The Euclid-Mullin graph

We introduce the Euclid-Mullin graph, which encodes all instances of Euclid's proof of the infinitude of primes. We investigate structural properties of the graph both theoretically and numerically; in particular, we prove that it is not a tree.Comment: 24 pages, 2 figures, to appear in Journal of Number Theor

Detecting squarefree numbers

We present an algorithm, based on the explicit formula for $L$-functions and conditional on GRH, for proving that a given integer is squarefree with little or no knowledge of its factorization. We analyze the algorithm both theoretically and practically, and use it to prove that several RSA challenge numbers are not squarefull.Comment: 31 pages, 3 figures, latest versio

Comprehensive HPTLC fingerprinting as a tool for a simplified analysis of purity of ginkgo products

Ethnopharmacological relevance: Herbal medicinal products based on ginkgo leaf refined dry extract (GBE) are an European development from the Eastern Asia traditionally used species Ginkgo biloba L. Nowadays, ginkgo products have increased the presence in the market, mainly as dietary supplements. Its adulteration with rutin and quercetin or herbal extracts rich in these compounds is a common practice. Tests featuring assays and detection of adulterants need to be performed on top of other existent methods (e.g. identification test). This may increase the costs of evaluating the quality of ginkgo products. Aim of the study: To prove that comprehensive HPTLC fingerprinting can provide information beyond identification of ginkgo products, avoiding additional chromatographic tests for detection of adulterations. Materials and methods: The information contained in the fingerprint obtained by HPTLC analysis of flavonoids was used for identification and for detection of adulterants, as well as to verify the limits of rutin and quercetin, which are normally determined by HPLC and used for detection of adulterants. For this purpose, peak profiles were generated from HPTLC chromatogram images. USP-HPLC methods were used for quantification of total flavonoids and testing the limits of rutin and quercetin. HPLC data were used to support the validity of the HPTLC method. An additional reversed phase HPTLC method was developed as a possible confirmatory method for the quercetin limit test. Results: The proposed HPTLC method uses a particular sequence of detections, resulting in a number of images, which are later interpreted in a certain order. It is able to identify ginkgo products, to detect adulterants (rutin, quercetin, sophora fruit and flower bud, and buckwheat), and, using peak profiles generated from the chromatogram images prior to and after derivatisation, to evaluate the limits of rutin and quercetin. Forty-eight out of fifty-nine ginkgo dietary supplements analysed contained one or more adulterants. Furthermore, results of the HPTLC and HPLC limit tests for rutin and quercetin were in agreement in 98% of the cases. Finally, a decision tree showing the sequence of interpretation of the fingerprints obtained with the different detections after a single HPTLC analysis is included to help the analyst to evaluate whether samples have the correct identity and whether they contain or not adulterants. Conclusion: A single HPTLC analysis is able to provide information on identity and purity of the products. This simplifies the analytical workflow and reduces the number of analyses prescribed in the USP powdered ginkgo extract monograph

Chrysanthemum species used as food and medicine: Understanding quality differences on the global market

Background Chrysanthemum flowers [Ch. x morifolium (Ramat.) Hemsl. and Ch. indicum L.] are a globally used and pharmacologically interesting botanical drug, however, with variable product quality. Objective We aim at understanding the chemical variability of primary material available commercially based on different origins and associated quality problems like contamination with heavy metals. This needs to be assessed in the context of the current regulations for this botanical drug and associated problems. Material and Methods 15 C. indicum L. and 50 C. x morifolium (Ramat.) Hemsl., including a range of geographical cultivars recognized in China, samples from the USA, Europe and China were analyzed using High Performance Thin Layer Chromatography (HPTLC) to compare their general chemical profile. Inductively Coupled Plasma Optical Emission Spectroscopy (ICP-OES) was used to quantify heavy metal contamination. Results The: HPTLC fingerprints of C. indicum samples are clearly distinguishable from C. x morifolium. Fingerprints of samples from the same cultivars collected from markets in different countries (USA and China) show different patterns. Large variance of fingerprints within each cultivar group was observed. The heavy metal analysis showed excessive amounts of some harmful heavy metal in some commercial products with excessive cadmium being the most frequent problem. Conclusions The Chinese medicinal cultivars vary. Differences between samples sourced from the USA and China might be ascribable to geographical factors (e.g. soil composition), degradation during transport/storage or adulteration, but geographical differences should also be taken into account. Importantly, a much more detailed definition of the drug are needed for better quality control. In addition, with continuous contamination problem observed, a more widespread regulation is an essential requirement for better quality

Mitochondrial Function as a Potential Tool for Assessing Function, Quality and Adulteration in Medicinal Herbal Teas

Quality control has been a significant issue in herbal medicine since herbs became widely used to heal. With the advent of modern technologies, evaluating the quality of medicinal herbs has become more sophisticated but so have the methods of adulterating them. In this paper we undertook a comprehensive literature search to identify the key analytical techniques used in the quality assurance of herbal medicine, reviewing their uses and limitations. We also present a new tool, based on mitochondrial profiling, that can be used to measure medicinal herbal quality. Besides being fundamental to the energy metabolism required for most cellular activities, mitochondria play a direct role in cellular signalling, apoptosis, stress responses, inflammation, cancer, ageing, and neurological function, mirroring some of the most common reasons people take herbal medicines. A fingerprint of the specific mitochondrial effects of medicinal herbs can be documented in order to assess their potential efficacy, detect adulterations that modulate these effects and determine the relative potency of batches. Furthermore, through this method it will be possible to assess whole herbs or complex formulas thus avoiding the issues inherent in identifying active ingredients which may be complex or unknown. Thus, while current analytical methods focus on determining the chemical quality of herbal medicines, including adulteration and contamination, mitochondrial functional analysis offers a new way of determining the quality of plant derived products that is more closely linked to the biological activity of a product and its potential clinical effectiveness

High floc strength with aged polyelectrolytes

The ageing of powdered polyelectrolyte solutions has shown that while the viscosity of these solutions decreases rapidly with time, the flocculation performance and the strength of the flocs produced does not alter over periods >200 days. This was shown for polyacrylamides of cationic, anionic and non-ionic charge. The use of tap or deionized water did not adversely affect the results unless a biocide capable of associating with the polyelectrolyte was added. These results contradict the common belief that solutions made with powdered polyelectrolytes should not be stored for long periods of time as their performance decreases after being stored for several days. The results indicate that powdered polyelectrolyte solutions are suitable for intermittent process operations, such as sewer overflow treatment and that dosing and handling of the solutions can be made easier by ageing of the solutions

LAB-AID: an interactive web application for visualization of multi-level data from biological experiments

A key step in understanding the results of biological experiments is visualization of the data. Many laboratory experiments contain a range of measurements that exist within a hierarchy of interdependence. An automated and facile way to visualize and interrogate such multi-level data, across many experimental variables, would: 1) lead to improved understanding of the results, 2) help to avoid misleading interpretation of statistics, and 3) easily identify outliers and sources of batch and confounding effects. While many excellent graphing solutions already exist, they are often geared towards the production of publication-ready plots, the analysis of a single variable at a time, require programming expertise, or are unnecessarily complex for the task at hand. Here we present LAB-AID (Laboratory Automated Interrogation of Data), an interactive tool specifically designed to automatically visualize and query hierarchical data resulting from biological experiment