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 classes of sequentially Cohen-Macaulay and sequentially homotopy Cohen-Macaulay complexes and posets are studied. First, some different versions of the definitions are discussed and the homotopy type is determined. Second, it is shown how various constructions, such as join, product and rank-selection preserve these properties. Third, a characterization of sequential Cohen-Macaulayness for ...

Let G be a simple undirected graph on n vertices, and let I(G) ⊆ R = k[x1, . . . , xn] 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 impl...

We show that for a smooth hypersurface X ⊂ P of degree at least 2, there exist arithmetically Cohen-Macaulay (ACM) codimension two subvarieties Y ⊂ X which are not an intersection X ∩ S for a codimension two subvariety S ⊂ P. We also show there exist Y ⊂ X as above for which the normal bundle sequence for the inclusion Y ⊂ X ⊂ P does not split. Dedicated to Spencer Bloch

1541-1672/17/$33.00 © 2017 IEEE 3 Published by the IEEE Computer Society the area. In particular, the challenge was in developing methodologies that would let researchers not just compare each other’s work in a theoretical sense but that allowed different models of systems to be compared to real-world situations. One of the people who recognized this early on and addressed it both in her writin...

As empirical work in identifying social effects becomes more prevalent, researchers are beginning to struggle with identifying the composition of social interactions within any given reference group. In this paper, we present a simple econometric methodology for the separate identification of multiple social interactions. The setting under which we achieve separation is special, but is likely t...

The purpose of this paper is to provide a detailed analysis of how lexical differences related to cohesion and connectionist models can distinguish first language (L1) writers of English from second language (L2) writers of English. Key to this analysis is the use of the computational tool Coh-Metrix, which measures cohesion and text difficulty at various levels of language, discourse, and conc...

This paper describes the results of an experiment designed to assess the effects of self-monitoring and 3 different kinds of secondary task on the development of ideas during planning, and on the quality of subsequently produced text. An LSAbased measure was used to assess the development of ideas during planning and Coh-Metrix was used to assess effects on text. The results suggest that the sp...

Epistemic contextualists think that the truth-conditions of ‘knowledge’ ascriptions depend in part on the context in which they are uttered. But what features of context play a role in determining truth-conditions? The idea that the making salient of error-possibilities is a central part of the story has often been attributed to contextualists, and a number of contextualists seem to endorse it ...

A commutative local Cohen-Macaulay ring R of finite Cohen-Macaulay type is known to be an isolated singularity; that is, Spec(R) \ {m} is smooth. This paper proves a non-commutative analogue. Namely, if A is a (non-commutative) graded Artin-Schelter Cohen-Macaulay algebra which is FBN and has finite Cohen-Macaulay type, then the non-commutative projective scheme determined by A is smooth.