Apportionment and Contribution of Workers\u27 Compensation Benefits

The apportionment of benefits between a claimant and a carrier and contribution of benefits between multiple carriers has been a confusing area of law which has generated conflicting appellate court opinions. This article will explore the differences between Florida Statutes sec. 44012(5)(a) in sec. 440.42(3). After discussing the differences, this article will then focus on the multiple applications of sec. 440.42(3), the section dealing with the contribution of responsibility between carriers

Continuum AB percolation and AB random geometric graphs

Consider a bipartite random geometric graph on the union of two independent homogeneous Poisson point processes in $d$-space, with distance parameter $r$ and intensities $\lambda,\mu$. We show for $d \geq 2$ that if $\lambda$ is supercritical for the one-type random geometric graph with distance parameter $2r$, there exists $\mu$ such that $(\lambda,\mu)$ is supercritical (this was previously known for $d=2$). For $d=2$ we also consider the restriction of this graph to points in the unit square. Taking $\mu = \tau \lambda$ for fixed $\tau$, we give a strong law of large numbers as $\lambda \to \infty$, for the connectivity threshold of this graph

Connectivity of soft random geometric graphs

Consider a graph on $n$ uniform random points in the unit square, each pair being connected by an edge with probability $p$ if the inter-point distance is at most $r$. We show that as $n\to\infty$ the probability of full connectivity is governed by that of having no isolated vertices, itself governed by a Poisson approximation for the number of isolated vertices, uniformly over all choices of $p,r$. We determine the asymptotic probability of connectivity for all $(p_n,r_n)$ subject to $r_n=O(n^{-\varepsilon})$, some $\varepsilon >0$. We generalize the first result to higher dimensions and to a larger class of connection probability functions.Comment: Published at http://dx.doi.org/10.1214/15-AAP1110 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Inhomogeneous random graphs, isolated vertices, and Poisson approximation

Consider a graph on randomly scattered points in an arbitrary space, with two points $x,y$ connected with probability $\phi(x,y)$. Suppose the number of points is large but the mean number of isolated points is $O(1)$. We give general criteria for the latter to be approximately Poisson distributed. More generally, we consider the number of vertices of fixed degree, the number of components of fixed order, and the number of edges. We use a general result on Poisson approximation by Stein's method for a set of points selected from a Poisson point process. This method also gives a good Poisson approximation for U-statistics of a Poisson process.Comment: 31 page

A study of inverse trigonometric integrals associated with three-variable Mahler measures, and some related identities

We prove several identities relating three-variable Mahler measures to integrals of inverse trigonometric functions. After deriving closed forms for most of these integrals, we obtain ten explicit formulas for three-variable Mahler measures. Several of these results generalize formulas due to Condon and Lal\'in. As a corollary, we also obtain three $q$-series expansions for the dilogarithm