Zone diagrams in Euclidean spaces and in other normed spaces

Zone diagrams are a variation on the classical concept of Voronoi diagrams. Given n sites in a metric space that compete for territory, the zone diagram is an equilibrium state in the competition. Formally it is defined as a fixed point of a certain “dominance” map. Asano, Matou?ek, and Tokuyama proved the existence and uniqueness of a zone diagram for point sites in the Euclidean plane, and Reem and Reich showed existence for two arbitrary sites in an arbitrary metric space. We establish existence and uniqueness for n disjoint compact sites in a Euclidean space of arbitrary (finite) dimension, and more generally, in a finite-dimensional normed space with a smooth and rotund norm. The proof is considerably simpler than that of Asano et?al. We also provide an example of non-uniqueness for a norm that is rotund but not smooth. Finally, we prove existence and uniqueness for two point sites in the plane with a smooth (but not necessarily rotund) norm.     

Assessment of Chemical Composition and Anti-Penicillium Activity of Vapours of Essential Oils from Abies Alba and Two Melaleuca Species in Food Model Systems

The possibilities of the practical utilization of essential oils (EOs) from various plant species in the food industry have attracted the attention of the scientific community. Following our previous studies, the antifungal activities of three further commercial EOs, Melaleuca armillaris subsp. armillaris (rosalina; REO), Melaleuca quinquenervia (niaouli; NEO), and Abies alba (fir; FEO), were evaluated in the present research in respect to their chemical profiles, over four different concentrations, 62.5 μL/L, 125 μL/L, 250 μL/L, and 500 μL/L. The findings revealed that the major compounds of REO, NEO, and FEO were linalool (47.5%), 1,8-cineole (40.8%), and α-pinene (25.2%), respectively. In vitro antifungal determinations showed that the inhibition zones of a Penicillium spp. mycelial growth ranged from no inhibitory effectiveness (00.00 ± 00.00 mm) to 16.00 ± 1.00 mm, indicating a very strong antifungal activity which was detected against P. citrinum after the highest REO concentration exposure. Furthermore, the in situ antifungal efficacy of all EOs investigated was shown to be dose-dependent. In this sense, we have found that the highest concentration (500 µL/L) of REO, NEO, and FEO significantly reduced (p < 0.05) the growth of all Penicillium strains inoculated on the bread, carrot, and potato models. These results indicate that the investigated EOs may be promising innovative agents in order to extend the shelf life of different types of food products, such as bread, carrot and potato.     

Conventional and rotating magnetoelectric effect of a half-filled spin-electron model on a doubly decorated square lattice

A conventional and rotating magnetoelectric effect of a half-filled spin-electron model on a doubly decorated square lattice is investigated by exact calculations. An importance of the electron hopping and spatial orientation of the electric field upon a magnetoelectric effect is examined in detail. A critical temperature may display one or two consecutive round maxima as a function of the electric field. Although the rotating magnetoelectric effect (RME) does not affect the ground-state ordering, the pronounced RME is found close to a critical temperature of continuous phase transition. It is shown that RME is amplified upon strengthening of the electric field, which additionally supports thermal fluctuations in destroying a spontaneous antiferromagnetic long-range order.     

A Cyclometalated IrIII Complex Conjugated to a Coumarin Derivative Is a Potent Photodynamic Agent against Prostate Differentiated and Tumorigenic Cancer Stem Cells

A cyclometalated Ir^III complex conjugated to a far-red-emitting coumarin, Ir^III-COUPY ( 3 ), was recently shown as a very promising photosensitizer suitable for photodynamic therapy of cancer. Therefore, the primary goal of this work was to deepen knowledge on the mechanism of its photoactivated antitumor action so that this information could be used to propose a new class of compounds as drug candidates for curing very hardly treatable human tumors, such as androgen resistant prostatic tumors of metastatic origin. Conventional anticancer chemotherapies exhibit several disadvantages, such as limited efficiency to target cancer stem cells (CSCs), which are considered the main reason for chemotherapy resistance, relapse, and metastasis. Herein, we show, using DU145 tumor cells, taken as the model of hormone-refractory and aggressive prostate cancer cells resistant to conventional antineoplastic drugs, that the photoactivated conjugate 3 very efficiently eliminates both prostate bulk (differentiated) and prostate hardly treatable CSCs simultaneously and with a similar efficiency. Notably, the very low toxicity of Ir^III-COUPY conjugate in the prostate DU145 cells in the dark and its pronounced selectivity for tumor cells compared with noncancerous cells could result in low side effects and reduced damage of healthy cells during the photoactivated therapy by this agent. Moreover, the experiments performed with the 3D spheroids formed from DU145 CSCs showed that conjugate 3 can penetrate the inner layers of tumor spheres, which might markedly increase its therapeutic effect. Also interestingly, this conjugate induces apoptotic cell death in prostate cancer DU145 cells associated with calcium signaling flux in these cells and autophagy. To the best of our knowledge, this is the first study demonstrating that a photoactivatable metal-based compound is an efficient agent capable of killing even hardly treatable CSCs.     

Types of likelihood maxima in mixture models and their implication on the performance of tests

In two-component mixtures of exponential distributions, different strategies for starting the likelihood maximization algorithm converge to different types of maxima. The power of an LR test of homogeneity against such a mixture strongly depends on the considered strategy, and global maximization need not result in the largest power. An explanation is given on basis of a systematic investigation of the likelihood function in a large number of simulations, using a variety of diagnostic tools. Thereby, we also gain a deeper insight into the properties of the samples that generate particular types of solutions of the likelihood equation. In particular, “spurious solutions” often occur; these are mainly responsible for the fact that global maximization may not result in a statistically meaningful estimator. Removing the smallest elements of a sample may drastically increase the power of previously inferior strategies. This research has been supported by a grant from the Deutsche Forschungsgemeinschaft.     

Oxidation State Specific Generation of Arsines from Methylated Arsenicals Based on L- Cysteine Treatment in Buffered Media for Speciation Analysis by Hydride Generation - Automated Cryotrapping - Gas Chromatography-Atomic Absorption Spectrometry with the Multiatomizer

An automated system for hydride generation - cryotrapping- gas chromatography - atomic absorption spectrometry with the multiatomizer is described. Arsines are preconcentrated and separated in a Chromosorb filled U-tube. An automated cryotrapping unit, employing nitrogen gas formed upon heating in the detection phase for the displacement of the cooling liquid nitrogen, has been developed. The conditions for separation of arsines in a Chromosorb filled U-tube have been optimized. A complete separation of signals from arsine, methylarsine, dimethylarsine, and trimethylarsine has been achieved within a 60 s reading window. The limits of detection for methylated arsenicals tested were 4 ng l(-1). Selective hydride generation is applied for the oxidation state specific speciation analysis of inorganic and methylated arsenicals. The arsines are generated either exclusively from trivalent or from both tri- and pentavalent inorganic and methylated arsenicals depending on the presence of L-cysteine as a prereductant and/or reaction modifier. A TRIS buffer reaction medium is proposed to overcome narrow optimum concentration range observed for the L-cysteine modified reaction in HCl medium. The system provides uniform peak area sensitivity for all As species. Consequently, the calibration with a single form of As is possible. This method permits a high-throughput speciation analysis of metabolites of inorganic arsenic in relatively complex biological matrices such as cell culture systems without sample pretreatment, thus preserving the distribution of tri- and pentavalent species.     

Recent advances in electrochemical analysis of biomacromolecules. Catalytic hydrogen evolution and modification of glycoproteins and glycans by Os(VI) complexes

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On the distortion required for embedding finite metric spaces into normed spaces

We investigate the minimum dimensionk such that anyn-point metric spaceM can beD-embedded into somek-dimensional normed spaceX (possibly depending onM), that is, there exists a mappingf: M→X with $$\frac{1}{D}dist_M (x,y) \leqslant \left| {f(x) - f(y)} \right| \leqslant dist_M (x,y) for any$$ Extending a technique of Arias-de-Reyna and Rodríguez-Piazza, we prove that, for any fixedD≥1,k≥c(D)n ^1/2D for somec(D)>0. For aD-embedding of alln-point metric spaces into the samek-dimensional normed spaceX we find an upper boundk≤12Dn ^1/[(D+1)/2]lnn (using thel _∞ ^k space forX), and a lower bound showing that the exponent ofn cannot be decreased at least forD?[1,7)∪[9,11), thus the exponent is in fact a jumping function of the (continuously varied) parameterD.