Cohomology of Heisenberg Lie Superalgebras

Suppose the ground field to be algebraically closed and of characteristic different from $2$ and $3$. All Heisenberg Lie superalgebras consist of two super versions of the Heisenberg Lie algebras, $\frak{h}_{2m,n}$ and $\frak{ba}_n$ with $m$ a nonnegative integer and $n$ a positive integer. The space of a "classical" Heisenberg Lie superalgebra $\frak{h}_{2m,n}$ is the direct sum of a superspace with a non-degenerate anti-supersymmetric even bilinear form and a one-dimensional space of values of this form constituting the even center. The other super analog of the Heisenberg Lie algebra, $\frak{ba}_n$, is constructed by means of a non-degenerate anti-supersymmetric odd bilinear form with values in the one-dimensional odd center. In this paper, we study the cohomology of $\frak{h}_{2m,n}$ and $\frak{ba}_n$ with coefficients in the trivial module by using the Hochschild-Serre spectral sequences relative to a suitable ideal. In characteristic zero case, for any Heisenberg Lie superalgebra, we determine completely the Betti numbers and associative superalgebra structure for their cohomology. In characteristic $p>3$ case, we determine the associative superalgebra structures for the divided power cohomology of $\frak{ba}_n$ and we also make an attempt to determine the cohomology of $\frak{h}_{2m,n}$ by computing it in a low-dimensional case.Comment: 19 page

Median evidential c-means algorithm and its application to community detection

Median clustering is of great value for partitioning relational data. In this paper, a new prototype-based clustering method, called Median Evidential C-Means (MECM), which is an extension of median c-means and median fuzzy c-means on the theoretical framework of belief functions is proposed. The median variant relaxes the restriction of a metric space embedding for the objects but constrains the prototypes to be in the original data set. Due to these properties, MECM could be applied to graph clustering problems. A community detection scheme for social networks based on MECM is investigated and the obtained credal partitions of graphs, which are more refined than crisp and fuzzy ones, enable us to have a better understanding of the graph structures. An initial prototype-selection scheme based on evidential semi-centrality is presented to avoid local premature convergence and an evidential modularity function is defined to choose the optimal number of communities. Finally, experiments in synthetic and real data sets illustrate the performance of MECM and show its difference to other methods

Defining relations of almost affine (hyperbolic) superalgebras

For all almost affine (hyperbolic) Lie superalgebras, the defining relations are computed in terms of their Chevalley generators.Comment: Published in the special issue of JNMP in memory of F.A. Berezi

Application of photosynthetic N2-fixing cyanobacteria to the CELSS program

Commercially available air lift fermentors were used to simultaneously monitor biomass production, N2-fixation, photosynthesis, respiration, and sensitivity to oxidative damage during growth under various nutritional and light regimes, to establish a data base for the integration of these organisms into a Closed Ecological Life Support System (CELSS) program. Certain cyanobacterial species have the unique ability to reduce atmospheric N2 to organic nitrogen. These organisms combine the ease of cultivation characteristics of prokaryotes with the fully developed photosynthetic apparatus of higher plants. This, along with their ability to adapt to changes in their environment by modulation of certain biochemical pathways, make them attractive candidates for incorporation into the CELSS program

Double Spin Asymmetry of Electrons from Heavy Flavor Decays in p+p Collisions at sqrt(s)=200 GeV

We report on the first measurement of double-spin asymmetry, A_LL, of electrons from the decays of hadrons containing heavy flavor in longitudinally polarized p+p collisions at sqrt(s)=200 GeV for p_T= 0.5 to 3.0 GeV/c. The asymmetry was measured at mid-rapidity (|eta|<0.35) with the PHENIX detector at the Relativistic Heavy Ion Collider. The measured asymmetries are consistent with zero within the statistical errors. We obtained a constraint for the polarized gluon distribution in the proton of |Delta g/g(log{_10}x= -1.6^+0.5_-0.4, {mu}=m_T^c)|^2 < 0.033 (1 sigma), based on a leading-order perturbative-quantum-chromodynamics model, using the measured asymmetry.Comment: 385 authors, 17 pages, 15 figures, 5 tables. Submitted to Phys. Rev. D. Plain text data tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.htm

The yield curve and macroeconomic dynamics

We show that microfounded DSGE models with nominal rigidities can be successful in replicating features of bond yield data which have previously been considered puzzling in general equilibrium frameworks. Consistent with empirical evidence, we obtain average holding period returns that are positive, increasing in maturity and sizable, as well as long-maturity bond yields that are almost as volatile as short-term interest rates. At the same time, we are able to fit sample moments of consumption and inflation relatively well. To improve our understanding of these results, we derive analytical solutions for yields that are valid up to a second order approximation and generally applicable, We demonstrate that the improved model performance does not arise directly from the presence of nominal rigidities: ceteris paribus, the introduction of sticky-prices in a simple model tend to reduce premia. Sticky prices help indirectly because they imply (short-run) monetary non-neutrality, so that the policy rule followed by the central bank affects consumption dynamics and the pricing of yields. A very high degree of “interest rate smoothing” in the policy rule is essential for our results