxvqsoibu=">aaab+hicbvdlsgnbejynrxgfwfxoztainskucoot6mvjllwgwcpspdczmjo7zswkccmxepggifc/xzt/4+rx0mschqkqm+6umofmg8/7dnirq2vrg/nnwtb2zm7r3dtv6dhvfoo05rfqhuqdzxlqhhkoruqbesghzji8nvjnr1caxbjmrgkegvqlixglxkpdt1i7wx3nbdxg37u/xf235jw9kfay8eekhoaodt2vti+mqqbpkcdat30vmufglgguw7jqstukha5jh9qwsijab9n08de+tkopr7gyjq2eqr8nmik0honqdgpibnrrm4j/ee3urbdbxmssgpb0tihkotyxnqsae0wbnxxkcagk2vsxhrbfqlfzfwwi/ully6rxwva9sn97vqpczepio0n0he6qj85rbd2gkqojill0jf7rm/pkvdjvzsesnefmzw7qhzifp5dgkbo=</latexit> <latexit sha1_base64="efla1oaterty+jscmfjxvqsoibu=">aaab+hicbvdlsgnbejynrxgfwfxoztainskucoot6mvjllwgwcpspdczmjo7zswkccmxepggifc/xzt/4+rx0mschqkqm+6umofmg8/7dnirq2vrg/nnwtb2zm7r3dtv6dhvfoo05rfqhuqdzxlqhhkoruqbesghzji8nvjnr1caxbjmrgkegvqlixglxkpdt1i7wx3nbdxg37u/xf235jw9kfay8eekhoaodt2vti+mqqbpkcdat30vmufglgguw7jqstukha5jh9qwsijab9n08de+tkopr7gyjq2eqr8nmik0honqdgpibnrrm4j/ee3urbdbxmssgpb0tihkotyxnqsae0wbnxxkcagk2vsxhrbfqlfzfwwi/ully6rxwva9sn97vqpczepio0n0he6qj85rbd2gkqojill0jf7rm/pkvdjvzsesnefmzw7qhzifp5dgkbo=</latexit> <latexit sha1_base64="efla1oaterty+jscmfjxvqsoibu=">aaab+hicbvdlsgnbejynrxgfwfxoztainskucoot6mvjllwgwcpspdczmjo7zswkccmxepggifc/xzt/4+rx0mschqkqm+6umofmg8/7dnirq2vrg/nnwtb2zm7r3dtv6dhvfoo05rfqhuqdzxlqhhkoruqbesghzji8nvjnr1caxbjmrgkegvqlixglxkpdt1i7wx3nbdxg37u/xf235jw9kfay8eekhoaodt2vti+mqqbpkcdat30vmufglgguw7jqstukha5jh9qwsijab9n08de+tkopr7gyjq2eqr8nmik0honqdgpibnrrm4j/ee3urbdbxmssgpb0tihkotyxnqsae0wbnxxkcagk2vsxhrbfqlfzfwwi/ully6rxwva9sn97vqpczepio0n0he6qj85rbd2gkqojill0jf7rm/pkvdjvzsesnefmzw7qhzifp5dgkbo=</latexit> <latexit sha1_base64="efla1oaterty+jscmfjxvqsoibu=">aaab+hicbvdlsgnbejynrxgfwfxoztainskucoot6mvjllwgwcpspdczmjo7zswkccmxepggifc/xzt/4+rx0mschqkqm+6umofmg8/7dnirq2vrg/nnwtb2zm7r3dtv6dhvfoo05rfqhuqdzxlqhhkoruqbesghzji8nvjnr1caxbjmrgkegvqlixglxkpdt1i7wx3nbdxg37u/xf235jw9kfay8eekhoaodt2vti+mqqbpkcdat30vmufglgguw7jqstukha5jh9qwsijab9n08de+tkopr7gyjq2eqr8nmik0honqdgpibnrrm4j/ee3urbdbxmssgpb0tihkotyxnqsae0wbnxxkcagk2vsxhrbfqlfzfwwi/ully6rxwva9sn97vqpczepio0n0he6qj85rbd2gkqojill0jf7rm/pkvdjvzsesnefmzw7qhzifp5dgkbo=</latexit> <latexit sha1_base64="b0djnwqxhzsi3onqiivsycqtdfu=">aaab83icbvbnswmxej31s9avqkcvwsj4khsr9vj04rgc/yduwrjptg1nskusfcrsv+hfgyje/tpe/dem7r609cha470zzuzfqedg+v63t7k6tr6xwdoqb+/s7u1xdg5bjsk0zu2aier3imky4io1lbecdvlniiwea0ej26nffmla8eq92hhkqkkgiseceuukidbciuw/5vhy0qtu/zo/a1omucbvkndovb6cfkizyzslghjtxx5qw5xoy6lgk3kqgzysoiid1nvueclmmm9unqbtp/rrnghxyqkz+nsij9kysyxcpyr2aba9qfif181sfb3mxkwzzyrof8wzqdzb0wbqn2tgrrg7qqjm7lzeh0qtal1mzrccxnx5mbtoa9iv4fulav2mikmex3acz4dhcupwbw1oaouunuev3rzme/hevy9564pxzbzbh3ifp8ekknu=</latexit> <latexit sha1_base64="b0djnwqxhzsi3onqiivsycqtdfu=">aaab83icbvbnswmxej31s9avqkcvwsj4khsr9vj04rgc/yduwrjptg1nskusfcrsv+hfgyje/tpe/dem7r609cha470zzuzfqedg+v63t7k6tr6xwdoqb+/s7u1xdg5bjsk0zu2aier3imky4io1lbecdvlniiwea0ej26nffmla8eq92hhkqkkgiseceuukidbciuw/5vhy0qtu/zo/a1omucbvkndovb6cfkizyzslghjtxx5qw5xoy6lgk3kqgzysoiid1nvueclmmm9unqbtp/rrnghxyqkz+nsij9kysyxcpyr2aba9qfif181sfb3mxkwzzyrof8wzqdzb0wbqn2tgrrg7qqjm7lzeh0qtal1mzrccxnx5mbtoa9iv4fulav2mikmex3acz4dhcupwbw1oaouunuev3rzme/hevy9564pxzbzbh3ifp8ekknu=</latexit> <latexit sha1_base64="b0djnwqxhzsi3onqiivsycqtdfu=">aaab83icbvbnswmxej31s9avqkcvwsj4khsr9vj04rgc/yduwrjptg1nskusfcrsv+hfgyje/tpe/dem7r609cha470zzuzfqedg+v63t7k6tr6xwdoqb+/s7u1xdg5bjsk0zu2aier3imky4io1lbecdvlniiwea0ej26nffmla8eq92hhkqkkgiseceuukidbciuw/5vhy0qtu/zo/a1omucbvkndovb6cfkizyzslghjtxx5qw5xoy6lgk3kqgzysoiid1nvueclmmm9unqbtp/rrnghxyqkz+nsij9kysyxcpyr2aba9qfif181sfb3mxkwzzyrof8wzqdzb0wbqn2tgrrg7qqjm7lzeh0qtal1mzrccxnx5mbtoa9iv4fulav2mikmex3acz4dhcupwbw1oaouunuev3rzme/hevy9564pxzbzbh3ifp8ekknu=</latexit> <latexit sha1_base64="b0djnwqxhzsi3onqiivsycqtdfu=">aaab83icbvbnswmxej31s9avqkcvwsj4khsr9vj04rgc/yduwrjptg1nskusfcrsv+hfgyje/tpe/dem7r609cha470zzuzfqedg+v63t7k6tr6xwdoqb+/s7u1xdg5bjsk0zu2aier3imky4io1lbecdvlniiwea0ej26nffmla8eq92hhkqkkgiseceuukidbciuw/5vhy0qtu/zo/a1omucbvkndovb6cfkizyzslghjtxx5qw5xoy6lgk3kqgzysoiid1nvueclmmm9unqbtp/rrnghxyqkz+nsij9kysyxcpyr2aba9qfif181sfb3mxkwzzyrof8wzqdzb0wbqn2tgrrg7qqjm7lzeh0qtal1mzrccxnx5mbtoa9iv4fulav2mikmex3acz4dhcupwbw1oaouunuev3rzme/hevy9564pxzbzbh3ifp8ekknu=</latexit> Can You live to 1000? Total energy / gram is scale invariant TB/M ' 10 6 J/g Total number of heart beats is scale invariant TR ' 10 9 Respiratory complex turn overs constant per cell 10 16

19 References Geoffrey B. West, William H. Woodruff and James H. Brown PNAS February 19, Geoffrey B. West, James H. Brown, Brian J. Enquist Science 04 Apr 1997:Vol. 276, Issue 5309, pp Geoffrey B. West, James H. Brown, Brian J. Enquist Science 04 Jun 1999: Vol. 284, Issue 5420, pp