(ii) For any sequence of sets {Bn} with Bn ∈ An, whenever Pn(Bn) converges to 0, then EPn (| Xn | 1Bn) converges to 0. The following theorem illustrates the usefulness of uniform integrability; uniform integrability in conjunction with convergence in distribution implies convergence of moments. Theorem 1.1 Suppose that Xn ∈ Lr(P ) with 0 < r < ∞ and Xn →p X. Then, the following are equivalent. ...

Aggregating areas into larger regions is a common problem in spatial planning, geographic information science, and cartography. The aim can be to group administrative areal units into electoral districts or sales territories, in which case the problem is known as districting. In other cases, area aggregation is seen as a generalization or visualization task, which aims to reveal spatial pattern...

Ronald Reagan and Justice Brennan have both suggested that computers can remove the controversy and politics from redistricting. ' In fact proponents of automated redistricting claim that the "optimal" districting plan can be determined, given any set of specified values. The Supreme Court has expressed a similar sentiment by addressing such mechanical principles as contiguity and compactness i...

Hebbian Learning should not be reduced to contiguity, as it detects contingency and causality. Hebbian Learning accounts of mirror neurons make predictions that differ from associative learning: Through Hebbian Learning, mirror neurons become dynamic networks that calculate predictions and prediction errors and relate to ideomotor theories. The social force of imitation is important for mirror ...

Geographical considerations such as contiguity and compactness are necessary elements of political districting in practice. Yet an analysis the problem without constraints yields mathematical insights that can inform real-world model construction. In particular, it clarifies sharp contrast between proportionality competitiveness how might be overcome a properly formulated objective function. It...

Abstract While the cost and time for assembling a genome has drastically decreased, it still remains challenge to assemble highly contiguous genome. These challenges are rapidly being overcome by integration of long-read sequencing technologies. Here, we use improve contiguity threespine stickleback fish (Gasterosteus aculeatus) genome, prominent genetic model species. Using Pacific Biosciences...

Milk of calcium in the kidney is usually found in association with hydronephrosis or caliceal diverticula. A case of milk of calcium in a renal cyst is presented. Contiguity with an adjacent rib can make it difficult to detect the dependent layered milk of calcium.