7,558 research outputs found
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
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