Subfactors of index less than 5, part 1: the principal graph odometer

In this series of papers we show that there are exactly ten subfactors, other than $A_\infty$ subfactors, of index between 4 and 5. Previously this classification was known up to index $3+\sqrt{3}$. In the first paper we give an analogue of Haagerup's initial classification of subfactors of index less than $3+\sqrt{3}$, showing that any subfactor of index less than 5 must appear in one of a large list of families. These families will be considered separately in the three subsequent papers in this series.Comment: 36 pages (updated to reflect that the classification is now complete

On Haagerup's list of potential principal graphs of subfactors

We show that any graph, in the sequence given by Haagerup in 1991 as that of candidates of principal graphs of subfactors, is not realized as a principal graph except for the smallest two. This settles the remaining case of a previous work of the first author.Comment: 19 page

Effect of near‐bed turbulence on chronic detachment of epilithic biofilm: Experimental and modeling approaches.

The biomass dynamics of epilithic biofilm, a collective term for a complex microorganism community that grows on gravel bed rivers, was investigated by coupling experimental and numerical approaches focusing on epilithic biofilm‐flow interactions. The experiment was conducted during 65 days in an artificial rough open‐channel flow, where filtered river water circulated at a constant discharge. To characterize the effect of near‐bed turbulence on the chronic detachment process in the dynamics of epilithic biofilm, local hydrodynamic conditions were measured by laser Doppler anemometry and turbulent boundary layer parameters inferred from double‐averaged quantities. Numerical simulations of the EB biomass dynamics were performed using three different models of chronic detachment based upon three different descriptors for the flow conditions: Discharge Q, friction velocity u*, and roughness Reynolds number k+. Comparisons of numerical simulation results with experimental data revealed chronic detachment to be better simulated by taking the roughness Reynolds number as the external physical variable forcing chronic detachment. Indeed, the loss of epilithic matter through the chronic detachment process is related not only to hydrodynamic conditions, but also to change in bottom roughness. This suggests that changes in the behavior and dimensions of river bed roughness must be considered when checking the dynamics of epilithic biofilm in running waters

Constructing the extended Haagerup planar algebra

We construct a new subfactor planar algebra, and as a corollary a new subfactor, with the `extended Haagerup' principal graph pair. This completes the classification of irreducible amenable subfactors with index in the range $(4,3+\sqrt{3})$, which was initiated by Haagerup in 1993. We prove that the subfactor planar algebra with these principal graphs is unique. We give a skein theoretic description, and a description as a subalgebra generated by a certain element in the graph planar algebra of its principal graph. In the skein theoretic description there is an explicit algorithm for evaluating closed diagrams. This evaluation algorithm is unusual because intermediate steps may increase the number of generators in a diagram.Comment: 45 pages (final version; improved introduction

Topological Quantum Field Theories and Operator Algebras

We review "quantum" invariants of closed oriented 3-dimensional manifolds arising from operator algebras.Comment: For proceedings of "International Workshop on Quantum Field Theory and Noncommutative Geometry", Sendai, November 200

Native drivers of fish life history traits are lost during the invasion process

© 2020 The Authors. Ecology and Evolution published by John Wiley & Sons Ltd. Rapid adaptation to global change can counter vulnerability of species to population declines and extinction. Theoretically, under such circumstances both genetic variation and phenotypic plasticity can maintain population fitness, but empirical support for this is currently limited. Here, we aim to characterize the role of environmental and genetic diversity, and their prior evolutionary history (via haplogroup profiles) in shaping patterns of life history traits during biological invasion. Data were derived from both genetic and life history traits including a morphological analysis of 29 native and invasive populations of topmouth gudgeon Pseudorasbora parva coupled with climatic variables from each location. General additive models were constructed to explain distribution of somatic growth rate (SGR) data across native and invasive ranges, with model selection performed using Akaike's information criteria. Genetic and environmental drivers that structured the life history of populations in their native range were less influential in their invasive populations. For some vertebrates at least, fitness-related trait shifts do not seem to be dependent on the level of genetic diversity or haplogroup makeup of the initial introduced propagule, nor of the availability of local environmental conditions being similar to those experienced in their native range. As long as local conditions are not beyond the species physiological threshold, its local establishment and invasive potential are likely to be determined by local drivers, such as density-dependent effects linked to resource availability or to local biotic resistance

Quantum subgroups of the Haagerup fusion categories

We answer three related questions concerning the Haagerup subfactor and its even parts, the Haagerup fusion categories. Namely we find all simple module categories over each of the Haagerup fusion categories (in other words, we find the `"quantum subgroups" in the sense of Ocneanu), we find all subfactors whose principal even part is one of the Haagerup fusion categories, and we compute the Brauer-Picard groupoid of Morita equivalences of the Haagerup fusion categories. In addition to the two even parts of the Haagerup subfactor, there is exactly one more fusion category which is Morita equivalent to each of them. This third fusion category has six simple objects and the same fusion rules as one of the even parts of the Haagerup subfactor, but has not previously appeared in the literature. We also find the full lattice of intermediate subfactors for every subfactor whose even part is one of these three fusion categories, and we discuss how our results generalize to Izumi subfactors.Comment: Final version. 40 pages, many figure

Native drivers of fish life history traits are lost during the invasion process

Rapid adaptation to global change can counter vulnerability of species to population declines and extinction. Theoretically, under such circumstances both genetic variation and phenotypic plasticity can maintain population fitness, but empirical support for this is currently limited. Here, we aim to characterize the role of environmental and genetic diversity, and their prior evolutionary history (via haplogroup profiles) in shaping patterns of life history traits during biological invasion. Data were derived from both genetic and life history traits including a morphological analysis of 29 native and invasive populations of topmouth gudgeon Pseudorasbora parva coupled with climatic variables from each location. General additive models were constructed to explain distribution of somatic growth rate (SGR) data across native and invasive ranges, with model selection performed using Akaike's information criteria. Genetic and environmental drivers that structured the life history of populations in their native range were less influential in their invasive populations. For some vertebrates at least, fitness-related trait shifts do not seem to be dependent on the level of genetic diversity or haplogroup makeup of the initial introduced propagule, nor of the availability of local environmental conditions being similar to those experienced in their native range. As long as local conditions are not beyond the species physiological threshold, its local establishment and invasive potential are likely to be determined by local drivers, such as density-dependent effects linked to resource availability or to local biotic resistance

Application of a two dimensional model to predict the effects of the curtain method on algal blooming in reservoirs

As one of the ways of reducing algal blooming in T-Dam reservoir, two vertical curtains, having depths to cover the epilimnion thickness, are installed across the reservoir in order to curtail the nutrient supply from nutrient-rich inflow to the downstream epilimnion of the reservoir. The physical and biological process in the reservoir ecosystem have been modelled, by assuming stratified layered and parcels structure, to predict the water quality and algal species composition in the reservoir. The state variables, temperature, four types of phytoplankton as chlorophyll-a, soluble phosphorus, nitrate, ammonium, dissolved oxygen, biochemical oxygen demand, internal nitrogen, internal phosphorus, and when diatoms are modelled explicitly silica, are considered in the model