A Kazhdan–Lusztig Correspondence for $$L_{-\frac{3}{2}}(\mathfrak {sl}_3)$$

A class of $L_1$-to-$L_1$ and $L_\infty$-to-$L_\infty$ interval observers for (delayed) Markov jump linear systems

We exploit recent results on the stability and performance analysis of positive Markov jump linear systems (MJLS) for the design of interval observers for MJLS with and without delays. While the conditions for the L1 performance are necessary and sufficient, those for the L∞ performance are only sufficient. All the conditions are stated as linear programs that can be solved very efficiently. Tw...

Direct l_(2, p)-Norm Learning for Feature Selection

In this paper , we propose a novel sparse learning based feature selection method that directly optimizes a large margin linear classification model’s sparsity with -norm ( ) subject to data-fitt ing constraints, rather than using the sparsity as a regularizat ion term. To solve the d irect sparsity opt imizat ion p rob lem that is non-s mooth and non-convex when , we prov ide an efficient iter...

An Algorithm for $L_\infty$ Approximation by Step Functions

We give an algorithm for determining an optimal step function approximation of weighted data, where the error is measured with respect to the L∞ norm. The algorithm takes Θ(n+ log n · b(1 + log n/b)) time and Θ(n) space, where b is the number of steps. Thus the time is Θ(n log n) in the worst case and Θ(n) when b = O(n/ log n log log n). A minor change determines the optimal reduced isotonic re...

Affine inequalities for Lp$L_{p}$-mixed mean zonoids

$L_{p}$ Consonant Approximations of Belief Functions

In this paper we solve the problem of approximating a belief measure with a necessity measure or “consonant belief function” in a geometric framework. Consonant belief functions form a simplicial complex in both the space of all belief functions and the space of all mass vectors: partial approximations are first sought in each component of the complex, while global solutions are selected among ...