Wild Character Research Articles

Toda Systems, Cluster Characters, and Spectral Networks

We show that the Hamiltonians of the open relativistic Toda system are elements of the generic basis of a cluster algebra, and in particular are cluster characters of nonrigid representations of a quiver with potential. Using cluster coordinates defined via spectral networks, we identify the phase space of this system with the wild character variety related to the periodic nonrelativistic Toda system by the wild nonabelian Hodge correspondence. We show that this identification takes the relativistic Toda Hamiltonians to traces of holonomies around a simple closed curve. In particular, this provides nontrivial examples of cluster coordinates on SLn-character varieties for n > 2 where canonical functions associated to simple closed curves can be computed in terms of quivers with potential, extending known results in the SL2 case.

Study of volatile compounds of Pyrus mamorensis Trab. a characteristic plant of Mamora forest (north-western Morocco)

Pyrus mamorensis Trab. commonly called “wild pear” was considered for long time as an endemic of the Mamora forest of Morocco (north-west). Although lack of protection and it is threatened with extinction in its range, this tree is of great interest due to its ecological and medicinal properties . This study focused on evaluation of volatiles in Pyrus mamorensis for its valorisation as a natural resource. So, the volatile compounds from different parts (leaves, stems, fruits, and flowers) were investigated after extraction by cold maceration in ethyl ether and analyzed by gas chromatography coupled to the mass spectrometry (GC - MS). Thirty one (31) compounds were identified and quantified including fifteen (15) terpenes, seven (7) alcans, two (2) aldehydes, four (4) esters and three (3) allyl alkoxybenzen derivatives. Estragol was the dominant component of the plant and that was only detected in leaves (83,09 %), while hexadecane (36,92 %) and allyl hexanoate (29,39 %) were mainly detected in the stems. The fruits showed relatively high levels (20,59 %) of benzyl butanoate, whereas in the flowers, limonene is the most abundant constituent (30,12 %). The analysis of the relative rates of different classes of volatile compounds, revealed the diversity of these compounds in P. mamorensis compared to two cultivars of edible species : P. communis L. et P. pyrifolia . The significant difference in composition in this case could be due to the wild character of P. mamorensis .

Global Weyl groups and a new theory of multiplicative quiver varieties

In previous work a relation between a large class of Kac-Moody algebras and meromorphic connections on global curves was established---notably the Weyl group gives isomorphisms between different moduli spaces of connections, and the root system is also seen to play a role. This involved a modular interpretation of many Nakajima quiver varieties, as moduli spaces of connections, whenever the underlying graph was a complete k-partite graph (or more generally a supernova graph). However in the isomonodromy story, or wild nonabelian Hodge theory, slightly larger moduli spaces of connections are considered. This raises the question of whether the full moduli spaces admit Weyl group isomorphisms, rather than just the open parts isomorphic to quiver varieties. This question will be solved here, by developing a "multiplicative version" of the previous approach. This amounts to constructing many algebraic symplectic isomorphisms between wild character varieties. This approach also enables us to state a conjecture for certain irregular Deligne--Simpson problems and introduce some noncommutative algebras, generalising the "generalised double affine Hecke algebras".

Dynamics on Wild Character Varieties

In the present paper, we will first present briefly a general research program about the study of the "natural dynamics" on character varieties and wild character varieties. Afterwards, we will illustrate this program in the context of the Painlev\'e differential equations $P_{\rm VI}$ and $P_{\rm V}$.

Poisson varieties from Riemann surfaces

Short survey based on talk at the Poisson 2012 conference. The main aim is to describe and give some examples of wild character varieties (naturally generalising the character varieties of Riemann surfaces by allowing more complicated behaviour at the boundary), their Poisson/symplectic structures (generalising both the Atiyah–Bott approach and the quasi-Hamiltonian approach), and the wild mapping class groups.

Geometry and braiding of Stokes data; Fission and wild character varieties

A family of new algebraic Poisson varieties will be constructed, generalising the complex character varieties of Riemann surfaces. Then the well-known (Poisson) mapping class group actions on the character varieties will be generalised.

A study of intraspecific hybrid lines derived from the reciprocal crosses between wild accessions and cultivated cowpeas (Vigna unguiculata (L.) Walp.)

Cowpea (Vigna unguiculata (L.) Walp.) is an essential food legume in the (sub) tropical areas. Reciprocal crosses were performed using wild accessions for transferring genes of interest to cultivars (524-B/IT84S-2049). Of these, a low number of seeds were obtained because of crossing barriers. A seed sample of 17 F1 hybrids germinated after germination was 69.09%. A subdivision into seed sterility, partial seed fertility and seed fertility was observed. Seed sterility was possibly due to chromosomal disturbances that occur in endosperms and embryos during early seed development. In partial seed fertility, vigorous plants flowered about 128 DAE but no pods were formed because of floral abscission at anthesis. In plants of (524-B (♀) × tenuis (♀)) combination, partial sterility was caused by incomplete male sterility. In 13 F1 hybrids, viability among populations was reduced (67.25%). Eleven F1 hybrids were grown in the greenhouse to produce F2 seeds by natural self-pollination. Plants were characterised through using cowpea descriptors. Variability, in terms of morphological characters in adult F1 plants, was established. Differences in vegetative, inflorescence and fruit characters were described after full plant development. The results show that the adult F1 plants appear to be dominant for wild vegetative and inflorescence characters expressed by one or two of the parents in bi-parental and reciprocal crosses, for exception plants derived from crosses in which alba wild forms served as male parent showing the same morphological characteristics as the cultivated female parents, as evidenced by the traits inherited from cultivars. The heterotic status exhibited by emerged plants, supposes that the latter types inbred at the first generation confirm that the wild parents involved in these hybrids represent a wide diversity of germplasm. Seed characteristic studied in F2 has not shown segregation because of recessive type absence, suggesting that morphological traits should be monitored. Key words: Reproductive barriers, seed fertility, introgressive hybridisation, wild character inheritance.

Pirates, merchants and anarchists: Representations of international business

This article considers the relationship between historical and fictional accounts of piracy, and relates them to contemporary issues about the legitimacy of states and global business. I begin by showing how privateers were gradually distinguished into pirates and navies. At the same time, the pirate becomes a character in the popular imagination, a ‘trickster’ figure on the side of the people, and against authority.The second main section of the paper moves from‘history’ to ‘representation’ and shows how the image of the pirate moved from a wild character on the edge of the world, to a stock cliché for Hollywood swashbucklers. I then investigate the legacy of radical histories and representations of piracy, focusing particularly on the idea of alternative organization on the ship and the pirate utopias on the land. The final section pulls together the historical figure, the stock character and the radical rogue in order to suggest that the pirate can mean what we want him (or to her) to mean.Nonetheless, the biggest historical irony is that the golden age pirate emerges at the beginnings of international business, and is only wiped out when the state and the businessman strike an alliance that lasts to the present day.

A differential quadrature analysis of vibration and buckling of an SS-C-SS-C rectangular plate loaded by linearly varying in-plane stresses

Thin rectangular plates having two opposite edges simply supported, with those edges subjected to linearly varying in-plane stresses, and the other two edges clamped, are encountered in engineering practice. Recently, Leissa and Kang used the classical power series method and obtained the first known exact vibration and some buckling solutions. The classical plate theory based on the Kirchhoff hypothesis is employed in the analysis. The relatively wild character of the convergence is observed, however, and 20 or 30 more terms of the series are needed to obtain reasonably accurate results. The differential quadrature (DQ) method has proved an accurate and computationally efficient numerical method. Thus, the DQ method is used to study the vibration and buckling of an SS-C-SS-C rectangular plate loaded by linearly varying in-plane stresses. Convergence study shows that DQ method with 15×15 or more non-uniform grid points can yield very accurate results for cases considered. Exactly the same, accurate results as of Leissa and Kang are easy to reproduce.

P-268 - Establishment of mouse proximal tubule cell line maintaining a wild character, ammoniagenesis

P-268 - Establishment of mouse proximal tubule cell line maintaining a wild character, ammoniagenesis