Betti numbers for numerical semigroup rings

We survey results related to the magnitude of the Betti numbers of numerical semigroup rings and of their tangent cones.Comment: 22 pages; v2: updated references. To appear in Multigraded Algebra and Applications (V. Ene, E. Miller Eds.

Regularity of Edge Ideals and Their Powers

We survey recent studies on the Castelnuovo-Mumford regularity of edge ideals of graphs and their powers. Our focus is on bounds and exact values of $\text{ reg } I(G)$ and the asymptotic linear function $\text{ reg } I(G)^q$, for $q \geq 1,$ in terms of combinatorial data of the given graph $G.$Comment: 31 pages, 15 figure

Four lectures on secant varieties

This paper is based on the first author's lectures at the 2012 University of Regina Workshop "Connections Between Algebra and Geometry". Its aim is to provide an introduction to the theory of higher secant varieties and their applications. Several references and solved exercises are also included.Comment: Lectures notes to appear in PROMS (Springer Proceedings in Mathematics & Statistics), Springer/Birkhause

Growth of Inclined GaAs Nanowires by Molecular Beam Epitaxy: Theory and Experiment

The growth of inclined GaAs nanowires (NWs) during molecular beam epitaxy (MBE) on the rotating substrates is studied. The growth model provides explicitly the NW length as a function of radius, supersaturations, diffusion lengths and the tilt angle. Growth experiments are carried out on the GaAs(211)A and GaAs(111)B substrates. It is found that 20° inclined NWs are two times longer in average, which is explained by a larger impingement rate on their sidewalls. We find that the effective diffusion length at 550°C amounts to 12 nm for the surface adatoms and is more than 5,000 nm for the sidewall adatoms. Supersaturations of surface and sidewall adatoms are also estimated. The obtained results show the importance of sidewall adatoms in the MBE growth of NWs, neglected in a number of earlier studies

Human papillomavirus ‘reflex' testing as a screening method in cases of minor cytological abnormalities

The aim was to evaluate human papillomavirus (HPV) ‘reflex genotyping' in cases of minor cytological abnormalities detected in the gynaecological screening programme in Stockholm, Sweden. Liquid-based cytology samples showing minor cytological abnormalities were analysed using HPV genotyping (Linear Array, Roche diagnostics). Colposcopically directed cervical biopsies were obtained and the HPV test results were correlated with the histological results. In all, 63% (70/112) of the samples were high-risk (HR) HPV (HR-HPV) positive. A statistically significant correlation was found between high-grade cervical lesions and HR-HPV (P=0.019), among which HPV 16, 18, and 31 were the most important. The negative predictive value of HR-HPV detection for histologically confirmed high-grade lesions was 100%. An age limit for HPV reflex testing may be motivated in cases of low-grade squamous intraepithelial neoplasia (LSIL), because of high HR-HPV prevalence among younger women. By using HPV reflex genotyping, additional extensive workup can safely be avoided in about 50% of all cases of atypical squamous cells of undetermined significance (ASCUS) and LSIL among women ⩾30 years. This screening strategy could potentially reduce the total abnormal cytology-reporting rate in the Swedish screening programme by about 1% and provide more accurately directed follow-up, guided by cytological appearance and HPV test results

Radiolabeled CCK/gastrin peptides for imaging and therapy of CCK2 receptor-expressing tumors

Cholecystokinin (CCK) receptors are overexpressed in numerous human cancers, like medullary thyroid carcinomas, small cell lung cancers and stromal ovarian cancers. The specific receptor-binding property of the endogenous ligands for these receptors can be exploited by labeling peptides with a radionuclide and using these as carriers to guide the radioactivity to the tissues that express the receptors. In this way, tumors can be visualized using positron emission tomography and single photon emission computed tomography imaging. A variety of radiolabeled CCK/gastrin-related peptides has been synthesized and characterized for imaging. All peptides have the C-terminal CCK receptor-binding tetrapeptide sequence Trp-Met-Asp-Phe-NH2 in common or derivatives thereof. This review focuses on the development and application of radiolabeled CCK/gastrin peptides for radionuclide imaging and radionuclide therapy of tumors expressing CCK receptors. We discuss both preclinical studies as well as clinical studies with CCK and gastrin peptides

Radiolabelled peptides for oncological diagnosis

Radiolabelled receptor-binding peptides targeting receptors (over)expressed on tumour cells are widely under investigation for tumour diagnosis and therapy. The concept of using radiolabelled receptor-binding peptides to target receptor-expressing tissues in vivo has stimulated a large body of research in nuclear medicine. The 111In-labelled somatostatin analogue octreotide (OctreoScan™) is the most successful radiopeptide for tumour imaging, and was the first to be approved for diagnostic use. Based on the success of these studies, other receptor-targeting peptides such as cholecystokinin/gastrin analogues, glucagon-like peptide-1, bombesin (BN), chemokine receptor CXCR4 targeting peptides, and RGD peptides are currently under development or undergoing clinical trials. In this review, we discuss some of these peptides and their analogues, with regard to their potential for radionuclide imaging of tumours

Oribatid communities and heavy metal bioaccumulation in selected species associated with lichens in a heavily contaminated habitat

The study examines oribatid communities and heavy metal bioaccumulation in selected species associated with different microhabitats of a post-smelting dump, i.e. three lichen species of Cladonia with various growth forms and the slag substrate. The abundance of oribatids collected from the substrate was significantly lower than observed in lichen thalli. The morphology and chemical properties of lichens, and to some extent varying concentrations of heavy metals in thalli, are probably responsible for significant differences in oribatid communities inhabiting different Cladonia species. Some oribatids demonstrate the ability to accumulate zinc and cadmium with unusual efficiency, whereas lead is the most effectively regulated element by all species. A positive correlation was found between Zn content in all studied oribatids and their microhabitats. Oribatids exploring different food resources, i.e. fungivorous and non-fungivorous grazers, show considerable differences in bioconcentrations of certain elements

One-dimensional nuclear dynamics in the time-dependent Hartree-Fock approximation

The time-dependent Hartree-Fock theory is applied to the large amplitude dynamics of slabs of spin and isospin symmetric nuclear matter. The slabs are translationally invariant in two transverse dimensions, and with the simplified effective interaction used in this work, the problem is reduced to a set of coupled nonlinear equations for time-dependent functions of a single spatial variable. By specification of appropriate initial conditions, large amplitude oscillations of a single slab, the scattering of a slab from an external potential barrier, and collisions of two slabs have been investigated. The results evidence a wide variety of dynamic phenomena, including fusion, compound nucleus formation, dissipation, strongly damped collisions, shock wave propagation, and fragmentation. The microscopic aspects of the dynamics, the relation to fluid mechanics, and the practical and conceptual problems arising from the theory are discussed in detail