The very idea of an \EEective Vapnik Chervonenkis (VC) dimension" (Vapnik, Levin and Le Cun, 1993) relies on the hypothesis that the relation between the generalization error and the number of training examples can be expressed by a formula algebraically similar to the VC bound. This hypothesis calls for a serious discussion since the traditional VC bound widely overestimates the generalization...

VC-minimality is a recent notion in model theory which generalizes strong minimality, o-minimality, weak o-minimality and c-minimality, but is strong enough to imply various other properties of interest such as NIP and dp-minimality. In this paper, we answer several questions posed by Adler about the relationship of VC-minimality and older stability-theoretic notions in model theory. We also gi...

The coastal saline-alkali soil in eastern China is an important reserve arable land resource. Adding exogenous organic material effective way to improve fertility and promote the conversion of agricultural soil. In this study, a field plot experiment was used investigate influences different materials (vinegar residue, VR; sewage sludge, SS; vermicompost, VC) on reduction salinity-alkalinity ba...

Enzyme activity measurement showed that L-ascorbic acid (vitamin C (Vc)) competitively inhibits the hyaluronan degradation by Streptococcus pneumoniae hyaluronate lyase. The complex crystal structure of this enzyme with Vc was determined at 2.0 A resolution. One Vc molecule was found to bind to the active site of the enzyme. The Vc carboxyl group provides the negative charges that lead the mole...

Abstract. We study the optimal rates of convergence for estimating a prior distribution over a VC class from a sequence of independent data sets respectively labeled by independent target functions sampled from the prior. We specifically derive upper and lower bounds on the optimal rates under a smoothness condition on the correct prior, with the number of samples per data set equal the VC dime...

For any class of binary functions on [n] = {1, . . . , n} a classical result by Sauer states a sufficient condition for its VC-dimension to be at least d: its cardinality should be at least O(n). A necessary condition is that its cardinality be at least 2 (which is O(1) with respect to n). How does the size of a ‘typical’ class of VC-dimension d compare to these two extreme thresholds ? To answ...

The paper 3] gives lower bounds on the VC-dimension of various smoothly parametrized function classes. The results were proven by showing a relationship between the uniqueness of decision boundaries and the VC-dimension of smoothly parametrized function classes. The proof is incorrect; there is no such relationship under the conditions stated in 3]. For the case of neural networks with tanh act...

These questions contrast the roles of information and complexity in learning. While the two roles share some ground, they are conceptually and technically different. In the common language of learning, the information question is that of generalization and the complexity question is that of scaling. The work of Vapnik and Chervonenkis (1971) provides the key tools for dealing with the informati...

Site evaluation for bioremediation of chlorinated ethenes may need treatability studies to assess the reductive dechlorination potential of vinyl chloride (VC). Dehalogenation of vinyl bromide (VB) was investigated as a surrogate measurement for the dechlorination potential of VC. VB dehalogenation rates and kinetics were studied and compared with those of VC by a methanogenic reductive dechlor...

We review recent progress in the study of the vertex-cover problem (VC). The VC belongs to the class of NP-complete graph theoretical problems, which plays a central role in theoretical computer science. On ensembles of random graphs, VC exhibits a coverable–uncoverable phase transition. Very close to this transition, depending on the solution algorithm, easy–hard transitions in the typical run...