[{"title":"Stability and semiclassics in self-generated fields","department":[{"_id":"LaEr"}],"author":[{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"first_name":"Søren","full_name":"Fournais, Søren","last_name":"Fournais"},{"last_name":"Solovej","full_name":"Solovej, Jan","first_name":"Jan"}],"publist_id":"4198","external_id":{"arxiv":["1105.0506"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"apa":"Erdös, L., Fournais, S., & Solovej, J. (2013). Stability and semiclassics in self-generated fields. Journal of the European Mathematical Society. European Mathematical Society. https://doi.org/10.4171/JEMS/416","ama":"Erdös L, Fournais S, Solovej J. Stability and semiclassics in self-generated fields. Journal of the European Mathematical Society. 2013;15(6):2093-2113. doi:10.4171/JEMS/416","short":"L. Erdös, S. Fournais, J. Solovej, Journal of the European Mathematical Society 15 (2013) 2093–2113.","ieee":"L. Erdös, S. Fournais, and J. Solovej, “Stability and semiclassics in self-generated fields,” Journal of the European Mathematical Society, vol. 15, no. 6. European Mathematical Society, pp. 2093–2113, 2013.","mla":"Erdös, László, et al. “Stability and Semiclassics in Self-Generated Fields.” Journal of the European Mathematical Society, vol. 15, no. 6, European Mathematical Society, 2013, pp. 2093–113, doi:10.4171/JEMS/416.","ista":"Erdös L, Fournais S, Solovej J. 2013. Stability and semiclassics in self-generated fields. Journal of the European Mathematical Society. 15(6), 2093–2113.","chicago":"Erdös, László, Søren Fournais, and Jan Solovej. “Stability and Semiclassics in Self-Generated Fields.” Journal of the European Mathematical Society. European Mathematical Society, 2013. https://doi.org/10.4171/JEMS/416."},"date_updated":"2021-01-12T06:59:07Z","status":"public","type":"journal_article","_id":"2698","volume":15,"date_published":"2013-10-16T00:00:00Z","doi":"10.4171/JEMS/416","issue":"6","date_created":"2018-12-11T11:59:07Z","page":"2093 - 2113","day":"16","publication":"Journal of the European Mathematical Society","language":[{"iso":"eng"}],"year":"2013","publication_status":"published","month":"10","intvolume":" 15","publisher":"European Mathematical Society","quality_controlled":"1","main_file_link":[{"url":"http://arxiv.org/abs/1105.0506","open_access":"1"}],"oa":1,"oa_version":"Preprint","abstract":[{"text":"We consider non-interacting particles subject to a fixed external potential V and a self-generated magnetic field B. The total energy includes the field energy β∫B2 and we minimize over all particle states and magnetic fields. In the case of spin-1/2 particles this minimization leads to the coupled Maxwell-Pauli system. The parameter β tunes the coupling strength between the field and the particles and it effectively determines the strength of the field. We investigate the stability and the semiclassical asymptotics, h→0, of the total ground state energy E(β,h,V). The relevant parameter measuring the field strength in the semiclassical limit is κ=βh. We are not able to give the exact leading order semiclassical asymptotics uniformly in κ or even for fixed κ. We do however give upper and lower bounds on E with almost matching dependence on κ. In the simultaneous limit h→0 and κ→∞ we show that the standard non-magnetic Weyl asymptotics holds. The same result also holds for the spinless case, i.e. where the Pauli operator is replaced by the Schrödinger operator.","lang":"eng"}]},{"abstract":[{"lang":"eng","text":"We consider Hermitian and symmetric random band matrices H = (h xy ) in d⩾1 d ⩾ 1 dimensions. The matrix entries h xy , indexed by x,y∈(Z/LZ)d x , y ∈ ( Z / L Z ) d , are independent, centred random variables with variances sxy=E|hxy|2 s x y = E | h x y | 2 . We assume that s xy is negligible if |x − y| exceeds the band width W. In one dimension we prove that the eigenvectors of H are delocalized if W≫L4/5 W ≫ L 4 / 5 . We also show that the magnitude of the matrix entries |Gxy|2 | G x y | 2 of the resolvent G=G(z)=(H−z)−1 G = G ( z ) = ( H - z ) - 1 is self-averaging and we compute E|Gxy|2 E | G x y | 2 . We show that, as L→∞ L → ∞ and W≫L4/5 W ≫ L 4 / 5 , the behaviour of E|Gxy|2 E | G x y | 2 is governed by a diffusion operator whose diffusion constant we compute. Similar results are obtained in higher dimensions."}],"intvolume":" 323","month":"10","oa":1,"main_file_link":[{"url":"http://arxiv.org/abs/1205.5669","open_access":"1"}],"quality_controlled":0,"publisher":"Springer","publication":"Communications in Mathematical Physics","day":"01","year":"2013","publication_status":"published","date_created":"2018-12-11T11:59:07Z","date_published":"2013-10-01T00:00:00Z","issue":"1","doi":"10.1007/s00220-013-1773-3","volume":323,"page":"367 - 416","_id":"2697","status":"public","type":"journal_article","extern":1,"date_updated":"2021-01-12T06:59:07Z","citation":{"ista":"Erdös L, Knowles A, Yau H, Yin J. 2013. Delocalization and diffusion profile for random band matrices. Communications in Mathematical Physics. 323(1), 367–416.","chicago":"Erdös, László, Antti Knowles, Horng Yau, and Jun Yin. “Delocalization and Diffusion Profile for Random Band Matrices.” Communications in Mathematical Physics. Springer, 2013. https://doi.org/10.1007/s00220-013-1773-3.","short":"L. Erdös, A. Knowles, H. Yau, J. Yin, Communications in Mathematical Physics 323 (2013) 367–416.","ieee":"L. Erdös, A. Knowles, H. Yau, and J. Yin, “Delocalization and diffusion profile for random band matrices,” Communications in Mathematical Physics, vol. 323, no. 1. Springer, pp. 367–416, 2013.","apa":"Erdös, L., Knowles, A., Yau, H., & Yin, J. (2013). Delocalization and diffusion profile for random band matrices. Communications in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-013-1773-3","ama":"Erdös L, Knowles A, Yau H, Yin J. Delocalization and diffusion profile for random band matrices. Communications in Mathematical Physics. 2013;323(1):367-416. doi:10.1007/s00220-013-1773-3","mla":"Erdös, László, et al. “Delocalization and Diffusion Profile for Random Band Matrices.” Communications in Mathematical Physics, vol. 323, no. 1, Springer, 2013, pp. 367–416, doi:10.1007/s00220-013-1773-3."},"title":"Delocalization and diffusion profile for random band matrices","publist_id":"4199","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","full_name":"László Erdös","orcid":"0000-0001-5366-9603"},{"first_name":"Antti","full_name":"Knowles, Antti","last_name":"Knowles"},{"full_name":"Yau, Horng-Tzer","last_name":"Yau","first_name":"Horng"},{"first_name":"Jun","last_name":"Yin","full_name":"Yin, Jun"}]},{"department":[{"_id":"NiBa"},{"_id":"CaGu"}],"file_date_updated":"2020-07-14T12:45:45Z","ddc":["570"],"date_updated":"2021-01-12T06:59:15Z","status":"public","pubrep_id":"564","type":"conference","conference":{"name":"GECCO: Genetic and evolutionary computation conference","start_date":"2013-07-06","location":"Amsterdam, Netherlands","end_date":"2013-07-10"},"_id":"2718","ec_funded":1,"file":[{"relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_id":"5159","checksum":"9d9be9090ce5c20766e0eb076ace5b98","creator":"system","file_size":475844,"date_updated":"2020-07-14T12:45:45Z","file_name":"IST-2016-564-v1+1_NickGECCO_2013_1_-1.pdf","date_created":"2018-12-12T10:15:38Z"}],"language":[{"iso":"eng"}],"publication_status":"published","month":"07","scopus_import":1,"oa_version":"Submitted Version","abstract":[{"lang":"eng","text":"Even though both population and quantitative genetics, and evolutionary computation, deal with the same questions, they have developed largely independently of each other. I review key results from each field, emphasising those that apply independently of the (usually unknown) relation between genotype and phenotype. The infinitesimal model provides a simple framework for predicting the response of complex traits to selection, which in biology has proved remarkably successful. This allows one to choose the schedule of population sizes and selection intensities that will maximise the response to selection, given that the total number of individuals realised, C = ∑t Nt, is constrained. This argument shows that for an additive trait (i.e., determined by the sum of effects of the genes), the optimum population size and the maximum possible response (i.e., the total change in trait mean) are both proportional to √C."}],"title":"Can quantitative and population genetics help us understand evolutionary computation?","publist_id":"4174","author":[{"first_name":"Nicholas H","id":"4880FE40-F248-11E8-B48F-1D18A9856A87","full_name":"Barton, Nicholas H","orcid":"0000-0002-8548-5240","last_name":"Barton"},{"id":"2C5658E6-F248-11E8-B48F-1D18A9856A87","first_name":"Tiago","orcid":"0000-0003-2361-3953","full_name":"Paixao, Tiago","last_name":"Paixao"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Barton NH, Paixao T. 2013. Can quantitative and population genetics help us understand evolutionary computation? Proceedings of the 15th annual conference on Genetic and evolutionary computation. GECCO: Genetic and evolutionary computation conference, 1573–1580.","chicago":"Barton, Nicholas H, and Tiago Paixao. “Can Quantitative and Population Genetics Help Us Understand Evolutionary Computation?” In Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation, 1573–80. ACM, 2013. https://doi.org/10.1145/2463372.2463568.","short":"N.H. Barton, T. Paixao, in:, Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation, ACM, 2013, pp. 1573–1580.","ieee":"N. H. Barton and T. Paixao, “Can quantitative and population genetics help us understand evolutionary computation?,” in Proceedings of the 15th annual conference on Genetic and evolutionary computation, Amsterdam, Netherlands, 2013, pp. 1573–1580.","ama":"Barton NH, Paixao T. Can quantitative and population genetics help us understand evolutionary computation? In: Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation. ACM; 2013:1573-1580. doi:10.1145/2463372.2463568","apa":"Barton, N. H., & Paixao, T. (2013). Can quantitative and population genetics help us understand evolutionary computation? In Proceedings of the 15th annual conference on Genetic and evolutionary computation (pp. 1573–1580). Amsterdam, Netherlands: ACM. https://doi.org/10.1145/2463372.2463568","mla":"Barton, Nicholas H., and Tiago Paixao. “Can Quantitative and Population Genetics Help Us Understand Evolutionary Computation?” Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation, ACM, 2013, pp. 1573–80, doi:10.1145/2463372.2463568."},"project":[{"grant_number":"250152","name":"Limits to selection in biology and in evolutionary computation","call_identifier":"FP7","_id":"25B07788-B435-11E9-9278-68D0E5697425"}],"date_published":"2013-07-01T00:00:00Z","doi":"10.1145/2463372.2463568","date_created":"2018-12-11T11:59:14Z","page":"1573 - 1580","day":"01","publication":"Proceedings of the 15th annual conference on Genetic and evolutionary computation","has_accepted_license":"1","year":"2013","quality_controlled":"1","publisher":"ACM","oa":1},{"oa":1,"publisher":"Genetics Society of America","quality_controlled":"1","publication":"Genetics","day":"01","year":"2013","date_created":"2018-12-11T11:59:15Z","date_published":"2013-10-01T00:00:00Z","doi":"10.1534/genetics.113.153536","page":"527-540","project":[{"grant_number":"250152","name":"Limits to selection in biology and in evolutionary computation","call_identifier":"FP7","_id":"25B07788-B435-11E9-9278-68D0E5697425"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Long H, Paixao T, Azevedo R, Zufall R. 2013. Accumulation of spontaneous mutations in the ciliate Tetrahymena thermophila. Genetics. 195(2), 527–540.","chicago":"Long, Hongan, Tiago Paixao, Ricardo Azevedo, and Rebecca Zufall. “Accumulation of Spontaneous Mutations in the Ciliate Tetrahymena Thermophila.” Genetics. Genetics Society of America, 2013. https://doi.org/10.1534/genetics.113.153536.","short":"H. Long, T. Paixao, R. Azevedo, R. Zufall, Genetics 195 (2013) 527–540.","ieee":"H. Long, T. Paixao, R. Azevedo, and R. Zufall, “Accumulation of spontaneous mutations in the ciliate Tetrahymena thermophila,” Genetics, vol. 195, no. 2. Genetics Society of America, pp. 527–540, 2013.","apa":"Long, H., Paixao, T., Azevedo, R., & Zufall, R. (2013). Accumulation of spontaneous mutations in the ciliate Tetrahymena thermophila. Genetics. Genetics Society of America. https://doi.org/10.1534/genetics.113.153536","ama":"Long H, Paixao T, Azevedo R, Zufall R. Accumulation of spontaneous mutations in the ciliate Tetrahymena thermophila. Genetics. 2013;195(2):527-540. doi:10.1534/genetics.113.153536","mla":"Long, Hongan, et al. “Accumulation of Spontaneous Mutations in the Ciliate Tetrahymena Thermophila.” Genetics, vol. 195, no. 2, Genetics Society of America, 2013, pp. 527–40, doi:10.1534/genetics.113.153536."},"title":"Accumulation of spontaneous mutations in the ciliate Tetrahymena thermophila","external_id":{"pmid":["23934880"]},"article_processing_charge":"No","author":[{"first_name":"Hongan","full_name":"Long, Hongan","last_name":"Long"},{"orcid":"0000-0003-2361-3953","full_name":"Paixao, Tiago","last_name":"Paixao","id":"2C5658E6-F248-11E8-B48F-1D18A9856A87","first_name":"Tiago"},{"first_name":"Ricardo","last_name":"Azevedo","full_name":"Azevedo, Ricardo"},{"full_name":"Zufall, Rebecca","last_name":"Zufall","first_name":"Rebecca"}],"publist_id":"4172","pmid":1,"oa_version":"Submitted Version","abstract":[{"text":"Knowledge of the rate and fitness effects of mutations is essential for understanding the process of evolution. Mutations are inherently difficult to study because they are rare and are frequently eliminated by natural selection. In the ciliate Tetrahymena thermophila, mutations can accumulate in the germline genome without being exposed to selection. We have conducted a mutation accumulation (MA) experiment in this species. Assuming that all mutations are deleterious and have the same effect, we estimate that the deleterious mutation rate per haploid germline genome per generation is U = 0.0047 (95% credible interval: 0.0015, 0.0125), and that germline mutations decrease fitness by s = 11% when expressed in a homozygous state (95% CI: 4.4%, 27%). We also estimate that deleterious mutations are partially recessive on average (h = 0.26; 95% CI: –0.022, 0.62) and that the rate of lethal mutations is <10% of the deleterious mutation rate. Comparisons between the observed evolutionary responses in the germline and somatic genomes and the results from individual-based simulations of MA suggest that the two genomes have similar mutational parameters. These are the first estimates of the deleterious mutation rate and fitness effects from the eukaryotic supergroup Chromalveolata and are within the range of those of other eukaryotes.","lang":"eng"}],"intvolume":" 195","month":"10","main_file_link":[{"url":"http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3781978/","open_access":"1"}],"scopus_import":1,"language":[{"iso":"eng"}],"publication_status":"published","ec_funded":1,"issue":"2","volume":195,"_id":"2720","status":"public","type":"journal_article","date_updated":"2021-01-12T06:59:16Z","department":[{"_id":"NiBa"},{"_id":"CaGu"}]},{"type":"conference","conference":{"start_date":"2013-07-06","location":"Amsterdam, Netherlands","end_date":"2013-07-10","name":"GECCO: Genetic and evolutionary computation conference"},"status":"public","project":[{"grant_number":"250152","name":"Limits to selection in biology and in evolutionary computation","call_identifier":"FP7","_id":"25B07788-B435-11E9-9278-68D0E5697425"}],"_id":"2719","publist_id":"4173","author":[{"id":"2C5658E6-F248-11E8-B48F-1D18A9856A87","first_name":"Tiago","last_name":"Paixao","orcid":"0000-0003-2361-3953","full_name":"Paixao, Tiago"},{"last_name":"Barton","full_name":"Barton, Nicholas H","orcid":"0000-0002-8548-5240","id":"4880FE40-F248-11E8-B48F-1D18A9856A87","first_name":"Nicholas H"}],"title":"A variance decomposition approach to the analysis of genetic algorithms","department":[{"_id":"NiBa"},{"_id":"CaGu"}],"date_updated":"2021-01-12T06:59:15Z","citation":{"mla":"Paixao, Tiago, and Nicholas H. Barton. “A Variance Decomposition Approach to the Analysis of Genetic Algorithms.” Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation, ACM, 2013, pp. 845–52, doi:10.1145/2463372.2463470.","short":"T. Paixao, N.H. Barton, in:, Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation, ACM, 2013, pp. 845–852.","ieee":"T. Paixao and N. H. Barton, “A variance decomposition approach to the analysis of genetic algorithms,” in Proceedings of the 15th annual conference on Genetic and evolutionary computation, Amsterdam, Netherlands, 2013, pp. 845–852.","ama":"Paixao T, Barton NH. A variance decomposition approach to the analysis of genetic algorithms. In: Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation. ACM; 2013:845-852. doi:10.1145/2463372.2463470","apa":"Paixao, T., & Barton, N. H. (2013). A variance decomposition approach to the analysis of genetic algorithms. In Proceedings of the 15th annual conference on Genetic and evolutionary computation (pp. 845–852). Amsterdam, Netherlands: ACM. https://doi.org/10.1145/2463372.2463470","chicago":"Paixao, Tiago, and Nicholas H Barton. “A Variance Decomposition Approach to the Analysis of Genetic Algorithms.” In Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation, 845–52. ACM, 2013. https://doi.org/10.1145/2463372.2463470.","ista":"Paixao T, Barton NH. 2013. A variance decomposition approach to the analysis of genetic algorithms. Proceedings of the 15th annual conference on Genetic and evolutionary computation. GECCO: Genetic and evolutionary computation conference, 845–852."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"ACM","quality_controlled":"1","scopus_import":1,"month":"07","abstract":[{"text":"Prediction of the evolutionary process is a long standing problem both in the theory of evolutionary biology and evolutionary computation (EC). It has long been realized that heritable variation is crucial to both the response to selection and the success of genetic algorithms. However, not all variation contributes in the same way to the response. Quantitative genetics has developed a large body of work trying to estimate and understand how different components of the variance in fitness in the population contribute to the response to selection. We illustrate how to apply some concepts of quantitative genetics to the analysis of genetic algorithms. In particular, we derive estimates for the short term prediction of the response to selection and we use variance decomposition to gain insight on local aspects of the landscape. Finally, we propose a new population based genetic algorithm that uses these methods to improve its operation.","lang":"eng"}],"oa_version":"None","page":"845 - 852","date_published":"2013-07-01T00:00:00Z","doi":"10.1145/2463372.2463470","ec_funded":1,"date_created":"2018-12-11T11:59:15Z","year":"2013","publication_status":"published","day":"01","publication":"Proceedings of the 15th annual conference on Genetic and evolutionary computation","language":[{"iso":"eng"}]}]