We study the parameter space of D-dimensional cosmological Einstein gravity together with quadratic curvature terms. In D > 4 there are in general two distinct (anti)-de Sitter vacua. We show that for appropriate choice of the parameters there exists a critical point for one of the vacua, for which there are only massless tensor, but neither massive tensor nor scalar, gravitons. At criticality, the linearized excitations have vanishing energy (as do black hole solutions). A further restriction of the parameters gives a one-parameter cosmological Einstein plus Weyl 2 model with a unique vacuum, whose Λ is determined.

Semantic Data Mining refers to the data mining tasks that systematically incorporate domain knowledge, especially for mal semantics, into the process. In the past, many research efforts have attested the benefits of incorporating domain knowledge in data mining. At the same time, the proliferation of knowledge engineering has enriched the family of domain knowledge, espe cially formal semantics and Semantic Web ontologies. Ontology is an explicit specification of conceptualization and a formal way to define the semantics of knowledge and data. The formal structure of ontology makes it a nature way to encode domain knowledgefor the data mining use. In this survey paper, we introduce general concepts of semantic data mining. We investigate why ontology has the potential to help semantic data mining and how formal semantics in ontologies can be incorporated into the data mining process. We provide detail discussions for the advances and state of art of ontology-based approaches and an introduction of approaches that are based on other form of

An important phase transition in black hole thermodynamics is associated with the divergence of the specific heat with fixed charge and angular momenta, yet one can demonstrate that neither Ruppeiner's entropy metric nor Weinhold's energy metric reveals this phase transition. In this paper, we introduce a new thermodynamical metric based on the Hessian matrix of several free energy. We demonstrate, by studying various charged and rotating black holes, that the divergence of the specific heat corresponds to the curvature singularity of this new metric. We further investigate metrics on all thermodynamical potentials generated by Legendre transformations and study correspondences between curvature singularities and phase transition signals. We show in general that for a system with n-pairs of intensive/extensive variables, all thermodynamical potential metrics can be embedded into a flat (n, n)-dimensional space. We also generalize the Ruppeiner metrics and they are all conformal to the metrics constructed from the relevant thermodynamical potentials.