Weak commutation relations of unbounded operators and applications

Four possible definitions of the commutation relation [S,T]=\Id of two closable unbounded operators $S,T$ are compared. The {\em weak} sense of this commutator is given in terms of the inner product of the Hilbert space \H where the operators act. Some consequences on the existence of eigenvectors of two number-like operators are derived and the partial O*-algebra generated by $S,T$ is studied. Some applications are also considered.Comment: In press in Journal of Mathematical Physic

On the Space of KdV Fields

The space of functions A over the phase space of KdV-hierarchy is studied as a module over the ring D generated by commuting derivations. A D-free resolution of A is constructed by Babelon, Bernard and Smirnov by taking the classical limit of the construction in quantum integrable models assuming a certain conjecture. We propose another D-free resolution of A by extending the construction in the classical finite dimensional integrable system associated with a certain family of hyperelliptic curves to infinite dimension assuming a similar conjecture. The relation of two constructions is given.Comment: 13 page

Fusion of the qq-Vertex Operators and its Application to Solvable Vertex Models

We diagonalize the transfer matrix of the inhomogeneous vertex models of the 6-vertex type in the anti-ferroelectric regime intoducing new types of q-vertex operators. The special cases of those models were used to diagonalize the s-d exchange model\cite{W,A,FW1}. New vertex operators are constructed from the level one vertex operators by the fusion procedure and have the description by bosons. In order to clarify the particle structure we estabish new isomorphisms of crystals. The results are very simple and figure out representation theoretically the ground state degenerations.Comment: 35 page

Redescription of Milnesium alpigenum Ehrenberg, 1853 (Tardigrada: Apochela) and a description of Milnesium inceptum sp. nov., a tardigrade laboratory model

Intra- and interspecific variability, being at the very core of alpha taxonomy, has been a long-standing topic of debate among tardigrade taxonomists. Early studies tended to assume that tardigrades exhibit wide intraspecific variation. However, with more careful morphological studies, especially those incorporating molecular tools that allow for an independent verification of species identifications based on phenotypic traits, we now recognise that ranges of tardigrade intraspecific variability are narrower, and that differences between species may be more subtle than previously assumed. The taxonomic history of the genus Milnesium, and more specifically that of the nominal species, M. tardigradum described by Doyère in 1840, is a good illustration of the evolution of views on intraspecific variability in tardigrades. The assumption of wide intraspecific variability in claw morphology led Marcus (1928) to synonymise two species with different claw configurations, M. alpigenum and M. quadrifidum, with M. tardigradum. Currently claw configuration is recognised as one of the key diagnostic traits in the genus Milnesium, and the two species suppressed by Marcus have recently been suggested to be valid. In this study, we clarify the taxonomic status of M. alpigenum, a species that for nearly a century was considered invalid. We redescribe M. alpigenum, using a population collected from the locus typicus, by the means of integrative taxonomy, i.e. including light microscopy, scanning electron microscopy, ontogenetic observations, and genetic barcoding. Moreover, the redescription of M. alpigenum allowed us to verify the uncertain taxonomic status of two popular laboratory models that were originally considered to be M. tardigradum; though one was recently reidentified as M. cf. alpigenum. Our analysis showed that both laboratory strains, despite being morphologically and morphometrically nearly identical to M. alpigenum, in fact represent a new species, M. inceptum sp. nov. The two species, being disnguishable only by statistical morphometry and/or DNA sequences, are the first example of pseudocryptic species in tardigrades

Identifying metabolites by integrating metabolome databases with mass spectrometry cheminformatics.

Novel metabolites distinct from canonical pathways can be identified through the integration of three cheminformatics tools: BinVestigate, which queries the BinBase gas chromatography-mass spectrometry (GC-MS) metabolome database to match unknowns with biological metadata across over 110,000 samples; MS-DIAL 2.0, a software tool for chromatographic deconvolution of high-resolution GC-MS or liquid chromatography-mass spectrometry (LC-MS); and MS-FINDER 2.0, a structure-elucidation program that uses a combination of 14 metabolome databases in addition to an enzyme promiscuity library. We showcase our workflow by annotating N-methyl-uridine monophosphate (UMP), lysomonogalactosyl-monopalmitin, N-methylalanine, and two propofol derivatives

The group law on the tropical Hesse pencil

We show that the addition of points on the tropical Hesse curve can be realized via the intersection with a tropical line. Then the addition formula for the tropical Hesse curve is reduced from those for the level-three theta functions through the ultradiscretization procedure. A tropical analogue of the Hessian group, the group of linear automorphisms acting on the Hesse pencil, is also investigated; it is shown that the dihedral group of degree three is the group of linear automorphisms acting on the tropical Hesse pencil.Comment: 17 pages, 1 figure, submitted to Special Issue of the Journal Mathematics and Computers in Simulation on "Nonlinear Waves: Computation and Theory

Cultural modulation of face and gaze scanning in young children

Previous research has demonstrated that the way human adults look at others’ faces is modulated by their cultural background, but very little is known about how such a culture-specific pattern of face gaze develops. The current study investigated the role of cultural background on the development of face scanning in young children between the ages of 1 and 7 years, and its modulation by the eye gaze direction of the face. British and Japanese participants’ eye movements were recorded while they observed faces moving their eyes towards or away from the participants. British children fixated more on the mouth whereas Japanese children fixated more on the eyes, replicating the results with adult participants. No cultural differences were observed in the differential responses to direct and averted gaze. The results suggest that different patterns of face scanning exist between different cultures from the first years of life, but differential scanning of direct and averted gaze associated with different cultural norms develop later in life

Diagonalization of the XXZ Hamiltonian by Vertex Operators

We diagonalize the anti-ferroelectric XXZ-Hamiltonian directly in the thermodynamic limit, where the model becomes invariant under the action of affine U_q( sl(2) ). Our method is based on the representation theory of quantum affine algebras, the related vertex operators and KZ equation, and thereby bypasses the usual process of starting from a finite lattice, taking the thermodynamic limit and filling the Dirac sea. From recent results on the algebraic structure of the corner transfer matrix of the model, we obtain the vacuum vector of the Hamiltonian. The rest of the eigenvectors are obtained by applying the vertex operators, which act as particle creation operators in the space of eigenvectors. We check the agreement of our results with those obtained using the Bethe Ansatz in a number of cases, and with others obtained in the scaling limit --- the $su(2)$-invariant Thirring model.Comment: 65 page

Discovery of essential kinetoplastid-insect adhesion proteins and their function in Leishmania -sand fly interactions

Leishmania species, members of the kinetoplastid parasites, cause leishmaniasis, a neglected tropical disease, in millions of people worldwide. Leishmania has a complex life cycle with multiple developmental forms, as it cycles between a sand fly vector and a mammalian host; understanding their life cycle is critical to understanding disease spread. One of the key life cycle stages is the haptomonad form, which attaches to insect tissues through its flagellum. This adhesion, conserved across kinetoplastid parasites, is implicated in having an important function within their life cycles and hence in disease transmission. Here, we discover the kinetoplastid-insect adhesion proteins (KIAPs), which localise in the attached Leishmania flagellum. Deletion of these KIAPs impairs cell adhesion in vitro and prevents Leishmania from colonising the stomodeal valve in the sand fly, without affecting cell growth. Additionally, loss of parasite adhesion in the sand fly results in reduced physiological changes to the fly, with no observable damage of the stomodeal valve and reduced midgut swelling. These results provide important insights into a comprehensive understanding of the Leishmania life cycle, which will be critical for developing transmission-blocking strategies