Self-adjoint symmetry operators connected with the magnetic Heisenberg ring

We consider symmetry operators a from the group ring C[S_N] which act on the Hilbert space H of the 1D spin-1/2 Heisenberg magnetic ring with N sites. We investigate such symmetry operators a which are self-adjoint (in a sence defined in the paper) and which yield consequently observables of the Heisenberg model. We prove the following results: (i) One can construct a self-adjoint idempotent symmetry operator from every irreducible character of every subgroup of S_N. This leads to a big manifold of observables. In particular every commutation symmetry yields such an idempotent. (ii) The set of all generating idempotents of a minimal right ideal R of C[S_N] contains one and only one idempotent which ist self-adjoint. (iii) Every self-adjoint idempotent e can be decomposed into primitive idempotents e = f_1 + ... + f_k which are also self-adjoint and pairwise orthogonal. We give a computer algorithm for the calculation of such decompositions. Furthermore we present 3 additional algorithms which are helpful for the calculation of self-adjoint operators by means of discrete Fourier transforms of S_N. In our investigations we use computer calculations by means of our Mathematica packages PERMS and HRing.Comment: 13 page

Different approaches to community detection

A precise definition of what constitutes a community in networks has remained elusive. Consequently, network scientists have compared community detection algorithms on benchmark networks with a particular form of community structure and classified them based on the mathematical techniques they employ. However, this comparison can be misleading because apparent similarities in their mathematical machinery can disguise different reasons for why we would want to employ community detection in the first place. Here we provide a focused review of these different motivations that underpin community detection. This problem-driven classification is useful in applied network science, where it is important to select an appropriate algorithm for the given purpose. Moreover, highlighting the different approaches to community detection also delineates the many lines of research and points out open directions and avenues for future research.Comment: 14 pages, 2 figures. Written as a chapter for forthcoming Advances in network clustering and blockmodeling, and based on an extended version of The many facets of community detection in complex networks, Appl. Netw. Sci. 2: 4 (2017) by the same author

Oxygen Activation by Mononuclear Mn, Co, and Ni Centers in Biology and Synthetic Complexes

The active sites of metalloenzymes that catalyze O2-dependent reactions generally contain iron or copper ions. However, several enzymes are capable of activating O2 at manganese or nickel centers instead, and a handful of dioxygenases exhibit activity when substituted with cobalt. This minireview summarizes the catalytic properties of oxygenases and oxidases with mononuclear Mn, Co, or Ni active sites, including oxalate-degrading oxidases, catechol dioxygenases, and quercetin dioxygenase. In addition, recent developments in the O2 reactivity of synthetic Mn, Co, or Ni complexes are described, with an emphasis on the nature of reactive intermediates featuring superoxo-, peroxo-, or oxo-ligands. Collectively, the biochemical and synthetic studies discussed herein reveal the possibilities and limitations of O2 activation at these three “overlooked” metals

A Synthetic Model of the Nonheme Iron–Superoxo Intermediate of Cysteine Dioxygenase

A nonheme Fe(II) complex (1) that models substrate-bound cysteine dioxygenase (CDO) reacts with O2 at −80 °C to yield a purple intermediate (2). Analysis with spectroscopic and computational methods determined that 2 features a thiolate-ligated Fe(III) center bound to a superoxide radical, mimicking the putative structure of a key CDO intermediate

Spectroscopic and Computational Studies of Reversible O\u3csub\u3e2\u3c/sub\u3e Binding by a Cobalt Complex of Relevance to Cysteine Dioxygenase

The substitution of non-native metal ions into metalloenzyme active sites is a common strategy for gaining insights into enzymatic structure and function. For some nonheme iron dioxygenases, replacement of the Fe(II) center with a redox-active, divalent transition metal (e.g., Mn, Co, Ni, Cu) gives rise to an enzyme with equal or greater activity than the wild-type enzyme. In this manuscript, we apply this metal-substitution approach to synthetic models of the enzyme cysteine dioxygenase (CDO). CDO is a nonheme iron dioxygenase that initiates the catabolism of L-cysteine by converting this amino acid to the corresponding sulfinic acid. Two mononuclear Co(II) complexes (3 and 4) have been prepared with the general formula [Co2+(TpR2)(CysOEt)] (R = Ph (3) or Me (4); TpR2 = hydrotris(pyrazol-1-yl)borate substituted with R-groups at the 3- and 5-positions, and CysOEt is the anion of L-cysteine ethyl ester). These Co(II) complexes mimic the active-site structure of substrate-bound CDO and are analogous to functional iron-based CDO models previously reported in the literature. Characterization with X-ray crystallography and/or 1H NMR spectroscopy revealed that 3 and 4 possess five-coordinate structures featuring facially-coordinating TpR2 and S,N-bidentate CysOEt ligands. The electronic properties of these high-spin (S = 3/2) complexes were interrogated with UV-visible absorption and X-band electron paramagnetic resonance (EPR) spectroscopies. The air-stable nature of complex 3 replicates the inactivity of cobalt-substituted CDO. In contrast, complex 4 reversibly binds O2 at reduced temperatures to yield an orange chromophore (4-O2). Spectroscopic (EPR, resonance Raman) and computational (density functional theory, DFT) analyses indicate that 4-O2 is a S = 1/2 species featuring a low-spin Co(III) center bound to an end-on (η1) superoxo ligand. DFT calculations were used to evaluate the energetics of key steps in the reaction mechanism. Collectively, these results have elucidated the role of electronic factors (e.g., spin-state, d-electron count, metal–ligand covalency) in facilitating O2 activation and S-dioxygenation in CDO and related models

Synchronization Properties of Network Motifs

We address the problem of understanding the variable abundance of 3-node and 4-node subgraphs (motifs) in complex networks from a dynamical point of view. As a criterion in the determination of the functional significance of a n-node subgraph, we propose an analytic method to measure the stability of the synchronous state (SSS) the subgraph displays. We show that, for undirected graphs, the SSS is correlated with the relative abundance, while in directed graphs the correlation exists only for some specific motifs.Comment: 7 pages, 3 figure

The large core limit of spiral waves in excitable media: A numerical approach

We modify the freezing method introduced by Beyn & Thuemmler, 2004, for analyzing rigidly rotating spiral waves in excitable media. The proposed method is designed to stably determine the rotation frequency and the core radius of rotating spirals, as well as the approximate shape of spiral waves in unbounded domains. In particular, we introduce spiral wave boundary conditions based on geometric approximations of spiral wave solutions by Archimedean spirals and by involutes of circles. We further propose a simple implementation of boundary conditions for the case when the inhibitor is non-diffusive, a case which had previously caused spurious oscillations. We then utilize the method to numerically analyze the large core limit. The proposed method allows us to investigate the case close to criticality where spiral waves acquire infinite core radius and zero rotation frequency, before they begin to develop into retracting fingers. We confirm the linear scaling regime of a drift bifurcation for the rotation frequency and the core radius of spiral wave solutions close to criticality. This regime is unattainable with conventional numerical methods.Comment: 32 pages, 17 figures, as accepted by SIAM Journal on Applied Dynamical Systems on 20/03/1

Puritanism: The Persistence of a Myth

A study of the impact on subsequent literature and criticism of the myth of American Puritanism invented in Victorian times and given its classic formulation by Hawthorne in The Scarlet Letter

Chronic Stress Triggers Expression of Immediate Early Genes and Differentially Affects the Expression of AMPA and NMDA Subunits in Dorsal and Ventral Hippocampus of Rats

Indexación: Web of Science; Scopus.Previous studies in rats have demonstrated that chronic restraint stress triggers anhedonia, depressive-like behaviors, anxiety and a reduction in dendritic spine density in hippocampal neurons. In this study, we compared the effect of repeated stress on the expression of α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) and N-methyl-D-aspartate (NMDA) receptor subunits in dorsal and ventral hippocampus (VH). Adult male Sprague-Dawley rats were randomly divided into control and stressed groups, and were daily restrained in their motion (2.5 h/day) during 14 days. We found that chronic stress promotes an increase in c-Fos mRNA levels in both hippocampal areas, although it was observed a reduction in the immunoreactivity at pyramidal cell layer. Furthermore, Arc mRNAs levels were increased in both dorsal and VH, accompanied by an increase in Arc immunoreactivity in dendritic hippocampal layers. Furthermore, stress triggered a reduction in PSD-95 and NR1 protein levels in whole extract of dorsal and VH. Moreover, a reduction in NR2A/NR2B ratio was observed only in dorsal pole. In synaptosomal fractions, we detected a rise in NR1 in dorsal hippocampus (DH). By indirect immunofluorescence we found that NR1 subunits rise, especially in neuropil areas of dorsal, but not VH. In relation to AMPA receptor (AMPAR) subunits, chronic stress did not trigger any change, either in dorsal or ventral hippocampal areas. These data suggest that DH is more sensitive than VH to chronic stress exposure, mainly altering the expression of NMDA receptor (NMDAR) subunits, and probably favors changes in the configuration of this receptor that may influence the function of this area.https://www.frontiersin.org/articles/10.3389/fnmol.2017.00244/ful