Matrix elements of U(2n) generators in a multishell spin-orbit basis. I. The del-operator MEs in a two-shell composite Gelfand-Paldus basis

This is the first in a series of three articles which aimed to derive the matrix elements of the U(2n) generators in a multishell spin-orbit basis. This is a basis appropriate to many-electron systems which have a natural partitioning of the orbital space and where also spin-dependent terms are included in the Hamiltonian. The method is based on a new spin-dependent unitary group approach to the many-electron correlation problem due to Gould and Paldus [M. D. Gould and J. Paldus, J. Chem. Phys. 92, 7394, (1990)]. In this approach, the matrix elements of the U(2n) generators in the U(n) x U(2)-adapted electronic Gelfand basis are determined by the matrix elements of a single Ll(n) adjoint tensor operator called the del-operator, denoted by Delta(j)(i) (1 less than or equal to i, j less than or equal to n). Delta or del is a polynomial of degree two in the U(n) matrix E = [E-j(i)]. The approach of Gould and Paldus is based on the transformation properties of the U(2n) generators as an adjoint tensor operator of U(n) x U(2) and application of the Wigner-Eckart theorem. Hence, to generalize this approach, we need to obtain formulas for the complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The nonzero shift coefficients are uniquely determined and may he evaluated by the methods of Gould et al. [see the above reference]. In this article, we define zero-shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis which are appropriate to the many-electron problem. By definition, these are proportional to the corresponding two-shell del-operator matrix elements, and it is shown that the Racah factorization lemma applies. Formulas for these coefficients are then obtained by application of the Racah factorization lemma. The zero-shift adjoint reduced Wigner coefficients required for this procedure are evaluated first. All these coefficients are needed later for the multishell case, which leads directly to the two-shell del-operator matrix elements. Finally, we discuss an application to charge and spin densities in a two-shell molecular system. (C) 1998 John Wiley & Sons.

The assessment of oral cytology utilizing ploidy analysis and virtual microscopy for the early detection of epithelial dysplasia and neoplasia in oral mucosal lesions

Oral squamous cell carcinoma (OSCC) is associated with high morbidity and mortality which is due, at least in part, to late detection. Precancerous and cancerous oral lesions may mimic any number of benign oral lesions, and as such may be left without investigation and treatment until they are well advanced. Over the past several years there has been renewed interest in oral cytology as an adjuvant clinical tool in the investigation of oral mucosal lesions. The purpose of the present study was to compare the usefulness of ploidy analysis after Feulgen stained cytological thin-prep specimens with traditional incisional biopsy and routine histopathological examination for the assessment of the pre-malignant potential of oral mucosal lesions. An analysis of the cytological specimens was undertaken with virtual microscopy which allowed for rapid and thorough analysis of the complete cytological specimen. 100 healthy individuals between 30 and 70 years of age, who were non-smokers, non-drinkers and not taking any medication, had cytological specimens collected from both the buccal mucosa and lateral margin of tongue to establish normal cytology parameters within a control population. Patients with a presumptive clinical diagnosis of lichen planus, leukoplakia or OSCC had lesional cytological samples taken prior to their diagnostic biopsy. Standardised thin preparations were prepared and each specimen stained by both Feuglen and Papanicolau methods. High speed scanning of the complete slide at 40X magnification was undertaken using the Aperio Scanscope TM and the green channel of the resultant image was analysed after threshold segmentation to isolate only nuclei and the integrated optical density of each nucleus taken as a gross measure of the DNA content (ploidy). Preliminary results reveal that ploidy assessment of oral cytology holds great promise as an adjunctive prognostic factor in the analysis of the malignant potential of oral mucosal lesions.

Emerging concepts in colorectal neoplasia

An understanding of the mechanisms that explain the initiation and early evolution of colorectal cancer should facilitate the development of new approaches to effective prevention and intervention. This review highlights deficiencies in the current model for colorectal neoplasia in which APC mutation is placed at the point of initiation. Other genes implicated in the regulation of apoptosis and DNA repair may underlie the early development of colorectal cancer. Inactivation of these genes may occur not by mutation or loss but through silencing mediated by methylation of the gene's promoter region. hMLH1 and MGMT are examples of DNA repair genes that are silenced by methylation. Loss of expression of hMLH1 and MGMT protein has been demonstrated immunohistochemically in serrated polyps. Multiple lines of evidence point to a serrated pathway of neoplasia that is driven by inhibition of apoptosis and the subsequent inactivation of DNA repair genes by promoter methylation. The earliest lesions in this pathway are aberrant crypt foci (ACF). These may develop Into hyperplastic polyps or transform while still of microscopic size into admixed polyps, serrated adenomas, or traditional adenomas. Cancers developing from these lesions may show high- or low-level microsatellite instability (MSI-H and MSI-L, respectively) or may be microsatellite stable (MSS). The suggested clinical model for this alternative pathway is the condition hyperplastic polyposis. If colorectal cancer is a heterogeneous disease comprising discrete subsets that evolve through different pathways, it is evident that these subsets will need to be studied individually in the future.

Petrology and geochemistry of the Bandas del Sur Formation, Las Canadas Edifice, Tenerife (Canary Islands)

The Bandas del Sur Formation preserves a Quaternary extra-caldera record of central phonolitic explosive volcanism of the Las Canadas volcano at Tenerife. Volcanic rocks are bimodal in composition, being predominantly phonolitic pyroclastic deposits, several eruptions of which resulted in summit caldera collapse, alkali basaltic lavas erupted from many fissures around the flanks. For the pyroclastic deposits, there is a broad range of pumice glass compositions from phonotephrite to phonolite. The phonolite pyroclastic deposits are also characterized by a diverse, 7-8-phase phenocryst assemblage (alkali feldspar + biotite + sodian diopside + titanomagnetite + ilmenite + nosean-hauyne + titanite + apatite) with alkali feldspar dominant, in contrast to interbedded phonolite lavas that typically have lower phenocryst contents and lack hydrous phases. Petrological and geochemical data are consistent with fractional crystallization (involving the observed phenocryst assemblages) as the dominant process in the development of phonolite magmas. New stratigraphically constrained data indicate that petrological and geochemical differences exist between pyroclastic deposits of the last two explosive cycles of phonolitic volcanism. Cycle 2 (0.85-0.57 Ma) pyroclastic fall deposits commonly show a cryptic compositional zonation indicating that several eruptions tapped chemically, and probably thermally stratified magma systems. Evidence for magma mixing is most widespread in the pyroclastic deposits of Cycle 3 (0.37-0.17 Ma), which includes the presence of reversely and normally zoned phenocrysts, quenched mafic glass blebs in pumice, banded pumice, and bimodal to polymodal phenocryst compositional populations. Syn-eruptive mixing events involved mostly phonolite and tephriphonolite magmas, whereas a pre-eruptive mixing event involving basaltic magma is recorded in several banded pumice-bearing ignimbrites of Cycle 3. The periodic addition and mixing of basaltic magma ultimately may have triggered several eruptions. Recharge and underplating by basaltic magma is interpreted to have elevated sulphur contents (occurring as an exsolved gas phase) in the capping phonolitic magma reservoir. This promoted nosean-hauyne crystallization over nepheline, elevated SO3 contents in apatite, and possibly resulted in large, climatologically important SO2 emissions.

Familial adult renal neoplasia

Our understanding of the molecular mechanisms underlying the tumorigenesis of renal cell carcinoma (RCC) has partially come from studies of RCC related familial cancer syndromes such as von Hippel-Lindau (VHL) disease and hereditary papillary RCC (HPRC). These studies have led to the identification of RCC related genes, which, besides allowing accurate diagnosis of these diseases, have been found mutated or abnormally expressed in the sporadic counterparts of these familial renal tumours. To date, a number of renal tumour related syndromes have been described. We review recent advances in this field and discuss a genetic approach to managing familial cases of renal tumours occasionally encountered by cancer geneticists and urologists.