Flag varieties and interpretations of Young tableau algorithms

The conjugacy classes of nilpotent $n\times n$ matrices can be parametrised by partitions $\lambda$ of $n$, and for a nilpotent $\eta$ in the class parametrised by $\lambda$, the variety $F_\eta$ of $\eta$-stable flags has its irreducible components parametrised by the standard Young tableaux of shape $\lambda$. We indicate how several algorithmic constructions defined for Young tableaux have significance in this context, thus extending Steinberg's result that the relative position of flags generically chosen in the irreducible components of $F_\eta$ parametrised by tableaux $P$ and $Q$, is the permutation associated to $(P,Q)$ under the Robinson-Schensted correspondence. Other constructions for which we give interpretations are Sch\"utzenberger's involution of the set of Young tableaux, jeu de taquin (leading also to an interpretation of Littlewood-Richardson coefficients), and the transpose Robinson-Schensted correspondence (defined using column insertion). In each case we use a doubly indexed family of partitions, defined in terms of the flag (or pair of flags) determined by a point chosen in the variety under consideration. We show that for generic choices, the family satisfies certain combinatorial relations, whence the family describes the computation of the algorithmic operation being interpreted, as we described in a previous publication.Comment: 16 page

Bulk Viscosity of Interacting Hadrons

We show that first approximations to the bulk viscosity $\eta_v$ are expressible in terms of factors that depend on the sound speed $v_s$, the enthalpy, and the interaction (elastic and inelastic) cross section. The explicit dependence of $\eta_v$ on the factor $(\frac 13 - v_s^2)$ is demonstrated in the Chapman-Enskog approximation as well as the variational and relaxation time approaches. The interesting feature of bulk viscosity is that the dominant contributions at a given temperature arise from particles which are neither extremely nonrelativistic nor extremely relativistic. Numerical results for a model binary mixture are reported.Comment: 4 pages, 1 figure, Contribution to Quark Matter 2009, Knoxville, Tennessee, US

Learning by a nerual net in a noisy environment - The pseudo-inverse solution revisited

A recurrent neural net is described that learns a set of patterns in the presence of noise. The learning rule is of Hebbian type, and, if noise would be absent during the learning process, the resulting final values of the weights would correspond to the pseudo-inverse solution of the fixed point equation in question. For a non-vanishing noise parameter, an explicit expression for the expectation value of the weights is obtained. This result turns out to be unequal to the pseudo-inverse solution. Furthermore, the stability properties of the system are discussed.Comment: 16 pages, 3 figure

Constrained speaker linking

In this paper we study speaker linking (a.k.a.\ partitioning) given constraints of the distribution of speaker identities over speech recordings. Specifically, we show that the intractable partitioning problem becomes tractable when the constraints pre-partition the data in smaller cliques with non-overlapping speakers. The surprisingly common case where speakers in telephone conversations are known, but the assignment of channels to identities is unspecified, is treated in a Bayesian way. We show that for the Dutch CGN database, where this channel assignment task is at hand, a lightweight speaker recognition system can quite effectively solve the channel assignment problem, with 93% of the cliques solved. We further show that the posterior distribution over channel assignment configurations is well calibrated.Comment: Submitted to Interspeech 2014, some typos fixe