Unsupervised identification of topological order using predictive models

Machine-learning driven models have proven to be powerful tools for the identification of phases of matter. In particular, unsupervised methods hold the promise to help discover new phases of matter without the need for any prior theoretical knowledge. While for phases characterized by a broken symmetry, the use of unsupervised methods has proven to be successful, topological phases without a local order parameter seem to be much harder to identify without supervision. Here, we use an unsupervised approach to identify topological phases and transitions out of them. We train artificial neural nets to relate configurational data or measurement outcomes to quantities like temperature or tuning parameters in the Hamiltonian. The accuracy of these predictive models can then serve as an indicator for phase transitions. We successfully illustrate this approach on both the classical Ising gauge theory as well as on the quantum ground state of a generalized toric code.Comment: 12 pages, 13 figure

Discordant introgression in a rapidly expanding hybrid swarm

The erosion of species boundaries can involve rapid evolutionary change. Consequently, many aspects of the process remain poorly understood, including the formation, expansion, and evolution of hybrid swarms. Biological invasions involving hybridization present exceptional opportunities to study the erosion of species boundaries because timelines of interactions and outcomes are frequently well known. Here, we examined clinal variation across codominant and maternally inherited genetic markers as well as phenotypic traits to characterize the expansion and evolution of a hybrid swarm between native Cyprinella venusta and invasive Cyprinella lutrensis minnows. Discordant introgression of phenotype, microsatellite multilocus genotype, and mtDNA haplotype indicates that the observable expansion of the C. venusta × C. lutrensis hybrid swarm is a false invasion front. Both parental and hybrid individuals closely resembling C. lutrensis are numerically dominant in the expansion wake, indicating that the non-native parental phenotype may be selectively favored. These findings show that cryptic introgression can extend beyond the phenotypic boundaries of hybrid swarms and that hybrid swarms likely expand more rapidly than can be documented from phenotypic variation alone. Similarly, dominance of a single parental phenotype following an introduction event may lead to instances of species erosion being mistaken for species displacement without hybridization

Unsupervised identification of topological phase transitions using predictive models

Machine-learning driven models have proven to be powerful tools for the identification of phases of matter. In particular, unsupervised methods hold the promise to help discover new phases of matter without the need for any prior theoretical knowledge. While for phases characterized by a broken symmetry, the use of unsupervised methods has proven to be successful, topological phases without a local order parameter seem to be much harder to identify without supervision. Here, we use an unsupervised approach to identify boundaries of the topological phases. We train artificial neural nets to relate configurational data or measurement outcomes to quantities like temperature or tuning parameters in the Hamiltonian. The accuracy of these predictive models can then serve as an indicator for phase transitions. We successfully illustrate this approach on both the classical Ising gauge theory as well as on the quantum ground state of a generalized toric code.ISSN:1367-263