The Betti numbers of forests

This paper produces a recursive formula of the Betti numbers of certain Stanley-Reisner ideals (graph ideals associated to forests). This gives a purely combinatorial definition of the projective dimension of these ideals, which turns out to be a new numerical invariant of forests. Finally, we propose a possible extension of this invariant to general graphs

The Betti numbers of forests

This paper produces a recursive formula of the Betti numbers of certain Stanley-Reisner ideals (graph ideals associated to forests). This gives a purely combinatorial definition of the projective dimension of these ideals, which turns out to be a new numerical invariant of forests. Finally, we propose a possible extension of this invariant to general graphs

Characterization of low thermal conductivity PAN-based carbon fibers

The microstructure and surface chemistry of eight low thermal conductivity (LTC) PAN-based carbon fibers were determined and compared with PAN-based fibers heat treated to higher temperatures. Based on wide-angle x ray diffraction, the LTC PAN fibers all appear to have a similar turbostratic structure with large 002 d-spacings, small crystallite sizes, and moderate preferred orientation. Limited small-angle x ray scattering (SAXS) results indicate that, with the exception of LTC fibers made by BASF, the LTC fibers do not have well developed pores. Transmission electron microscopy shows that the texture of the two LTC PAN-based fibers studied (Amoco T350/23X and /25X) consists of multiple sets of parallel, wavy, bent layers that interweave with each other forming a complex three dimensional network oriented randomly around the fiber axis. X ray photoelectron spectroscopy (XPS) analysis finds correlations between heat treated temperatures and the surface composition chemistry of the carbon fiber samples

Global parameter test ideals

This paper shows the existence of ideals whose localizations and completions at prime ideals are parameter test ideals of the localized and completed rings. We do this for Cohen-Macaulay localizations (resp., completions) of non-local rings, for generalized Cohen-Macaulay rings, and for non-local rings with isolated non Cohen-Macaulay points, each being an isolated non $F$-rational point. The tools used to prove this results are constructive in nature and as a consequence our results yield algorithms for the computation of these global parameter test ideals. Finally, we illustrate the power of our methods by analyzing the HSL numbers of local cohomology modules with support at any prime ideal

Women’s changing domestic responsibilities in neoliberal Africa: a relational time-space analysis of Lesotho’s garment industry

Since 2001 when Lesotho embraced the neoliberal African Growth and Opportunities Act that offers preferential access to the US market, its garment industry has expanded dramatically to become the nation’s leading employer. Elsewhere, large-scale employment of women in low-paid factory jobs has entailed spatial restructuring of gender and age relations. Lesotho is a distinctive context, with socio-spatial relations historically adjusted to male labour migration, high levels of contemporary male unemployment and alarming AIDS prevalence. Based on semi-structured interviews with 40 female factoryworkers and 37 dependents, this article applies a relational time-space analysis to explore how financial and spatio-temporal aspects of factory employment articulate to alter women’s relationships with those for whom they have culturally determined responsibilities: their children, those suffering from ill health and their (generally rural) home communities. The analysis highlights that such employment is not merely adding to women’s responsibilities, but transforming how they are able to undertake social reproduction, as practical, social and emotional roles are converted to largely financial obligations

GC-Biased Evolution Near Human Accelerated Regions

Regions of the genome that have been the target of positive selection specifically along the human lineage are of special importance in human biology. We used high throughput sequencing combined with methods to enrich human genomic samples for particular targets to obtain the sequence of 22 chromosomal samples at high depth in 40 kb neighborhoods of 49 previously identified 100–400 bp elements that show evidence for human accelerated evolution. In addition to selection, the pattern of nucleotide substitutions in several of these elements suggested an historical bias favoring the conversion of weak (A or T) alleles into strong (G or C) alleles. Here we found strong evidence in the derived allele frequency spectra of many of these 40 kb regions for ongoing weak-to-strong fixation bias. Comparison of the nucleotide composition at polymorphic loci to the composition at sites of fixed substitutions additionally reveals the signature of historical weak-to-strong fixation bias in a subset of these regions. Most of the regions with evidence for historical bias do not also have signatures of ongoing bias, suggesting that the evolutionary forces generating weak-to-strong bias are not constant over time. To investigate the role of selection in shaping these regions, we analyzed the spatial pattern of polymorphism in our samples. We found no significant evidence for selective sweeps, possibly because the signal of such sweeps has decayed beyond the power of our tests to detect them. Together, these results do not rule out functional roles for the observed changes in these regions—indeed there is good evidence that the first two are functional elements in humans—but they suggest that a fixation process (such as biased gene conversion) that is biased at the nucleotide level, but is otherwise selectively neutral, could be an important evolutionary force at play in them, both historically and at present

Regularity of squarefree monomial ideals

We survey a number of recent studies of the Castelnuovo-Mumford regularity of squarefree monomial ideals. Our focus is on bounds and exact values for the regularity in terms of combinatorial data from associated simplicial complexes and/or hypergraphs.Comment: 23 pages; survey paper; minor changes in V.

A data-driven approach for predicting printability in metal additive manufacturing processes

Metal powder-bed fusion additive manufacturing technologies offer numerous benefits to the manufacturing industry. However, the current approach to printability analysis, determining which components are likely to build unsuccessfully, prior to manufacture, is based on ad-hoc rules and engineering experience. Consequently, to allow full exploitation of the benefits of additive manufacturing, there is a demand for a fully systematic approach to the problem. In this paper we focus on the impact of geometry in printability analysis. For the first time, we detail a machine learning framework for determining the geometric limits of printability in additive manufacturing processes. This framework consists of three main components. First, we detail how to construct strenuous test artefacts capable of pushing an additive manufacturing process to its limits. Secondly, we explain how to measure the printability of an additively manufactured test artefact. Finally, we construct a predictive model capable of estimating the printability of a given artefact before it is additively manufactured. We test all steps of our framework, and show that our predictive model approaches an estimate of the maximum performance obtainable due to inherent stochasticity in the underlying additive manufacturing process. © 2020, The Author(s)