Metaphysics and Law

The dichotomy between questions of fact and questions of law serves as a starting point for the following discussion of the nature of legal reasoning. In the course of the dialogue the author notes similarities and dissimilarities between legal reasoning and philosophical and mathematical reasoning. In the end we are left with a clearer insight into the distinctive features of the adjudicative process

Stochastic Ising model with flipping sets of spins and fast decreasing temperature

This paper deals with the stochastic Ising model with a temperature shrinking to zero as time goes to infinity. A generalization of the Glauber dynamics is considered, on the basis of the existence of simultaneous flips of some spins. Such dynamics act on a wide class of graphs which are periodic and embedded in $\mathbb{R}^d$. The interactions between couples of spins are assumed to be quenched i.i.d. random variables following a Bernoulli distribution with support $\{-1,+1\}$. The specific problem here analyzed concerns the assessment of how often (finitely or infinitely many times, almost surely) a given spin flips. Adopting the classification proposed in \cite{GNS}, we present conditions in order to have models of type $\mathcal{F}$ (any spin flips finitely many times), $\mathcal{I}$ (any spin flips infinitely many times) and $\mathcal{M}$ (a mixed case). Several examples are provided in all dimensions and for different cases of graphs. The most part of the obtained results holds true for the case of zero-temperature and some of them for the cubic lattice $\mathbb{L}_d=(\mathbb{Z}^d, \mathbb{E}_d)$ as well.Comment: 31 pages, 6 figures, Accepted for publication in "Annales de l'Institut Henri Poincar\'e, Probabilit\'es et Statistiques

Metaphysics and Law

The dichotomy between questions of fact and questions of law serves as a starting point for the following discussion of the nature of legal reasoning. In the course of the dialogue the author notes similarities and dissimilarities between legal reasoning and philosophical and mathematical reasoning. In the end we are left with a clearer insight into the distinctive features of the adjudicative process

Magnifying Lens Abstraction for Stochastic Games with Discounted and Long-run Average Objectives

Turn-based stochastic games and its important subclass Markov decision processes (MDPs) provide models for systems with both probabilistic and nondeterministic behaviors. We consider turn-based stochastic games with two classical quantitative objectives: discounted-sum and long-run average objectives. The game models and the quantitative objectives are widely used in probabilistic verification, planning, optimal inventory control, network protocol and performance analysis. Games and MDPs that model realistic systems often have very large state spaces, and probabilistic abstraction techniques are necessary to handle the state-space explosion. The commonly used full-abstraction techniques do not yield space-savings for systems that have many states with similar value, but does not necessarily have similar transition structure. A semi-abstraction technique, namely Magnifying-lens abstractions (MLA), that clusters states based on value only, disregarding differences in their transition relation was proposed for qualitative objectives (reachability and safety objectives). In this paper we extend the MLA technique to solve stochastic games with discounted-sum and long-run average objectives. We present the MLA technique based abstraction-refinement algorithm for stochastic games and MDPs with discounted-sum objectives. For long-run average objectives, our solution works for all MDPs and a sub-class of stochastic games where every state has the same value

Growth in expenditure on high cost drugs in Australia

The paper provides an overview of the expenditure of high cost drugs in Australia and examines the average annual growth of these programs. The outlook for expenditure on high cost medicines and possible policy responses is also considered. Executive summary • Despite an overall slowing of growth in expenditure on the Pharmaceutical Benefits Scheme (PBS), the section 100 (s 100) program is showing rapid rates of growth. • The s 100 program provides pharmaceuticals to those living in isolated areas and for the treatment of  complex conditions that require specialist monitoring. • A number of programs make up the s 100 program.  Those with high growth rates include : • Expenditure on the Efficient Funding of Chemotherapy  is the fastest growing s 100 program with an average annual growth rate of 62.61 % from 2009–10 to 2013–14 . • The Highly Specialised Drugs Program grew at a rate of 6.38 % for the same period. • Although not part of the PBS, the Life Saving Drugs Programme provides access to a limited number of expensive drugs for rare diseases. This programme  grew at a rate of 12.68 % from 2009–10 to 2013–14 . • The s 100 and LSD P programs provide access to high cost drugs to treat a range of diseases including cancers, HIV /AIDS, Alzheimer’s diseases and a number of rare and life threatening conditions. Patients are protected  from the true cost of these drugs. • Given predictions about  the  increasing rates  of diseases such as cancer and Alzheimer’s disease, it is likely  that expenditure on these medicines is likely to continue to rise as more people require treatment.  As a general rule, new drugs are usually more expensive than existing treatments. • One of the objectives of the National Medicines Policy is timely access to medicines that Australians need,  and at cost the community and individuals can afford. Examination of  the expenditure on high cost drugs is warranted to ensure that this policy objective is met