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The transition to low-carbon power systems necessitates cost-effective energy storage solutions. This study provides the first continental-scale assessment of micro-pumped hydro energy storage and proposes using agricultural reservoirs (farm dams) to significantly reduce construction costs. The continent of Australia is used as a representative case study for other arid and temperate regions internationally. From a new survey of its 1.7 million farm dams, we identified 30,295 promising pumped hydro sites in dam-to-dam and dam-to-river reservoir configurations. The average site had nearby reservoirs (132 m) with a high head height (32 m) and substantial discharge capacity (52 kWh). We then benchmarked a representative micro-pumped hydro site to a commercially available lithium-ion battery for a solar-powered irrigation system. Despite a low discharge efficiency (68%), pumped hydro storage was 30% less expensive (0.215 USD/kWh) for larger single-cycle loads (∼41 kWh/day) due to its high storage capacity. By capitalising on existing farm dams, micro-pumped hydro energy storage may support the uptake of reliable, low-carbon power systems in agricultural communities.

In this paper, we construct a number of 4-GDDs where the group sizes are all congruent to 2 (mod 3). We also show that 4-GDDs of type 2t8s exist for all but a finite number of feasible values of s and t. The largest unknown case has type 24818 and has 152 points. A number of 4-GDDs with at most 50 points are also constructed. These include one of type 4811101, the last feasible type of the form 4s1tn1 with at most 50 points for which no 4-GDD was known.

This note briefly gives advice on how to write a Parabola article - or any mathematical article.

A frequency square is a matrix in which each row and column is a permutation of the same multiset of symbols. We consider only binary frequency squares of order n with n/2 zeros and n/2 ones in each row and column. Two such frequency squares are orthogonal if, when superimposed, each of the 4 possible ordered pairs of entries occurs equally often. In this context we say that a set of k-MOFS(n) is a set of k binary frequency squares of order n in which each pair of squares is orthogonal.

You undoubtedly know about Fibonacci numbers. But did you know these facts about them? Interesting history and fun challenges await.

We extend and provide new proofs of the Wei-type duality theorems, due to Ducoat and Ravagnani, for Gabidulin–Roth rank-metric codes and for Delsarte rank-metric codes. These results follow as corollaries from fundamental Wei-type duality theorems that we prove for certain general combinatorial structures.

Simple mathematical expressions are given for the betweenness centrality of nodes in trees, forests and cycles. As application, a centrality test is given for when a network might be a forest.

Objectives: To investigate the organisation and characteristics of general practice in Australia by applying novel network analysis methods to national Medicare claims data. Design: We analysed Medicare claims for general practitioner consultations during 1994-2014 for a random 10% sample of Australian residents, and applied hierarchical block modelling to identify provider practice communities (PPCs). Participants: About 1.7 million patients per year. Main outcome measures: Numbers and characteristics of PPCs (including numbers of providers, patients and claims), proportion of bulk-billed claims, continuity of care, patient loyalty, patient sharing. Results: The number of PPCs fluctuated during the 21-year period; there were 7747 PPCs in 2014. The proportion of larger PPCs (six or more providers) increased from 32% in 1994 to 43% in 2014, while that of sole provider PPCs declined from 50% to 39%. The median annual number of claims per PPC increased from 5000 (IQR, 40-19 940) in 1994 to 9980 (190-23 800) in 2014; the proportion of PPCs that bulk-billed all patients was lowest in 2004 (21%) and highest in 2014 (29%). Continuity of care and patient loyalty were stable; in 2014, 50% of patients saw the same provider and 78% saw a provider in the same PPC for at least 75% of consultations. Density of patient sharing in a PPC was correlated with patient loyalty to that PPC. Conclusions: During 1994-2014, Australian GP practice communities have generally increased in size, but continuity of care and patient loyalty have remained stable. Our novel approach to the analysis of routinely collected data allows continuous monitoring of the characteristics of Australian general practices and their influence on patient care.

Mubayi's conjecture states that if \scrF is a family of k-sized subsets of [n] = \{ 1, . . ., n\} which, for k \geq d \geq 3 and n \geqddk- 1, satisfies A1 \cap \cap Ad \not = \emptyset whenever | A1 \cup \cup Ad| \leq 2k for all distinct sets A1, . . ., Ad \in \scrF , then | \scrF | \leq \bigl(nk --11\bigr) , with equality occurring only if \scrF is the family of all k-sized subsets containing some fixed element. This paper proves that Mubayi's conjecture is true for all families that are invariant with respect to shifting; indeed, these families satisfy a stronger version of Mubayi's conjecture. Relevant to the conjecture, we prove a fundamental bijective duality between what we call (i, j)-unstable families and (j, i)-unstable families. Generalizing previous intersecting conditions, we introduce the (d, s, t)-conditionally intersecting condition for families of sets and prove general results thereon. We prove fundamental theorems on two (d, s)-conditionally intersecting families that generalize previous intersecting families, and we pose an extension of a previous conjecture by Frankl and F\" uredi. Finally, we generalize a classical result by Erdos, Ko, and Rado by proving tight upper bounds on the size of (2, s)-conditionally intersecting families \scrF \subseteq 2[n] and by characterizing the families that attain these bounds. We extend this theorem for sufficiently large n to families \scrF \subseteq 2[n] whose members have at most a fixed size u.

The current paper aimed to investigate the effectiveness of five law enforcement interventions in disrupting and dismantling criminal networks. We tested three law enforcement interventions that targeted social capital in criminal networks (betweenness, degree and cut-set) and two interventions that targeted human capital (actors who possess money and those who possess precursor chemicals). These five interventions are compared with each other and with random (opportunistic) removal of actors in two settings: (i) with network adaptation incorporated into the simulations and (ii) without network adaptation. Results illustrate that the removal of actors based on betweenness centrality was the most efficient strategy, leading to network disruption in the least number of steps and was relatively consistent across replications. Targeting actors who possessed money was the second most effective overall and was also relatively consistent in its disruptive effect.

This paper introduces the covering dimension of a linear code over a finite field, which is analogous to the critical exponent of a representable matroid and, thus, generalizes invariants that lie at the heart of several fundamental problems in a coding theory. An upper bound on the covering dimension is proved, improving Kung's classical bound for the critical exponent. In addition, a construction is given for linear codes that attain equality in this covering dimension bound.