Chemotopological study of positron emitter radionuclides used in PET diagnostic imaging: physical, physico-chemical, dosimetric, quantum and nuclear properties

We carried out a chemotopological study of two groups of positron emitter radionuclides of current and potential use in positron emission tomography (PET) diagnostic imaging. The aim was to look for potential β⁺ radionuclides not yet in use for PET imaging, taking into account the similarities of these radionuclides with radionuclides already used in PET imaging. The similarity was studied through physical, physico-chemical, dosimetric, quantum and nuclear properties of the radionuclides. We applied cluster analysis (two similarity functions and three grouping methodologies) and generated six dendrograms. One dendrogram was selected in each group, which was used to build up a basis for a topology. From the calculation of topological properties of several subsets of interest, we propose β⁺ radionuclides ⁴⁷V, ⁴⁸V, ⁶³Zn, ⁷⁰As, ⁹⁰Nb, ¹⁰⁶Ag, ¹¹⁵Sb, ¹¹⁶Sb, ¹²⁰Sb, ¹³⁰Cs, ¹³⁴La and ¹⁴⁰Pr, as potential new radionuclides of use in PET imaging.     

A simple GAP-canceling algorithm for the generalized maximum flow problem

We give a simple primal algorithm for the generalized maximum flow problem that repeatedly finds and cancels generalized augmenting paths (GAPs). We use ideas of Wallacher (A generalization of the minimum-mean cycle selection rule in cycle canceling algorithms, 1991) to find GAPs that have a good trade-off between the gain of the GAP and the residual capacity of its arcs; our algorithm may be viewed as a special case of Wayne’s algorithm for the generalized minimum-cost circulation problem (Wayne in Math Oper Res 27:445–459, 2002). Most previous algorithms for the generalized maximum flow problem are dual-based; the few previous primal algorithms (including Wayne in Math Oper Res 27:445–459, 2002) require subroutines to test the feasibility of linear programs with two variables per inequality (TVPIs). We give an O(mn) time algorithm for finding negative-cost GAPs which can be used in place of the TVPI tester. This yields an algorithm with O(m log(mB/ε)) iterations of O(mn) time to compute an ε-optimal flow, or O(m ² log (mB)) iterations to compute an optimal flow, for an overall running time of O(m ³ nlog(mB)). The fastest known running time for this problem is , and is due to Radzik (Theor Comput Sci 312:75–97, 2004), building on earlier work of Goldfarb et al. (Math Oper Res 22:793–802, 1997). David P. Williamson is supported in part by an IBM Faculty Partnership Award and NSF grant CCF-0514628.     

Emergence of coherence in complex networks of heterogeneous dynamical systems

We present a general theory for the onset of coherence in collections of heterogeneous maps interacting via a complex connection network. Our method allows the dynamics of the individual uncoupled systems to be either chaotic or periodic, and applies generally to networks for which the number of connections per node is large. We find that the critical coupling strength at which a transition to synchrony takes place depends separately on the dynamics of the individual uncoupled systems and on the largest eigenvalue of the adjacency matrix of the coupling network. Our theory directly generalizes the Kuramoto model of equal strength all-to-all coupled phase oscillators to the case of oscillators with more realistic dynamics coupled via a large heterogeneous network.     

A path integral method for data assimilation

Described here is a path integral, sampling-based approach for data assimilation, of sequential data and evolutionary models. Since it makes no assumptions on linearity in the dynamics, or on Gaussianity in the statistics, it permits consideration of very general estimation problems. The method can be used for such tasks as computing a smoother solution, parameter estimation, and data/model initialization.Speedup in the Monte Carlo sampling process is essential if the path integral method has any chance of being a viable estimator on moderately large problems. Here a variety of strategies are proposed and compared for their relative ability to improve the sampling efficiency of the resulting estimator. Provided as well are details useful for its implementation and testing.The method is applied to a problem in which standard methods are known to fail, an idealized flow/drifter problem, which has been used as a testbed for assimilation strategies involving Lagrangian data. It is in this kind of context that the method may prove to be a useful assimilation tool in oceanic studies.     

Quantum correlations between two cavity QED systems coupled by a mechanical resonator

Achieving quantum correlations between two distant systems is a desirable feature for quantum networking. In this work, we study a system composed of two quantum emitter-cavity subsystems spatially separated. A mechanical resonator couples to either both quantum emitters or both cavities leading to quantum correlations between both subsystems such as non-local light-matter dressed states and cavity–cavity normal mode splitting. These indirect couplings can be explained by an effective Hamiltonian for large energy detuning between the mechanical resonator and the atoms/cavities. Moreover, it is found that the optimal conditions of the physical parameters maximize the entanglement of phonon-mediated couplings.     

Characterizing the dynamical importance of network nodes and links

The largest eigenvalue of the adjacency matrix of networks is a key quantity determining several important dynamical processes on complex networks. Based on this fact, we present a quantitative, objective characterization of the dynamical importance of network nodes and links in terms of their effect on the largest eigenvalue. We show how our characterization of the dynamical importance of nodes can be affected by degree-degree correlations and network community structure. We discuss how our characterization can be used to optimize techniques for controlling certain network dynamical processes and apply our results to real networks.     

Desynchronization waves and localized instabilities in oscillator arrays

We consider a ring of identical or near-identical coupled periodic oscillators in which the connections have randomly heterogeneous strength. We use the master stability function method to determine the possible patterns at the desynchronization transition that occurs as the coupling strengths are increased. We demonstrate Anderson localization of the modes of instability and show that such localized instability generates waves of desynchronization that spread to the whole array. Similar results should apply to other networks with regular topology and heterogeneous connection strengths.     

Insight into the Mechanism of the Michael Reaction

The mechanism for the nucleophilic addition step of the Michael reaction between methanethiol as a model Michael donor and several α‐substituted methyl acrylates (X=F, Cl, Me, H, CN, NO₂) as model Michael acceptors is described in detail. We suggest a novel way to condense electrophilic Fukui functions at specific atoms in terms of the contributions from the atomic orbitals to the LUMO or, more generally, to the orbital controlling the reaction. This procedure correctly associates activation energies to local electrophilic Fukui indices for the cases treated in this work. The calculated reaction barriers strongly depend on the nature of the substituent. As a general rule, activation energies are governed by structural changes, although electronic factors are significant for electron‐withdrawing groups. Nucleophilic addition to Michael receptors is best described as a highly nonsynchronous process, in which the geometry of the transition state comprises a nonplanar six‐membered ring. Formation of the S ??? C bond, which defines the interaction between the reactants, progresses ahead of all other primitive processes in the early stages of the transformation. In view of our results, we postulate that highly complex chemical reactions, as is the case for the nucleophilic addition step studied herein, that involve cleavage/formation of a total of six bonds, lower their activation energies by favoring nonsynchronicity, that is, for these types of systems, primitive changes should advance at different rates.