On the eigenvalues and eigenvectors of certain finite, vertex-weighted, bipartite graphs

AbstractThe established, spectral characterisation of bipartite graphs with unweighted vertices (which are here termed homogeneous graphs) is extended to those bipartite graphs (called heterogeneous) in which all of the vertices in one set are weighted h1 , and each of those in the other set of the bigraph is weighted h2. All the eigenvalues of a homogeneous bipartite graph occur in pairs, around zero, while some of the eigenvalues of an arbitrary, heterogeneous graph are paired around 12(h1 + h2), the remainder having the value h2 (or hl). The well-documented, explicit relations between the eigenvectors belonging to “paired” eigenvalues of homogeneous graphs are extended to relate the components of the eigenvectors associated with each couple of “paired” eigenvalues of the corresponding heterogeneous graph. Details are also given of the relationships between the eigenvectors of an arbitrary, homogeneous, bipartite graph and those of its heterogeneous analogue

Chronic sclerosing osteomyelitis of the mandible treated with hemimandibulectomy and fibular free flap reconstruction

Primary chronic osteomyelitis of the mandible is a rare condition that presents with a long-standing chronic facial swelling over the mandible, pain with mastication, and trismus. With no clinically appreciated acute phase, the aetiology often remains unknown. Many patients achieve adequate symptom control with broad-spectrum antibiotics, hyperbaric oxygen therapy and surgical debridement, or decortication of bone sequestration. However, because of the rarity of primary chronic osteomyelitis and the extensive involvement of the mandible that can result, we present a case of a 32-year-old woman with chronic disease of the left mandible requiring a left hemimandibulectomy and fibular free flap reconstruction. Few such cases have been reported in the literature, which require such extensive resection and reconstruction to control long-standing symptoms

The position of graptolites within Lower Palaeozoic planktic ecosystems.

An integrated approach has been used to assess the palaeoecology of graptolites both as a discrete group and also as a part of the biota present within Ordovician and Silurian planktic realms. Study of the functional morphology of graptolites and comparisons with recent ecological analogues demonstrates that graptolites most probably filled a variety of niches as primary consumers, with modes of life related to the colony morphotype. Graptolite coloniality was extremely ordered, lacking any close morphological analogues in Recent faunas. To obtain maximum functional efficiency, graptolites would have needed varying degrees of coordinated automobility. A change in lifestyle related to ontogenetic changes was prevalent within many graptolite groups. Differing lifestyle was reflected by differing reproductive strategies, with synrhabdosomes most likely being a method for rapid asexual reproduction. Direct evidence in the form of graptolithophage 'coprolitic' bodies, as well as indirect evidence in the form of probable defensive adaptations, indicate that graptolites comprised a food item for a variety of predators. Graptolites were also hosts to a variety of parasitic organisms and provided an important nutrient source for scavenging organisms

Serum microRNA profiling to distinguish papillary thyroid cancer from benign thyroid masses

Objectives: Papillary thyroid cancer (PTC) is increasing in incidence. Fine needle aspiration is the gold standard for diagnosis, but results can be indeterminate. Identifying tissue and serum biomarkers, like microRNA, is therefore desirable. We sought to identify miRNA that is differentially expressed in the serum of patients with PTC. Methods: Serum miRNA was quantified in 31 female thyroidectomy patients: 13 with benign disease and 18 with PTC. qPCR results were compared for significant fold-changes in 175 miRNAs, against a pooled control. Results: 128 miRNA qualified for analysis. There were identifiable fold-changes in miRNA levels between benign and control, and between PTC and control. There were statistically significant fold changes in the level of four miRNAs between benign and PTC: hsa-miR-146a-5p and hsa-miR-199b-3p were down-regulated, while hsa-let7b-5p and hsa-miR-10a-5p were up-regulated. Conclusions: MicroRNA is differentially expressed in the serum of patients with PTC. Serum miRNA has the potential to aid in thyroid cancer diagnosis

The Hippo component YAP localizes in the nucleus of human papilloma virus positive oropharyngeal squamous cell carcinoma

Background: HPV infection causes cervical cancer, mediated in part by the degradation of Scribble via the HPV E6 oncoprotein. Recently, Scribble has been shown to be an important regulator of the Hippo signaling cascade. Deregulation of the Hippo pathway induces an abnormal cellular transformation, epithelial to mesenchymal transition, which promotes oncogenic progression. Given the recent rise in oropharyngeal HPV squamous cell carcinoma we sought to determine if Hippo signaling components are implicated in oropharyngeal squamous cell carcinoma. Methods: Molecular and cellular techniques including immunoprecipiations, Western blotting and immunocytochemistry were used to identify the key Hippo pathway effector Yes-Associated Protein (YAP)1. Oropharyngeal tissue was collected from CO2 laser resections, and probed with YAP1 antibody in tumor and pre-malignant regions of HPV positive OPSCC tissue. Results: This study reveals that the Scribble binding protein Nitric Oxide Synthase 1 Adaptor Protein (NOS1AP) forms a complex with YAP. Further, the NOS1APa and NOS1APc isoforms show differential association with activated and non-activated YAP, and impact cellular proliferation. Consistent with deregulated Hippo signaling in OPSCC HPV tumors, we see a delocalization of Scribble and increased nuclear accumulation of YAP1 in an HPV-positive OPSCC. Conclusion: Our preliminary data indicates that NOS1AP isoforms differentially associate with YAP1, which, together with our previous findings, predicts that loss of YAP1 enhances cellular transformation. Moreover, YAP1 is highly accumulated in the nucleus of HPV-positive OPSCC, implying that Hippo signaling and possibly NOS1AP expression are de-regulated in OPSCC. Further studies will help determine if NOS1AP isoforms, Scribble and Hippo components will be useful biomarkers in OPSCC tumor biology

High-spin proton alignments and evidence for a second band with enhanced deformation in 171Hf

High-spin properties of the nucleus 171Hf were studied through the 128Te(48Ca,5n) reaction. Previously known bands have been extended to significantly higher spins and four new bands have been extracted from these data. The results are discussed within the framework of the cranked shell model aided by a comparison with level structures in the neighboring nuclei. The band crossings at rotational frequencies ∼500 keV are interpreted as caused by the alignments of h11/2 and h9/2 proton orbitals. Band ED2 exhibits an alignment pattern similar to that of band ED1 which was reported in a recent paper and proposed to be built on a second potential energy minimum involving the deformation-driving proton i13/2 - h9/2 configuration. It is likely that band ED2 is also associated with a deformation enhanced with respect to that of the normal deformed structures. Further experimental investigation is needed to ascertain the nature of this band

Nuclear shapes of highly deformed bands in Hf171,172 and neighboring Hf isotopes

A Gammasphere experiment was carried out to search for triaxial strongly deformed (TSD) structures in Hf171,172 and the wobbling mode, a unique signature of nuclei with stable triaxiality. Three strongly deformed bands in Hf172 and one in Hf171 were identified through Ca48(Te128, xn) reactions. Linking transitions were established for the band in Hf171 and, consequently, its excitation energies and spins (up to 111/2) were firmly established. However, none of the Hf172 sequences were linked to known structures. Experimental evidence of triaxiality was not observed in these bands. The new bands are compared with other known strongly deformed bands in neighboring Hf isotopes. Theoretical investigations within various models have been performed. Cranking calculations with the Ultimate Cranker code suggest that the band in Hf171 and two previously proposed TSD candidates in Hf170 and Hf175 are built on proton (i13/2h9/2) configurations, associated with near-prolate shapes and deformations enhanced with respect to the normal deformed bands. Cranked relativistic mean-field calculations suggest that band 2 in Hf175 has most likely a near-prolate superdeformed shape involving the πi13/2νj15/2 high-j intruder orbitals. It is quite likely that the bands in Hf172 are similar in character to this band