The Widom-Rowlinson Model on the Delaunay Graph

We establish phase transitions for continuum Delaunay multi-type particle systems (continuum Potts or Widom-Rowlinson models) with a repulsive interaction between particles of different types. Our interaction potential depends solely on the length of the Delaunay edges. We show that a phase transition occurs for sufficiently large activities and for sufficiently large potential parameter proving an old conjecture of Lebowitz and Lieb extended to the Delaunay structure. Our approach involves a Delaunay random-cluster representation analogous to the Fortuin-Kasteleyn representation of the Potts model. The phase transition manifests itself in the mixed site-bond percolation of the corresponding random-cluster model. Our proofs rely mainly on geometric properties of Delaunay tessellations in $\mathbb{R}^2$ and on recent studies [DDG12] of Gibbs measures for geometry-dependent interactions. The main tool is a uniform bound on the number of connected components in the Delaunay graph which provides a novel approach to Delaunay Widom Rowlinson models based on purely geometric arguments. The interaction potential ensures that shorter Delaunay edges are more likely to be open and thus offsets the possibility of having an unbounded number of connected components.Comment: 36 pages, 11 figure

Phase transitions in Delaunay Potts models

We establish phase transitions for classes of continuum Delaunay multi-type particle systems (continuum Potts models) with infinite range repulsive interaction between particles of different type. In one class of the Delaunay Potts models studied the repulsive interaction is a triangle (multi-body) interaction whereas in the second class the interaction is between pairs (edges) of the Delaunay graph. The result for the edge model is an extension of finite range results in \cite{BBD04} for the Delaunay graph and in \cite{GH96} for continuum Potts models to an infinite range repulsion decaying with the edge length. This is a proof of an old conjecture of Lebowitz and Lieb. The repulsive triangle interactions have infinite range as well and depend on the underlying geometry and thus are a first step towards studying phase transitions for geometry-dependent multi-body systems. Our approach involves a Delaunay random-cluster representation analogous to the Fortuin-Kasteleyn representation of the Potts model. The phase transitions manifest themselves in the percolation of the corresponding random-cluster model. Our proofs rely on recent studies \cite{DDG12} of Gibbs measures for geometry-dependent interactions

Digital manufacturing for spare parts: scenarios for the automotive supply chain

Additive Manufacturing for spare parts is often discussed from a supply chain perspective, extoling the opportunities to reduce inventory and improve service in the supply chain. This paper examines possible scenarios for the mechanisms through which additively-manufactured automotive spare parts might be realised in the future, building on previous reviews of literature in this field. The paper also examines the technical challenges which may exist in the transition from traditional manufacturing processes to Additive processes for automotive spare parts

On Delaunay random cluster models

We examine continuum percolative problems on the Delaunay hypergraph structure. In particular, we investigate the existence of a percolation transition for a class of Gibbsian particle systems with random hyperedges between groups of particles. Each such system will take the form of a random cluster representation of a corresponding continuum Potts model with geometric interactions on hyperedges of the Delaunay hypergraph structure. Any percolation results in the random cluster representation will lead to the existence of a phase transition for the continuum Potts model: that is, the existence of more than one Gibbs measure. The original components of this research are as follows. After extending the random cluster representation of [GH96] to hypergraph structures, we achieve a phase transition for Delaunay continuum Potts models with infinite range type interactions – extending the work of [BBD03] in the process. Our main result is the existence of a phase transition for Delaunay continuum Potts models with no background interaction and just a soft type interaction. This is an extension of the phase transition results for the hardcore (resp. softcore) Widom–Rowlinson model of [R71] and later [CCK94], (resp. [LL72]). Our final piece of originality comes in the guise of an overview of the obstacles faced when investigating further percolative problems in the Delaunay hypergraph structure such as the Russo–Seymour–Welsh Theorem

3D printing the future: scenarios for supply chains reviewed

Purpose: The aim of this paper is to evaluate existing scenarios for 3D Printing in order to identify the “white space” where future opportunities have not been proposed or developed to date. Based around aspects of order penetration points, geographical scope and type of manufacturing, these gaps are identified. Design/methodology/approach: A structured literature review has been carried out on both academic and trade publications. As of the end of May 2016, this identified 128 relevant articles containing 201 future scenarios. Coding these against aspects of existing manufacturing and supply chain theory has led to the development of a framework for identify “white space” in existing thinking. Findings: The coding shows that existing future scenarios are particularly concentrated on job shop applications and pull based supply chain processes, although there are fewer constraints on geographical scope. Five distinct areas of “white space” are proposed, reflecting various opportunities for future 3DP supply chain development. Research limitations: Being a structured literature review, there are potentially articles not identified through the search criteria used. The nature of the findings is also dependent upon the coding criteria selected. However, these are theoretically derived and reflect important aspect of strategic supply chain management. Practical implications: Practitioners may wish to explore the development of business models within the “white space” areas. Originality/value: Currently, existing future 3DP scenarios are scattered over a wide, multi-disciplinary literature base. By providing a consolidated view of these scenarios, it is possible to identify gaps in current thinking. These gaps are multidisciplinary in nature and represent opportunities for both academics and practitioners to exploit

DRP-1 is required for BH3 mimetic-mediated mitochondrial fragmentation and apoptosis

The concept of using BH3 mimetics as anticancer agents has been substantiated by the efficacy of selective drugs, such as Navitoclax and Venetoclax, in treating BCL-2-dependent haematological malignancies. However, most solid tumours depend on MCL-1 for survival, which is highly amplified in multiple cancers and a major factor determining chemoresistance. Most MCL-1 inhibitors that have been generated so far, while demonstrating early promise in vitro, fail to exhibit specificity and potency in a cellular context. To address the lack of standardised assays for benchmarking the in vitro binding of putative inhibitors before analysis of their cellular effects, we developed a rapid differential scanning fluorimetry (DSF)-based assay, and used it to screen a panel of BH3 mimetics. We next contrasted their binding signatures with their ability to induce apoptosis in a MCL-1 dependent cell line. Of all the MCL-1 inhibitors tested, only A-1210477 induced rapid, concentration-dependent apoptosis, which strongly correlated with a thermal protective effect on MCL-1 in the DSF assay. In cells that depend on both MCL-1 and BCL-XL, A-1210477 exhibited marked synergy with A-1331852, a BCL-XL specific inhibitor, to induce cell death. Despite this selectivity and potency, A-1210477 induced profound structural changes in the mitochondrial network in several cell lines that were not phenocopied following MCL-1 RNA interference or transcriptional repression, suggesting that A-1210477 induces mitochondrial fragmentation in an MCL-1-independent manner. However, A-1210477-induced mitochondrial fragmentation was dependent upon DRP-1, and silencing expression levels of DRP-1 diminished not just mitochondrial fragmentation but also BH3 mimetic-mediated apoptosis. These findings provide new insights into MCL-1 ligands, and the interplay between DRP-1 and the anti-apoptotic BCL-2 family members in the regulation of apoptosis