Begriie ohne Anschauungen sind leer Anschauungen ohne Begriie blind. Abstract Typical examples, that is, examples that are representative for a particular situation or concept, play an important r^ ole in human knowledge representation and reasoning. In real life situations more often than not, instead of a lengthy abstract characterization , a typical example is used to describe the situation....

Active learning algorithms attempt to accelerate the learning process by requesting labels for the most informative items first. In real-world problems, however, there may exist unlabeled items that are irrelevant to the user’s classification goals. Queries about these points slow down learning because they provide no information about the problem of interest. We have observed that when irrelev...

Modern classification applications necessitate supplementing the few available labeled examples with unlabeled examples to improve classification performance. We present a new tractable algorithm for exploiting unlabeled examples in discriminative classification. This is achieved essentially by expanding the input vectors into longer feature vectors via both labeled and unlabeled examples. The ...

G2-monopoles are solutions to gauge theoretical equations onG2-manifolds. If the G2-manifolds under consideration are compact, then any irreducible G2-monopole must have singularities. It is then important to understand which kind of singularities G2-monopoles can have. We give examples (in the noncompact case) of non-Abelian monopoles with Dirac type singularities, and examples of monopoles wh...

We deene a new PAC learning model. In this model, examples are drawn according to the universal distribution m(: j f) of Solomomoo-Levin, where f is the target concept. The consequence is that the simple examples of the target concept have a high probability to be provided to the learning algorithm. We prove an Occam's Razor theorem. We show that the class of poly-term DNF is learnable, and the...

Analysis of self-similarity in scale-free $N$-body simulations reveals the spatial and temporal scales for which statistics measured cosmological are converged to physical continuum limit. We examine how range two-point correlation function is depends on force softening length whether it held constant comoving or proper coordinates. find that a reaches roughly 1/30th inter-particle spacing by e...

We introduce a new Turing machine based concept of time complexity for functions on computable metric spaces. It generalizes the ordinary complexity of word functions and the complexity of real functions studied by Ko [19] et al. Although this definition of TIME as the maximum of a generally infinite family of numbers looks straightforward, at first glance, examples for which this maximum exist...