Classes of complex networks defined by role-to-role connectivity profiles

Interactions between units in phyical, biological, technological, and social systems usually give rise to intrincate networks with non-trivial structure, which critically affects the dynamics and properties of the system. The focus of most current research on complex networks is on global network properties. A caveat of this approach is that the relevance of global properties hinges on the premise that networks are homogeneous, whereas most real-world networks have a markedly modular structure. Here, we report that networks with different functions, including the Internet, metabolic, air transportation, and protein interaction networks, have distinct patterns of connections among nodes with different roles, and that, as a consequence, complex networks can be classified into two distinct functional classes based on their link type frequency. Importantly, we demonstrate that the above structural features cannot be captured by means of often studied global properties

Modes of magnetic resonance of S=1 dimer chain compound NTENP

The spin dynamics of a quasi one dimensional $S=1$ bond alternating spin-gap antiferromagnet Ni(C$_9$H$_{24}$N$_4$)NO$_2$(ClO$_4$) (abbreviated as NTENP) is studied by means of electron spin resonance (ESR) technique. Five modes of ESR transitions are observed and identified: transitions between singlet ground state and excited triplet states, three modes of transitions between spin sublevels of collective triplet states and antiferromagnetic resonance absorption in the field-induced antiferromagnetically ordered phase. Singlet-triplet and intra-triplet modes demonstrate a doublet structure which is due to two maxima in the density of magnon states in the low-frequency range. A joint analysis of the observed spectra and other experimental results allows to test the applicability of the fermionic and bosonic models. We conclude that the fermionic approach is more appropriate for the particular case of NTENP.Comment: 11 pages, 11 figures, published in Phys.Rev.

Quantum gauge boson propagators in the light front

Gauge fields in the light front are traditionally addressed via the employment of an algebraic condition $n\cdot A=0$ in the Lagrangian density, where $A_{\mu}$ is the gauge field (Abelian or non-Abelian) and $n^\mu$ is the external, light-like, constant vector which defines the gauge proper. However, this condition though necessary is not sufficient to fix the gauge completely; there still remains a residual gauge freedom that must be addressed appropriately. To do this, we need to define the condition $(n\cdot A)(\partial \cdot A)=0$ with $n\cdot A=0=\partial \cdot A$. The implementation of this condition in the theory gives rise to a gauge boson propagator (in momentum space) leading to conspicuous non-local singularities of the type $(k\cdot n)^{-\alpha}$ where $\alpha=1,2$. These singularities must be conveniently treated, and by convenient we mean not only matemathically well-defined but physically sound and meaningfull as well. In calculating such a propagator for one and two noncovariant gauge bosons those singularities demand from the outset the use of a prescription such as the Mandelstam-Leibbrandt (ML) one. We show that the implementation of the ML prescription does not remove certain pathologies associated with zero modes. However we present a causal, singularity-softening prescription and show how to keep causality from being broken without the zero mode nuisance and letting only the propagation of physical degrees of freedom.Comment: 10 page