Graphs and Reflection Groups

It is shown that graphs that generalize the ADE Dynkin diagrams and have appeared in various contexts of two-dimensional field theory may be regarded in a natural way as encoding the geometry of a root system. After recalling what are the conditions satisfied by these graphs, we define a bilinear form on a root system in terms of the adjacency matrices of these graphs and undertake the study of the group generated by the reflections in the hyperplanes orthogonal to these roots. Some ``non integrally laced " graphs are shown to be associated with subgroups of these reflection groups. The empirical relevance of these graphs in the classification of conformal field theories or in the construction of integrable lattice models is recalled, and the connections with recent developments in the context of ${\cal N}=2$ supersymmetric theories and topological field theories are discussed.Comment: 42 pages TEX file, harvmac and epsf macros, AMS fonts optional, uuencoded, 8 figures include

Study of Deformation Effects in the Charged Particle Emission from 46Ti

The 46Ti compound nucleus, as populated by the fusion-evaporation reaction 27Al + 19F at the bombarding energy of 144 MeV, has been investigated by charged particle spectroscopy using the multidetector array ICARE at the VIVITRON tandem facility of the IReS (Strasbourg). The light charged particles have been measured in coincidence with evaporation residues. The CACARIZO code, a Monte Carlo implementation of the statistical-model code CASCADE, has been used to calculate the spectral shapes of evaporated alpha-particles which are compared with the experimental spectra. This comparison indicates the possible signature of large deformations of the compound nucleus.Comment: 6 pages, 4 figures, Proceedings od the Zakopane 20004 Symposium, to be published in Acta Phys. Pol. B36 (2005

Depth and Differentiation of the Orientale Melt Lake

Impact melt emplacement and evolution in lunar multi-ring basins is poorly understood since impact melt deposits in basins are generally buried by mare basalt fill and obscured by subsequent impact cratering. The relatively young Orientale basin, which is only partially flooded with mare basalt, opens a rare window into basin-scale impact melts. We describe the geology of impact melt-related facies in Orientale and suggest that the central depression of Orientale may represent a solidified impact melt lake that vertically subsided shortly after basin formation due to solidification and cooling. We use Lunar Orbiter Laser Altimeter (LOLA) data to measure the depth (approx. 1.75 km) and diameter (approx 350 km) of this central depression. If all the observed subsidence of the central depression is due to solidification and cooling, the melt lake should be approx 12.5-16 km deep, far more voluminous (approx 106 km3) than the largest known differentiated igneous intrusions on Earth. We investigate the possibility that the Orientale melt lake has differentiated and model 1) the bulk composition of the melt lake, 2) the operation of melt mixing in the melt lake, and 3) the chemical evolution of the resulting liquids on the An-Fo-Qz ternary in order to predict the lithologies that might be present in the solidified Orientale melt lake. Finally, we consider the possible significance of these lithologies

Some properties of angular integrals

We find new representations for Itzykson-Zuber like angular integrals for arbitrary beta, in particular for the orthogonal group O(n), the unitary group U(n) and the symplectic group Sp(2n). We rewrite the Haar measure integral, as a flat Lebesge measure integral, and we deduce some recursion formula on n. The same methods gives also the Shatashvili's type moments. Finally we prove that, in agreement with Brezin and Hikami's observation, the angular integrals are linear combinations of exponentials whose coefficients are polynomials in the reduced variables (x_i-x_j)(y_i-y_j).Comment: 43 pages, Late

On FPL configurations with four sets of nested arches

The problem of counting the number of Fully Packed Loop (FPL) configurations with four sets of a,b,c,d nested arches is addressed. It is shown that it may be expressed as the problem of enumeration of tilings of a domain of the triangular lattice with a conic singularity. After reexpression in terms of non-intersecting lines, the Lindstr\"om-Gessel-Viennot theorem leads to a formula as a sum of determinants. This is made quite explicit when min(a,b,c,d)=1 or 2. We also find a compact determinant formula which generates the numbers of configurations with b=d.Comment: 22 pages, TeX, 16 figures; a new formula for a generating function adde

FLUORESCENCE AND CIRCULAR DICHROISM STUDIES ON THE PHYCOERYTHROCYANINS FROM THE CYANOBACTERIUM

Two phycoerythrocyanin (PEC) fractions have been obtained from the phycobilisomes of the cyanobac-terium Westiellopsis prolifica ARM 365. They have been characterized by absorption, fluorescence and circular dichroism spectroscopy. One of them is spectroscopically similar to a PEC trimer known from other organisms. Whereas efficient energy transfer from its violin (α-84) to the cyanin (β-84, 155) chromophores is efficient in the trimer (αβ it is impeded after dissociation to the monomer (α,β). A second fraction of PEC which we earlier termed PEC(X) (Maruthi Sai et al., Photochem. Photobiol. 55,119–124, 1992), exhibited the spectral properties similar to that of the α-subunit of PEC from Mastigocladus laminosus. With this highly photoactive fraction, the circular dichroism spectra of the violobilin chromophore in both photoreversible states were obtained

Correlation Functions of Harish-Chandra Integrals over the Orthogonal and the Symplectic Groups

The Harish-Chandra correlation functions, i.e. integrals over compact groups of invariant monomials prod tr{X^{p_1} Omega Y^{q_1} Omega^dagger X^{p_2} ... with the weight exp tr{X Omega Y Omega^dagger} are computed for the orthogonal and symplectic groups. We proceed in two steps. First, the integral over the compact group is recast into a Gaussian integral over strictly upper triangular complex matrices (with some additional symmetries), supplemented by a summation over the Weyl group. This result follows from the study of loop equations in an associated two-matrix integral and may be viewed as the adequate version of Duistermaat-Heckman's theorem for our correlation function integrals. Secondly, the Gaussian integration over triangular matrices is carried out and leads to compact determinantal expressions.Comment: 58 pages; Acknowledgements added; small corrections in appendix A; minor changes & Note Adde

Reversible suppression of an essential gene in adult mice using transgenic RNA interference

RNAi has revolutionized loss-of-function genetics by enabling sequence-specific suppression of virtually any gene. Furthermore, tetracycline response elements (TRE) can drive expression of short hairpin RNAs (shRNAs) for inducible and reversible target gene suppression. Here, we demonstrate the feasibility of transgenic inducible RNAi for suppression of essential genes. We set out to directly target cell proliferation by screening an RNAi library against DNA replication factors and identified multiple shRNAs against Replication Protein A, subunit 3 (RPA3). We generated transgenic mice with TRE-driven Rpa3 shRNAs whose expression enforced a reversible cell cycle arrest. In adult mice, the block in cell proliferation caused rapid atrophy of the intestinal epithelium which led to weight loss and lethality within 8-11 d of shRNA induction. Upon shRNA withdrawal, villus atrophy and weight loss were fully reversible. Thus, shRpa3 transgenic mice provide an interesting tool to study tissue maintenance and regeneration. Overall, we have established a robust system that serves the purpose of temperature-sensitive alleles in other model organisms, enabling inducible and reversible suppression of essential genes in a mammalian system

Affine extension of noncrystallographic Coxeter groups and quasicrystals

Unique affine extensions H^{\aff}_2, H^{\aff}_3 and H^{\aff}_4 are determined for the noncrystallographic Coxeter groups $H_2$, $H_3$ and $H_4$. They are used for the construction of new mathematical models for quasicrystal fragments with 10-fold symmetry. The case of H^{\aff}_2 corresponding to planar point sets is discussed in detail. In contrast to the cut-and-project scheme we obtain by construction finite point sets, which grow with a model specific growth parameter.Comment: (27 pages, to appear in J. Phys. A

PHOTOCHEMISTRY OF PHYCOBILIPROTEINS

Native PEC from the cyanobacterium, Mastigocladus laminosus, and its isolated α-subunit show photoreversibly photochromic reactions with difference-maxima around 502 and 570 nm in the spectral region of the α-84 phycoviolobilin chromophore. (b) Native PEC and its β-subunit show little if any reversible photochemistry in the 600–620 nm region, where the phycocyanobilin chromophores on the β-subunit absorb maximally, (c) Reversible photochemistry is retained in ureadenatured PEC at pH = 7.0 or pH ≤ 3. The difference maxima are shifted to 510 and 600 nm, and the amplitudes are decreased. An irreversible absorbance increase occurs around 670 nm (pH ≤ 3). (d) The amplitude of the reversible photoreaction difference spectrum is maximum in the presence of 4–5 M urea or 1 M KSCN, conditions known to dissociate phycobiliprotein aggregates into monomers. At the same time, the phycocyanobilin chromophore(s) are bleached irreversibly, (e) The amplitude becomes very small in high aggregates, e.g. in phycobilisomes. (f) In a reciprocal manner, the phototransformation of native PEC leads to a reversible shift of its aggregation equilibrium between trimer and monomer. The latter is favored by orange, the former by green light, (g) It is concluded that the phycoviolobilin chromophore of PEC is responsible for reversible photochemistry in PEC, and that there is not only an influence of aggregation state on photochemistry, but also vice versa an effect of the status of the chromophore on aggregation state. This could constitute a primary signal in the putative function as sensory pigment, either directly, or indirectly via the release of other polypeptides, via photodynamic effects, or the like