We prove a formula of Kac-Wakimoto type for the twining characters of irreducible highest weight modules of symmetric, noncritical, integrally dominant highest weights over affine Lie algebras. This formula describes the twining character in terms of the subgroup of the integral Weyl group consisting of elements which commute with the Dynkin diagram automorphism. The main tools in our proof are...

Once an emergency event (EE) happens, decision-making (EDM) plays a key role in mitigating the loss. EDM is complex problem. Compared with conventional problems, more experts participate decision-making. It usually has feature of large group (LGEDM). This paper proposes method based on Bayesian theory, relative entropy, and Euclidean distance, which used for uncertain probabilities occurrence, ...

We prove that a particular deep network architecture is more efficient at approximating radially symmetric functions than the best known 2 or 3 layer networks. We use this architecture to approximate Gaussian kernel SVMs, and subsequently improve upon them with further training. The architecture and initial weights of the Deep Radial Kernel Network are completely specified by the SVM and theref...

We extend our earlier results [1; 2; 4] on the issue of weighted aggregations to linguistic importance weighted aggregations when both the importances (interpreted as benchmarks) and the ratings are given by symmetric triangular fuzzy numbers. We show that (unlike the case with finite term sets) small changes in the membership functions of the weights can cause only small variations in the (cri...

1 Preliminaries In the following, W will be a symmetric n × n matrix with non-negative elements. The assumption is that W ij are weights corresponding to the edges ij of a (complete) graph (V, E) with vertices indexed by the numbers 1,. .. n. The indices k, l will be used to index subsets of V in a partition; we will call these subsets clusters. The indices i, j will index elements of V .

We study theoretically and numerically trigonometric interpolation on symmetric subintervals of [−π, π], based on a family of Chebyshevlike angular nodes (subperiodic interpolation). Their Lebesgue constant increases logarithmically in the degree, and the associated Fejérlike trigonometric quadrature formula has positive weights. Applications are given to the computation of the equilibrium meas...

In this paper we introduce a nonextensive quantum information theoretic measure which may be defined between any arbitrary number of density matrices, and we analyze its fundamental properties in the spectral graph-theoretic framework. Unlike other entropic measures, the proposed quantum divergence is symmetric, matrix-convex, theoretically upper-bounded, and has the advantage of being generali...

We consider the Uq[SU(2)] symmetric Heisenberg chain when q = e iπ/(m+1) and m is integer. We consider the cases m = 3 and m = 5 which correspond to the Ising and 3-state Potts models. We study the finite size scaling (FSS) of the ground states in different quantum spin sectors and restricting to highest weights of type-II representations. We compute the levels by a diagrammatic technique which...

We study the free energy of a most used deep architecture for restricted Boltzmann machines, where layers are disposed in series. Assuming independent Gaussian distributed random weights, we show that error term so-called replica symmetric sum rule can be optimised as saddle point. This leads us to conjecture approximation is given by minmax formula, which parallels one achieved two-layer case.