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

Moist turbulent Rayleigh-Benard convection with Neumann and Dirichlet boundary conditions

Turbulent Rayleigh-Benard convection with phase changes in an extended layer between two parallel impermeable planes is studied by means of three-dimensional direct numerical simulations for Rayleigh numbers between 10^4 and 1.5\times 10^7 and for Prandtl number Pr=0.7. Two different sets of boundary conditions of temperature and total water content are compared: imposed constant amplitudes which translate into Dirichlet boundary conditions for the scalar field fluctuations about the quiescent diffusive equilibrium and constant imposed flux boundary conditions that result in Neumann boundary conditions. Moist turbulent convection is in the conditionally unstable regime throughout this study for which unsaturated air parcels are stably and saturated air parcels unstably stratified. A direct comparison of both sets of boundary conditions with the same parameters requires to start the turbulence simulations out of differently saturated equilibrium states. Similar to dry Rayleigh-Benard convection the differences in the turbulent velocity fluctuations, the cloud cover and the convective buoyancy flux decrease across the layer with increasing Rayleigh number. At the highest Rayleigh numbers the system is found in a two-layer regime, a dry cloudless and stably stratified layer with low turbulence level below a fully saturated and cloudy turbulent one which equals classical Rayleigh-Benard convection layer. Both are separated by a strong inversion that gets increasingly narrower for growing Rayleigh number.Comment: 19 pages, 13 Postscript figures, Figures 10,11,12,13, in reduced qualit

Approximating Spectral Impact of Structural Perturbations in Large Networks

Determining the effect of structural perturbations on the eigenvalue spectra of networks is an important problem because the spectra characterize not only their topological structures, but also their dynamical behavior, such as synchronization and cascading processes on networks. Here we develop a theory for estimating the change of the largest eigenvalue of the adjacency matrix or the extreme eigenvalues of the graph Laplacian when small but arbitrary set of links are added or removed from the network. We demonstrate the effectiveness of our approximation schemes using both real and artificial networks, showing in particular that we can accurately obtain the spectral ranking of small subgraphs. We also propose a local iterative scheme which computes the relative ranking of a subgraph using only the connectivity information of its neighbors within a few links. Our results may not only contribute to our theoretical understanding of dynamical processes on networks, but also lead to practical applications in ranking subgraphs of real complex networks.Comment: 9 pages, 3 figures, 2 table

Biochemistry and functional aspects of human glandular kallikreins

Human urinary kallikrein was purified by gel filtration on Sephacryl S-200 and affinity chromatography on aprotinin-Sepharose, followed by ion exchange chromatography on DEAE-Sepharose. In dodecylsulfate gel electrophoresis two protein bands with molecular weights of 41,000 and 34,000 were separated. The amino acid composition and the carbohydrate content of the kallikrein preparation were determined; isoleucine was identified as the only aminoterminal amino acid. The bimolecular velocity constant for the inhibition by diisopropyl fluorophosphate was determined as 9±2 l mol–1 min–1. The hydrolysis of a number of substrates was investigated and AcPheArgOEt was found to be the most sensitive substrate for human urinary kallikrein. Using this substrate an assay method for kallikrein in human urine was developed. It was shown by radioimmunoassay that pig pancreatic kallikrein can be absorbed in the rat intestinal tract. Furthermore, in dogs the renal excretion of glandular kallikrein from blood was demonstrated by radioimmunological methods

Dynamic Computation of Network Statistics via Updating Schema

In this paper we derive an updating scheme for calculating some important network statistics such as degree, clustering coefficient, etc., aiming at reduce the amount of computation needed to track the evolving behavior of large networks; and more importantly, to provide efficient methods for potential use of modeling the evolution of networks. Using the updating scheme, the network statistics can be computed and updated easily and much faster than re-calculating each time for large evolving networks. The update formula can also be used to determine which edge/node will lead to the extremal change of network statistics, providing a way of predicting or designing evolution rule of networks.Comment: 17 pages, 6 figure

Finding community structure in very large networks

The discovery and analysis of community structure in networks is a topic of considerable recent interest within the physics community, but most methods proposed so far are unsuitable for very large networks because of their computational cost. Here we present a hierarchical agglomeration algorithm for detecting community structure which is faster than many competing algorithms: its running time on a network with n vertices and m edges is O(m d log n) where d is the depth of the dendrogram describing the community structure. Many real-world networks are sparse and hierarchical, with m ~ n and d ~ log n, in which case our algorithm runs in essentially linear time, O(n log^2 n). As an example of the application of this algorithm we use it to analyze a network of items for sale on the web-site of a large online retailer, items in the network being linked if they are frequently purchased by the same buyer. The network has more than 400,000 vertices and 2 million edges. We show that our algorithm can extract meaningful communities from this network, revealing large-scale patterns present in the purchasing habits of customers

Emotion and memory: Event-related potential indices predictive for subsequent successful memory depend on the emotional mood state.

The present research investigated the influencesof emotional mood states on cognitive processes and neural circuits during long-term memory encoding using event-related potentials (ERPs). We assessed whether the subsequent memory effect (SME), an electrophysiological index of successful memory encoding, varies as a function of participants’ current mood state. ERPs were recorded while participants in good or bad mood states were presented with words that had to be memorized for subsequent recall. In contrast to participants in bad mood, participants in good mood most frequently applied elaborative encoding styles. At the neurophysiological level, ERP analyses showed that potentials to subsequently recalled words were more positive than to forgotten words at central electrodes in the time interval of 500-650 ms after stimulus onset (SME). At fronto-central electrodes, a polarity-reversed SME was obtained. The strongest modulations of the SME by participants’ mood state were obtained at fronto-temporal electrodes. These differences in the scalp topography of the SME suggest that successful recall relies on partially separable neural circuits for good and bad mood states. The results are consistent with theoretical accounts of the interface between emotion and cognition that propose mood-dependent cognitive styles