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The electric grid in the United States has been suffering from underinvestment for years, and now faces pressing challenges from rising demand and deteriorating infrastructure. High congestion levels in transmission lines are greatly reducing the efficiency of electricity generation and distribution. In this paper, we assess the faults of the current electric grid and quantify the costs of maintaining the current system into the future. While the proposed “smart grid” contains many proposals to upgrade the ailing infrastructure of the electric grid, we argue that smart meter installation in each U.S. household will offer a significant reduction in peak demand on the current system. A smart meter is a device which monitors a household’s electricity consumption in real-time, and has the ability to display real-time pricing in each household. We conclude that these devices will provide short-term and long-term benefits to utilities and consumers. The smart meter will enable utilities to closely monitor electricity consumption in real-time, while also allowing households to adjust electricity consumption in response to real-time price adjustments.

Given a graph G, the tree cover number of the graph, denoted T (G), is the minimum number of vertex disjoint simple trees occurring as induced subgraphs that cover all the vertices of G. This graph parameter was introduced in 2011 as a tool for studying the maximum positive semidefinite nullity of a graph, and little is known about it. It is conjectured that the tree cover number of a graph is at most the maximum positive semidefinite nullity of the graph. In this paper, we establish bounds on the tree cover number of a graph, characterize when an edge is required to be in some tree of a minimum tree cover, and show that the tree cover number of the d-dimensional hypercube is 2 for all d ≥ 2.

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The concept of probiotics is well known and has developed into a high value commodity in recent times. Despite the ever-expanding number of probiotic products on our pharmacy, health food and supermarket shelves, the probiotic culture active ingredient has always been imported until now. In 2019, Probiotics Australia Pty Ltd opened Australia’s first and only Therapeutic Goods Administration/current Good Manufacturing Practice (TGA/cGMP) certified facility dedicated to the manufacture of probiotic active ingredients. This article outlines the significant export demand for Australian-made health products and the lengths to which Probiotics Australia have gone to create a facility to meet needs of the probiotics research, commercialisation and consumer market today and into the future.