A very well–covered graph is an unmixed without isolated vertices such that the height of its edge ideal half number vertices. We study these graphs by means Betti splittings and mapping cone constructions. show cover ideals Cohen–Macaulay are splittable. As a consequence, we compute explicitly minimal graded free resolution class prove have homological linear quotients. Finally, conjecture sam...

For an arbitrary curve Z ⊂ P (possibly reducible, non-reduced, unmixed) lying on a normal surface, the general surface S of high degree containing Z is also normal, but often singular. We compute the class groups of the very general such surface, thereby extending the Noether-Lefschetz theorem (the special case when Z is empty). Our method is an adaptation of Griffiths and Harris’ degeneration ...

We discuss whether the NuTeV anomaly can be explained, compatibly with all other data, by QCD effects (maybe, if the strange sea is asymmetric, or there is a tiny violation of isospin), new physics in propagators or couplings of the vector bosons (not really), loops of supersymmetric particles (no), dimension six operators (yes, for one specific SU(2)L-invariant operator), leptoquarks (not in a...

The chemical composition of core-shell nanoparticle clusters have been determined through principal component analysis (PCA) and independent component analysis (ICA) of an energy-dispersive X-ray (EDX) spectrum image (SI) acquired in a scanning transmission electron microscope (STEM). The method blindly decomposes the SI into three components, which are found to accurately represent the isolate...

Let G be a simple undirected graph on n vertices, and let I(G) ⊆ R = k[x 1 ,. .. , x n ] denote its associated edge ideal. We show that all chordal graphs G are sequentially Cohen-Macaulay; our proof depends upon showing that the Alexander dual of I(G) is componentwise linear. Our result complements Faridi's theorem that the facet ideal of a simplicial tree is sequentially Cohen-Macaulay and im...

The construction of the Bézout matrix in the hybrid resultant formulation involves theories from algebraic geometry. The underlying theory on toric varieties has very nice properties such as the properties of fan (or cones), homogeneous coordinate ring, normality, and Zariski closure are related to the structure of the lattice polytopes in R. This paper presents the application of these propert...

The reader of Parmenides should put himself in the place of the Clazomenian philosophers who have come to Athens to hear the great argument of Socrates with Zeno and Parmenides as recorded in the memory of Antiphon. From it they would learn what Anaxagoras had not made clear, how the nous, alone unmixed, could relate to the atoms in each of which were all difference, the endless process of sepa...

To assist with the development of intelligent mixing systems, it would be useful to be able to extract the loudness balance of sources in an existing musical mixture. The relative-to-mix loudness level of four instrument groups was predicted using the sources extracted by 12 audio source separation algorithms. The predictions were compared with the ground truth loudness data of the original unm...

In a multicellular organism different cell types express a gene in different amounts. Samples from which gene expression levels can be measured typically contain a mixture of different cell types; the resulting measurements thus give only averages over the different cell types present. Based on fluctuations in the mixture proportions from sample to sample it is in principle possible to reconstr...

In order to explore functional properties of the olfactory and common chemical senses as well as their relation to the total nasal sensation experienced, various concentrations of two pungent odorants were presented alone and in the presence of different backgrounds of the other irritant. Stimuli comprised formaldehyde (at 1.0, 3.5, 6.9, and 16.7 ppm), ammonia (at 210, 776, 1,172, and 1,716 ppm...