Tuning Photoinduced Electron Transfer Efficiency of Fluorogenic BODIPY‐α‐Tocopherol Analogues

Fluorogenic analogues of α‐tocopherol developed by our group have been instrumental in monitoring reactive oxygen species (ROS) within lipid membranes. Prepared as two‐segment trap‐reporter (chromanol‐BODIPY) probes, photoinduced electron transfer (PeT) was utilized to provide these probes with an off/on switch mechanism warranting the necessary sensitivity. Herein, we rationalize within the context of Marcus theory of electron transfer how substituents on the BODIPY core and linker length joining the trap and reporter segments, tune PeT efficiency. DFT and electrochemical studies were used to estimate the thermodynamic driving force of PeT in our constructs. By tuning the redox potential over a 400 mV range, we observed over an order of magnitude increase in PeT efficiency. Increasing the linker length between the chromanol and BODIPY by 2.8 angstroms, in turn, decreased PeT efficiency 2.7‐fold. Our results illustrate how substituent and linker choice enable “darkening” the off state of fluorogenic probes based on BODIPY fluorophores, by favoring PeT over radiative emission from the singlet excited state manifold. Ultimately, our work brings light to the sensitivity ceiling one may achieve in developing fluorogenic antioxidant analogues of α‐tocopherol. The work provides general guidelines applicable to those developing fluorogenic probes based on PeT.     

Exact relativistic models of conformastatic charged dust thick disks

We construct relativistic models of charged dust thick disks for a particular conformastatic spacetime through a Miyamoto–Nagai transformation used in Newtonian gravity to model disk like galaxies. Two simple families of thick disk models and a family of thick annular disks based on the field of an extreme Reissner–Nordström black hole and a Morgan–Morgan-like metric are considered. The electrogeodesic motion of test particles around the structures are analyzed. Also the stability of the particles against radial perturbation is studied using an extension of the Rayleigh criteria of stability of a fluid in rest in a gravitational field. The models built satisfy all the energy conditions.     

A causal quantum theory in phase space

The causal theory for the coherent state representation of quantum mechanics is derived. The general conditions for the classical limit are given and it is shown that phase space classical mechanics can be obtained as a limit even for stationary states, in contrast to the de Broglie-Bohm quantum theory of motion.     

Introspection and equilibrium selection in 2 × 2 matrix games

Game theory lacks an explanation of how players' beliefs are formed and why they are in equilibrium. This is the reason why it has failed to make significant advances with the problem of equilibrium selection even for quite simple games, as 2 × 2 games with two strict Nash equilibria. Our paper models the introspection process by which the selected equilibrium is achieved in this class of games. Players begin their analysis with imprecise priors, obtained under weak restrictions formulated as Axioms. For a large class of reasoning dynamics we obtain as the solution the risk dominant Nash equilibrium.     

n-ary fragmentation model with nearest point flaw and maximal net force fracture

Through the distinction between “real” and “virtual” links between the nodes of a graph, we develop a set of simple rules leading to scale-free networks with a tunable degree distribution exponent. Albeit sharing some similarities with preferential attachment, our procedure is both faster than a naïve implementation of the Barabási and Albert model and exhibits different clustering properties. The model is thoroughly studied numerically and suggests that reducing the set of partners a node can connect to is important in seizing the diversity of scale-free structures.     

Semi-discretization in time and numerical convergence of solutions of a nonlinear cross-diffusion population model

Summary. A positivity-preserving numerical scheme for a strongly coupled cross-diffusion model for two competing species is presented, based on a semi-discretization in time. The variables are the population densities of the species. Existence of strictly positive weak solutions to the semidiscrete problem is proved. Moreover, it is shown that the semidiscrete solutions converge to a non-negative solution of the continuous system in one space dimension. The proofs are based on a symmetrization of the problem via an exponential transformation of variables and the use of an entropy functional. Received September 10, 2001 / Revised version received February 25, 2002 / Published online June 17, 2002     

Indexing text with approximate q-grams

We present a new index for approximate string matching. The index collects text q-samples, that is, disjoint text substrings of length q, at fixed intervals and stores their positions. At search time, part of the text is filtered out by noticing that any occurrence of the pattern must be reflected in the presence of some text q-samples that match approximately inside the pattern. Hence the index points out the text areas that could contain occurrences and must be verified. The index parameters permit load balancing between filtering and verification work, and provide a compromise between the space requirement of the index and the error level for which the filtration is still efficient. We show experimentally that the index is competitive against others that take more space, being in fact the fastest choice for intermediate error levels, an area where no current index is useful.