Products of Borel fixed ideals of maximal minors

We study a large family of products of Borel fixed ideals of maximal minors. We compute their initial ideals and primary decompositions, and show that they have linear free resolutions. The main tools are an extension of straightening law and a very surprising primary decomposition formula. We study also the homological properties of associated multi-Rees algebra which are shown to be Cohen-Macaulay, Koszul and defined by a Gr\"obner basis of quadrics

The subdivision of large simplicial cones in Normaliz

Normaliz is an open-source software for the computation of lattice points in rational polyhedra, or, in a different language, the solutions of linear diophantine systems. The two main computational goals are (i) finding a system of generators of the set of lattice points and (ii) counting elements degree-wise in a generating function, the Hilbert Series. In the homogeneous case, in which the polyhedron is a cone, the set of generators is the Hilbert basis of the intersection of the cone and the lattice, an affine monoid. We will present some improvements to the Normaliz algorithm by subdividing simplicial cones with huge volumes. In the first approach the subdivision points are found by integer programming techniques. For this purpose we interface to the integer programming solver SCIP to our software. In the second approach we try to find good subdivision points in an approximating overcone that is faster to compute.Comment: To appear in the proceedings of the ICMS 2016, published by Springer as Volume 9725 of Lecture Notes in Computer Science (LNCS

Optimal maintenance strategies for systems with partial repair options and without assuming bounded costs

We study a repairable system with Markovian deterioration and partial repair options, carried out at fixed times $n=1,2,\ldots$ and look for optimal strategies under certain conditions. Two optimality criteria are considered: expected discounted cost and long-run average cost. Douer and Yechiali found conditions under which a policy in the class of generalized control limit policies is optimal. In this paper conditions are found under which an optimal policy is a control-limit policy. We explicitly explain how to derive this optimal policy; numerical examples are given, too

Citizen journalism in the 2007 Australian Federal Election

Citizen journalists and news and political bloggers are set to have a considerable impact on journalistic coverage of the 2007 Australian federal election campaign. Already, even before the election proper has been called, the alternative viewpoints of citizen journalists and bloggers can be seen to have significantly disrupted the previously relatively static arrangements between government and opposition parties and the journalistic establishment, and to have challenged standard modes of reporting and interpreting political events. This paper discusses the role of citizen journalists and news and political bloggers in the 2007 Australian federal election campaign by examining four key sites of such alternative reporting, analysis, and commentary: the hyperlocal citizen journalism site Youdecide2007.org, the leading left-of-centre political group blog Larvatus Prodeo, the influential psephologist blogger Possums Pollytics, and ABC Online’s attempt at blogging the election campaign, The Poll Vault. It analyses the content and style of such initiatives, and tracks the take-up of their work across the wider Australian blogosphere and beyond (in part building on network mapping methodologies as outlined in Bruns, 2007), and on that basis presents an insight into the place of news and political blogging and citizen journalism within the wider Australian mediasphere throughout the federal election campaign

A discounted model for a repairable system with continuous state space

We examine repairable systems with a continous state space and partial repair options, carried out at fixed times $n=1,2,...$. Every time interval $[n,n+1)$ there is a manufacturing cost and a repair cost. These cost functions are not restricted to the class of bounded functions in this study. Conditions are found under which a control-limit replacement policy minimizes the discounted cost. Hence these conditions guarantee that there is an optimal policy under the discounted cost criterion which does not use partial repairs. We explicitly explain how to derive this optimal policy