Let F be a k-uniform hypergraph on [n] where k − 1 is a power of some prime p and n ≥ n0(k). Our main result says that if |F | > ( n k−1 ) − logp n + k!kk , then there exists E0 ∈ F such that {E ∩ E0 : E ∈ F} contains all subsets of E0. This improves a longstanding bound of ( n k−1 ) due to Frankl and Pach [7].

Learning from hints is a generalization of learning from examples that allows for a variety of information about the unknown function to be used in the learning process. In this paper, we use the VC dimension, an established tool for analyzing learning from examples, to analyze learning from hints. In particular, we show how the VC dimension is affected by the introduction of a hint. We also de...

Note that the VC dimension of orthogonal rectangles is four and this is exactly the number of examples needed to represent the consistent orthogonal rectangle. A compression scheme of size k for a concept class C picks from any set of examples consistent with some concept in C a subset of up to k examples and this subset represents (via a mapping that that is specific to the class C) a hypothes...

The known O(dk log k) bound on the VC dimension of k-fold unions or intersections of a given concept class with VC dimension d is shown to be asymptotically tight.

We systematically investigate finite maximum classes, which play an important role in machine learning as concept classes meeting Sauer’s Lemma with equality. Simple arrangements of hyperplanes in Hyperbolic space are shown to represent maximum classes, generalizing the corresponding Euclidean result. We show that sweeping a generic hyperplane across such arrangements forms an unlabeled compres...

Aerobic bacteria that grow on vinyl chloride (VC) have been isolated previously, but their diversity and distribution are largely unknown. It is also unclear whether such bacteria contribute to the natural attenuation of VC at chlorinated-ethene-contaminated sites. We detected aerobic VC biodegradation in 23 of 37 microcosms and enrichments inoculated with samples from various sites. Twelve dif...

The effect of mugwort extract (ME) and vitamin C (VC), added individually or in combination, on color, lipid oxidation, and sensory characteristics of chicken nuggets stored for 12 d was investigated. Eight treatments of chicken nuggets contained the following: Control (no antioxidant added), VC (0.05% VC), ME 0.05 (0.05% ME), ME 0.1 (0.1% ME), ME 0.2 (0.2% ME), VC+ME 0.05 (0.05% VC + 0.05% ME)...

The present study was carried out to investigate biochemical responses of marigold (Calendula officinalis L.) to Bio-organic fertilizers. Effects of co-inoculation of two plant growth-promoting rhizobacteria (PGPR) (Azotobacter sp.145PI and Azospirillum sp.AC49I), humic acid (HA) (10 kg ha−1), vermicompost (VC) (7 T ha−1) and combinations of these treatments were evaluated in two marigold culti...

The aim of this study was to determine the effectiveness vinasse, which is known be a good source organic matter and potassium in production an aromatic plant. In context, food industry waste, composted applied soil alone mixed with chemical fertilizers different doses [Only fertilization-control (C), vinasse compost 0.5 t ha-1 (VC-0.5), + fertilization (VC-0.5+CF), 1 (VC-1), (VC-1+CF)] thus, b...

The initial processing of corneal sensory input in the rat occurs in two distinct regions of the spinal trigeminal nucleus, at the subnucleus interpolaris/caudalis transition (Vi/Vc) and in laminae I-II at the subnucleus caudalis/spinal cord transition (Vc/C1). Extracellular recording was used to compare the effects of morphine on the evoked activity of corneal-responsive neurons located in the...