On `maximal' poles of zeta functions, roots of b-functions and monodromy Jordan blocks

The main objects of study in this paper are the poles of several local zeta functions: the Igusa, topological and motivic zeta function associated to a polynomial or (germ of) holomorphic function in n variables. We are interested in poles of maximal possible order n. In all known cases (curves, non-degenerate polynomials) there is at most one pole of maximal order n which is then given by the log canonical threshold of the function at the corresponding singular point. For an isolated singular point we prove that if the log canonical threshold yields a pole of order n of the corresponding (local) zeta function, then it induces a root of the Bernstein-Sato polynomial of the given function of multiplicity n (proving one of the cases of the strongest form of a conjecture of Igusa-Denef-Loeser). For an arbitrary singular point we show under the same assumption that the monodromy eigenvalue induced by the pole has a Jordan block of size n on the (perverse) complex of nearby cycles.Comment: 8 pages, to be published in Journal of Topolog

Algorithmic Interpretations of Fractal Dimension

We study algorithmic problems on subsets of Euclidean space of low fractal dimension. These spaces are the subject of intensive study in various branches of mathematics, including geometry, topology, and measure theory. There are several well-studied notions of fractal dimension for sets and measures in Euclidean space. We consider a definition of fractal dimension for finite metric spaces which agrees with standard notions used to empirically estimate the fractal dimension of various sets. We define the fractal dimension of some metric space to be the infimum delta>0, such that for any eps>0, for any ball B of radius r >= 2eps, and for any eps-net N, we have |B cap N|=O((r/eps)^delta). Using this definition we obtain faster algorithms for a plethora of classical problems on sets of low fractal dimension in Euclidean space. Our results apply to exact and fixed-parameter algorithms, approximation schemes, and spanner constructions. Interestingly, the dependence of the performance of these algorithms on the fractal dimension nearly matches the currently best-known dependence on the standard Euclidean dimension. Thus, when the fractal dimension is strictly smaller than the ambient dimension, our results yield improved solutions in all of these settings. We remark that our definition of fractal definition is equivalent up to constant factors to the well-studied notion of doubling dimension. However, in the problems that we consider, the dimension appears in the exponent of the running time, and doubling dimension is not precise enough for capturing the best possible such exponent for subsets of Euclidean space. Thus our work is orthogonal to previous results on spaces of low doubling dimension; while algorithms on spaces of low doubling dimension seek to extend results from the case of low dimensional Euclidean spaces to more general metric spaces, our goal is to obtain faster algorithms for special pointsets in Euclidean space

The nesting ecology of weaverbirds in Ekona farms, Southwest Region, Cameroon

Ecological factors play a key role in determining nest construction and success in weaver birds. The objective of this survey was to determine the ecological role on the nest construction in weaver birds in Ekona farms. The research data was collected from March – August 2016, by randomly laying six transects of 1km long and 100m wide each within the study area, and four different locations were visited also to observe the daily nesting-activities of the weaver birds. The ecological data of the weaver birds nesting behaviour was observed and recorded, against the day-period, weather and seasonal changes. The data was analysed using Chi-square and Pearson correlation statistical models. The result showed a positive correlation between the weaver birds' population and nest density in both seasons (R2=0.5407 at P < 0.05). Moreover, from the analysis, the relationship between nest-building and plant-type used recorded significance (X2= 69.1040, df= 28 at P < 0.05). In addition, it was observed that nest-building in the sunny weather was more intense than in rainy weather, 54.57% for sunny, 42.86% for rainy and 2.7% for cloudy weather conditions. Furthermore, there was a significant relationship (X2= 830.752, df=44 at P< 0.05) between weaver birds' activities and the day-period. The study has revealed that both the seasonal and weather changes can affect the nest-building activities of the weaver birds in Ekona farming area

Late cardiac toxicity of neo-adjuvant chemoradiation in esophageal cancer survivors:A prospective cross-sectional pilot study

Purpose: Although cure rates in esophageal cancer (EC) have improved since the introduction of neoadjuvant chemoradiation (nCRT), evidence for treatment-related cardiac toxicity is growing, of which the exact mechanisms remain unknown. The primary objective of this study was to identify (subclinical) cardiac dysfunction in EC patients after nCRT followed by surgical resection as compared to surgery alone. Materials and Methods: EC survivors followed for 5-15 years after curative resection with (n = 20) or without (n = 20) nCRT were enrolled in this prospective cross-sectional pilot study. All patients underwent several clinical and diagnostic tests in order to objectify (sub)clinical cardiac toxicity including cardiac CT and MRI, echocardiography, ECG, 6-minutes walking test, physical examination and EORTC questionnaires. Results: We found an increased rate of myocardial fibrosis (Linear late gadolinium enhancement (LGE) 4 vs. 1; p = 0.13; mean extracellular volume (ECV) 28.4 vs. 24.0; p < 0.01), atrial fibrillation (AF) (6 vs. 2; p = 0.07) and conduction changes in ECG among patients treated with nCRT as compared to those treated with surgery alone. The results suggested an impact on quality of life in terms of worse role functioning for this patient group (95.0 vs. 88.8; p = 0.03). Conclusion: Based on our analyses we hypothesize that in EC patients, radiation-induced myocardial fibrosis plays a central role in cardiac toxicity leading to AF, conduction changes and ultimately to decreased role functioning. The results emphasize the need to verify these findings in larger cohorts of patients. (C) 2021 The Author(s). Published by Elsevier B.V

Engineering molecular chains in carbon nanotubes

A range of mono- and bis-functionalised fullerenes have been synthesised and inserted into single-walled carbon nanotubes. The effect of the size and shape of the functional groups of the fullerenes on the resultant 1D arrays formed within the nanotubes was investigated by high resolution transmission electron microscopy and X-ray diffraction. The addition of non-planar, sterically bulky chains to the fullerene cage results in highly ordered 1D structures in which the fullerenes are evenly spaced along the internal nanotube cavity. Theoretical calculations reveal that the functional groups interact with neighbouring fullerene cages to space the fullerenes evenly within the confines of the nanotube. The addition of two functional groups to opposite sides of the fullerene cages results in a further increase in the separation of the fullerene cages within the nanotubes at the cost of lower nanotube filling rates.This work was financially supported by FWF project I83-N20 (ESF IMPrESS), the Royal Society, the European Research Council (ERC), "Fundacao para a Ciencia ea Tecnologia" through the program Ciencia 2008, the project SeARCH (Services and Advanced Research Computing with HTC/HPC clusters) and Nottingham Nanoscience and Nanotechnology Centre (NNNC)

Self-assembled RGD dehydropeptide hydrogels for drug delivery applications

Peptide-based self-assembled hydrogels have triggered remarkable research interest in recent years owing to their biocompatibility and biomimetic properties and responsiveness, which warrant many technological and biomedical applications. Dehydrodipeptides N-capped with naproxen emerged from our research as effective hydrogelators endowed with resistance to proteolysis. Dehydrodipeptide-based hydrogels are promising nanocarriers for drug delivery applications. In this work, we demonstrate that dehydrodipetide Npx-L-Ala-Z-ΔPhe-OH can be deployed as a minimalist hydrogelator module for synthesizing a gelating construct Npx-L-Ala-Z-ΔPhe-G-R-G-D-G-OH bearing a GRGDG adhesion motif. The self-assembly of the peptide construct and the drug delivery properties of the hydrogel were studied in this work. The peptide construct showed no toxicity towards a fibroblast cell line expressing the αvβ3 integrin. Docking studies suggest that the hydrogelator block does not interfere with the recognition of the RGD motif by the integrin receptor. The self-assembly seems to be directed by intermolecular naphthalene π–π stacking interactions, with the peptide backbone assuming a random coil conformation both in solution and in the gel phase. TEM and STEM imaging revealed that the hydrogel is made of entangled bundles of long thin fibres (width circa 23 nm). The hydrogel exhibits viscoelastic properties, thermo-reversibility and recovery after mechanical fluidization. FRET studies showed that curcumin incorporated into the hydrogel interacts non-covalently with the hydrogel fibrils. Delivery of curcumin from the hydrogel into Nile red loaded model membranes (SUVs) was demonstrated by FRET. Naproxen N-capped dehydrodipeptides are efficacious minimalist hydrogelator modules for obtaining hydrogels functionalized with peptide ligands for cell receptors. These hydrogels are potential nanocarriers for drug delivery

Radiation-Induced Myocardial Fibrosis in Long-Term Esophageal Cancer Survivors

Purpose: Radiation-induced cardiac toxicity is a potential lethal complication. The aim of this study was to assess whether there is a dose-dependent relationship between radiation dose and myocardial fibrosis in patients who received neoadjuvant chemoradiation (nCRT) for esophageal cancer (EC). Methods and Materials: Forty patients with EC treated with a transthoracic esophagectomy with (n = 20) or without (n = 20) nCRT (CROSS study regimen) were included. Cardiovascular magnetic resonance imaging (1.5 Tesla) for left ventricular (LV) function, late gadolinium enhancement, and T1 mapping were performed. Extracellular volume (ECV), as a surrogate for collagen burden, was measured for all LV segments separately. The dose-response relationship between ECV and mean radiation dose per LV myocardial segment was evaluated using a mixed-model analysis. Results: Seventeen nCRT and 16 control patients were suitable for analysis. The mean time after treatment was 67.6 +/- 8.1 (nCRT) and 122 +/- 35 (controls) months (P = .02). In nCRT patients, we found a significantly higher mean global ECV of 28.2% compared with 24.0% in the controls (P < .001). After nCRT, LV myocardial segments with elevated ECV had received significantly higher radiation doses. In addition, a linear dose-effect relation was found with a 0.136% point increase of ECV for each Gy (P < .001). There were no differences in LV function measures and late gadolinium enhancement between both groups. Conclusions: Myocardial ECV was significantly higher in long-term EC survivors after nCRT compared with surgery only. Moreover, this ECV increase was linear with the radiation dose per LV segment, indicating radiation-induced myocardial fibrosis. (C) 2021 The Author(s). Published by Elsevier Inc