This paper proposes a multi-class semi-supervised learning algorithm of the graph based method. We make use of the Bayesian framework of Gaussian process to solve this problem. We propose the prior based on the normalized graph Laplacian, and introduce a new likelihood based on softmax function model. Both the transductive and inductive problems are regarded as MAP (Maximum A Posterior) problem...

We investigate a technique, suitable for process algebraic, nite-state machine (model-checking) automated tools, for formally modelling arbitrary network topologies. We model aspects of a protocol for multiservice networks, and demonstrate how the technique can be used to verify end-to-end properties of protocols designed for arbitrary numbers of intermediate nodes. Our models are presented in ...

Higher inductive types (HITs) in Homotopy Type Theory (HoTT) allow the definition of datatypes which have constructors for equalities over the defined type. HITs generalise quotient types, and allow to define types which are not sets in the sense of HoTT (i.e. do not satisfy uniqueness of equality proofs) such as spheres, suspensions and the torus. However, there are also interesting uses of HI...

We apply methods of abduction derived from propositional probabilistic reasoning to predicate probabilistic reasoning, in particular inductive logic, by treating finite predicate knowledge bases as potentially infinite propositional knowledge bases. It is shown that for a range of predicate knowledge bases (such as those typically associated with inductive reasoning) and several key proposition...

Abstract This introduction consists of two parts. In the first part, special issue editors introduce inductive metaphysics from a historical as well systematic point view and discuss what distinguishes it other modern approaches to metaphysics. second they give brief summary individual articles in this issue.

Surface Penning ionization (SPI) in the process He*(2lS, 23S) + CO + He(llS) + CO+ + eis investigated theoretically for CO molecules chemisorbed on a Pd(ll1) surface at low collision energy of metastable He*-beams. The actual process can well be explained in terms of Auger deexcitation. The entire SPI process occurs at the topmost layer, thereby increasing the surface sensitivity. The potential...

We examine the nature and statistical properties of electron-electron collisions in the recollision process in a strong laser field. The separation of the double ionization yield into sequential and nonsequential components leads to a bell-shaped curve for the nonsequential probability and a monotonically rising one for the sequential process. We identify key features of the nonsequential proce...

Ionization potential (ionization energy) is a fundamental quantity characterizing electronic structure of a molecule. It is known that the energy in solution phase is significantly different from that in the gas phase. In this report, vertical and adiabatic ionization processes in aqueous solution are studied based on a hybrid method of quantum chemistry and statistical mechanics called referen...

introduction computed tomography scans are a very important tool for diagnosis and assessment of response to treatment in the practice of medicine. ionizing radiation in medical imaging is undoubtedly one of the most powerful diagnostic tools in medicine. yet, as with all medical interventions, there are potential risks in addition to the clear potential benefits. materials and methods two refe...