Local cohomology was discovered in the 1960s as a tool to study sheaves and their cohomology in algebraic geometry, but have since seen wide use in commutative algebra. An example of their use is to answer the question: how many elements are necessary to generate a given ideal, up to radical? For example, consider two planes in 4-space meeting at a point. The vanishing ideal I = (x, y) ∩ (u, v)...

Convolutive decorrelation algorithms form a class of powerful algorithms for blind source separation. In contrast to ICA, they are based on vanishing second order cross correlation functions between sources. We provide an analyze an unifying approach for convolu-tive decorrelation procedures. The convolutive decor-relation procedures impose the problem of simultaneously diagonalizing a number o...

Simple transformation formulas between fermion matrices and observables, and numerical values of quark matrices, are obtained on a particular weak basis with one quark matrix diagonal and the other with vanishing elements 1-1, 1-3 and 3-1, and with only the element 2-2 complex. When we chooseMu diagonal, thenMd shows intriguing numerical properties which suggest a four parameter description of ...

We calculate the logarithmic corrections to the matrix elements for K → π and K → vacuum (which are used on the lattice to determine K → ππ amplitudes), in one-loop quenched and unquenched Chiral Perturbation Theory. We find that these corrections can be large. We also discuss, and present some results for, the direct determination of K → ππ amplitudes. In particular, we address effects from ch...

The current experimental status of neutrino physics is reviewed. It contains the evidences for a non-vanishing neutrino rest mass from neutrino oscillation searches. In addition an outlook is given on determining the various mixing matrix elements and mass differences more precisely with new experiments. Of special interest is the value of the mixing angle θ13 determining the possibility of det...

Test ideals play a crucial role in the theory of tight closure developed by Melvin Hochster and Craig Huneke. Recently, Karen Smith showed that test ideals are closely related to certain multiplier ideals that arise in vanishing theorems in algebraic geometry. In this paper we develop a generalization of the notion of test ideals: for complete local rings R and S, where S is a module-6nite exte...

In this note it is shown that the Maslov Index for pairs of Lagrangian Paths as introduced by Cappell, Lee and Miller ([1]) appears by parallel transporting elements of (a certain complex line-subbundle of) the symplectic spinorbundle over Euclidean space, when pulled back to an (embedded) Lagrangian submanifold L, along closed or non-closed paths therein. More precisely, the CLM-Index mod 4 de...

We consider communication over binary memoryless symmetric channels using random elements from irregular low density parity check code (LDPC) ensembles, and belief propagation (BP) decoding. Under the assumption that the corresponding Tanner graph includes a non-vanishing fraction of degree 2 variable nodes, we determine the large blocklength behavior of the bit error rate for noise levels belo...

Abstract. Let G be a reductive algebraic group over C and let N be a G-module. For any subspace M of N , the Brylinski-Kostant filtration on M is defined through the action of a principal nilpotent element in LieG. This filtration is related to a q-analog of weight multiplicity due to Lusztig. We generalize this filtration to other nilpotent elements and show that this generalized filtration is...