Transition Metal-Promoted Reactions in Aqueous Media and Biological Settings

During the last decade, there has been a tremendous interest for developing non-natural biocompatible transformations in biologically relevant media. Among the different encountered strategies, the use of transition metal complexes offers unique possibilities due to their high transformative power. However, translating the potential of metal catalysts to biological settings, including living cells or small-animal models such as mice or zebrafish, poses numerous challenges associated to their biocompatibility, and their stability and reactivity in crowded aqueous environments. Herein, we describe the most relevant advances in this direction, with a particular emphasis on the systems’ structure, their mode of action and the mechanistic bases of each transformation. Thus, the key challenges from an organometallic perspective might be more easily identified.     

On the simplicity of some kac-moody groups

Recently, Marcuson extended the classical construction of Tits systems in Steinberg groups to include the Kac-Moody Steinberg groups associated with the infinite dimensional versions of the great Lie algebras. If these Lie algebras and their Kac-Moody groups are viewed as limits of their finite dimensional counterparts, more direct methods may be employed. In fact, the Kac-Moody Chevalley groups of these Lie algebras are seen to be simple.     

Quantitative study of cellular heterogeneity in doxorubicin uptake and its pharmacological effect on cancer cells

Cellular heterogeneity in doxorubicin (DOX) uptake and its relationship with pharmacological effect on cancer cells were quantitatively investigated for the first time. An in vitro experimental model was established by treating human leukemia K562 and breast cancer MCF‐7 cells with different schedules of DOX with or without surface P‐glycoprotein (P‐gp) inhibitor verapamil (VER). The cellular heterogeneity in DOX uptake was quantitatively examined by single‐cell analysis using capillary electrophoresis coupled with laser‐induced fluorescence detection. The corresponding cytotoxic effect was tested by cellular morphology, 3‐(4,5‐dimethylthiazol‐2‐yl)‐2,5‐diphenyl‐tetrazolium and flow cytometry assays. The expression of cellular membrane surface P‐gp was determined by flow cytometry. Results showed that the cellular heterogeneity exists in DOX uptake. The single‐high DOX schedule leads to lower uptake heterogeneity and higher mean drug uptake. The cellular heterogeneity in DOX uptake was found to be negatively correlated with drug cytotoxicity and surface P‐gp expression, with r = ?0.7680 to ~ ?0.9587. VER reduces the cellular variation in DOX uptake, suggesting that surface P‐gp may be one of the causes of the cellular heterogeneity in DOX uptake. This research demonstrates the importance of quantitative study of cellular heterogeneity in drug uptake and its potential application in drug schedule design, response prediction and therapy modulation. Copyright © 2014 John Wiley & Sons, Ltd.     

Motzkin numbers out of Random Domino Automaton

Motzkin numbers are derived from a special case of Random Domino Automaton – recently proposed a slowly driven system being a stochastic toy model of earthquakes. It is also a generalisation of 1D Drossel–Schwabl forest-fire model. A solution of the set of equations describing stationary state of Random Domino Automaton in inverse-power case is presented. A link with Motzkin numbers allows to present explicit form of asymptotic behaviour of the automaton.     

Modeling fatigue of ascending stair evacuation with modified fine discrete floor field cellular automata

Fatigue even increases the complexity of the pedestrian dynamics which is regarded as a kind of nonlinear system, and might have a significant negative impact on the crowd evacuation. However, it has never been investigated completely and properly. Thus, the fine discrete floor field cellular automata model is modified by integrating the fatigue function to explore the influence of fatigue on the crowd ascending evacuation. The simulation fits well with the empirical data and the observations quantitatively and qualitatively, indicating the model captures the main features of evacuation considering fatigue impact. As a prediction, without merging streams, compared with the case of walking in constant speed, when fatigue is considered, it takes 71.4% longer for all persons to enter the stairs and 87.2% longer to evacuate. With merging streams, fatigue has little impact on the inflow, while it makes the total evacuation time 84.2% longer.     

Sobolev spaces on Lie groups: Embedding theorems and algebra properties

Let G be a noncompact connected Lie group, denote with ρ a right Haar measure and choose a family of linearly independent left-invariant vector fields X on G satisfying Hörmander's condition. Let χ be a positive character of G and consider the measure ${\mu }_{\chi }$ whose density with respect to ρ is χ. In this paper, we introduce Sobolev spaces $L_{\alpha }^p({\mu }_{\chi })$ adapted to X and ${\mu }_{\chi }$ ($1<p<\infty$, $\alpha \ge 0$) and study embedding theorems and algebra properties of these spaces. As an application, we prove local well-posedness and regularity results of solutions of some nonlinear heat and Schrödinger equations on the group.