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.     

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.     

Chemistry,a lingua philosophica

We analyze the connections of Lavoisier system of nomenclature with Leibniz’s philosophy, pointing out to the resemblance between what we call Leibnizian and Lavoisian programs. We argue that Lavoisier’s contribution to chemistry is something more subtle, in so doing we show that the system of nomenclature leads to an algebraic system of chemical sets. We show how Döbereiner and Mendeleev were able to develop this algebraic system and to find new interesting properties for it. We pointed out the resemblances between Leibniz program and Lavoisier legacy, particularly regarding the lingua philosophica for understanding and thinking Nature, in this particular case, chemistry. In the second part we discuss, from the linguistic viewpoint, how Lavoisian algebraic system may be taken further to build a language. We study the constituents of such a chemical language. Finally, we formalize some of the ideas here presented by using elements of network theory and discrete mathematics.     

The Mutation of the “Nobel Prize in Chemistry” into the “Nobel Prize in Chemistry or Life Sciences”: Several Decades of Transparent and Opaque Evidence of Change within the Nobel Prize Program

Over the past several decades, the Nobel Prize program has slowly but steadily been modified in both transparent and opaque ways. A transparent change has been the creation of the Nobel Prize in Economic Sciences, officially known as the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel. An opaque change has been the mutation of the Nobel Prize in Chemistry into what is effectively the “Nobel Prize in Chemistry or Life Sciences.” This paper presents a detailed study of this opaque change, including evidence that the disciplines of chemistry and biochemistry cover, today, intellectually quite distinct and generally scientifically-unrelated intellectual territory. This paper supports the evolution of the Nobel Prizes, and encourages the Nobel Prize program to move from opaque to transparent change processes for the next generations of achievement in the sciences.     

Ferrimagnetic to Paramagnetic Transition in Magnetite: Mössbauer versus Monte Carlo

Powder magnetite was analyzed in situ via Mössbauer with temperatures ranging from 170 K up to 900 K. Hyperfine fields of the tetrahedral and octahedral sites of magnetite as well as the corresponding average field were followed as a function of temperature in order to elucidate the critical behavior of magnetite at around the Curie temperature. Results evidence a progressive collapse of the Mössbauer spectra onto a singlet-type line at a critical temperature of around 870 K characterized by a critical exponent β = 0.28(2) for the hyperfine field. In order to describe such temperature dependence of the hyperfine field, a Monte Carlo-Metropolis simulation based on a stoichiometric magnetite and an Ising model with nearest magnetic neighbor interactions was also carried out. In the model, we have taken into account antiferromagnetic and ferromagnetic interactions depending on the involved ions. A discussion about the critical behavior of magnetite and a comparison between the hyperfine field obtained via Mössbauer and the magnetization obtained via Monte Carlo is finally presented.     

Nonresonant inelastic x-ray scattering and energy-resolved Wannier function investigation of d-d excitations in NiO and CoO

Nonresonant inelastic x-ray scattering measurements on NiO and CoO show that strong dipole-forbidden d-d excitations appear within the Mott gap at large wave vectors. These dominant excitations are highly anisotropic, and have [001] nodal directions for NiO. Theoretical analyses based on a novel, energy-resolved Wannier function (within the local density approximation+Hubbard U) show that the anisotropy reflects the local exciton wave functions and local point-group symmetry. The sensitivity to weak symmetry breaking in particle-hole wave functions suggests a wide application to strongly correlated systems.     

Beam shaping by spatial coherence modulation based on spatial coherence wavelets

A novel technique for designing specific shapes of power distributions is presented. It bases on the modulation of the spatial coherence of the optical field in amplitude and phase. The modulating functions are synthesized from the phase-space diagram of the field, provided by the marginal power spectrum. Numerical results for the phase modulation of the complex degree of spatial coherence are presented. This beam shaping technique is suitable in applications that require specific shapes and sizes.     

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.