An admissible Poisson algebra (or briefly, an adm-Poisson algebra) gives equivalent presentation with only one operation for a algebra. We establish bialgebra theory algebras independently and systematically, including but beyond the corresponding results on bialgebras given in [27]. Explicitly, we introduce notion of which are to Manin triples as well bialgebras. The direct correspondence betw...

We study a class of Markov chains that describe reversible stochastic dynamics of a large class of disordered mean field models at low temperatures. Our main purpose is to give a precise relation between the metastable time scales in the problem to the properties of the rate functions of the corresponding Gibbs measures. We derive the analog of the WentzellFreidlin theory in this case, showing ...

The state explosion problem is the main limitation of model checking. Symmetries in the system being veriied can be exploited in order to avoid this problem. A symmetry relation on the system is deened, which induces a semantically equivalent quotient system of smaller size. On the other hand, heuristic search algorithms can be applied to improve error detection. Such algorithms use heuristic f...

Let Xo and X, be two Banach spaces which are continuously embedded in a common Hausdort t topological vector space. An admissible operator for the pair (Xo, X,) is a linear operator whose domain contains the union of the two spaces and whose restrictions to Xi is a bounded operator on Xi ( i = 0 , 1). A space X is called an interpolation space for the pair (Xo, X,) if each admissible operator T...

We propose a novel approach to fault detection in rotating mechanical machines: fusion of multichannel measurements of machine vibration using Independent Component Analysis (ICA), followed by a description of the admissible domain (part of the feature space indicative of normal machine operation) with a Support Vector Domain Description (SVDD) method. The SVDD-method enables the determination ...

We study the equivalence relation on the set of acyclic orientations of an undirected graph Γ generated by source-to-sink conversions. These conversions arise in the contexts of admissible sequences in Coxeter theory, quiver representations, and asynchronous graph dynamical systems. To each equivalence class we associate a poset, characterize combinatorial properties of these posets, and in tur...