Whales leave the beach

The Crane Beach Conjecture

A language L over an alphabet A is said to have a neutral letter if there is a letter e ∈ A such that inserting or deleting e’s from any word inA does not change its membership (or non–membership) in L. The presence of a neutral letter affects the definability of a language in first–order logic. It was conjectured that it renders all numerical predicates apart from the order predicate useless, ...

Catalan Traffic at the Beach

The ubiquitous Catalan numbers Cn = (2n n ) / (n + 1) occur as t (n,−n) in the following table showing the number of ways to reach the point (n,m) on a rectangular grid under certain traffic restrictions, indicated by arrows. m 1↑→ 3↑→ 6↑→ 9↑→ 12↑→ 12↑→ 12↓→ ↘ 2 1↑→ 2↑→ 3↑→ 3↑→ 3↓→ ↘ 12↓→↘ 1 1↑→ 1↑→ 1↓→ ↘ 3↓→↘ 3↓→↘ 12↓→↘ start here 1↑→gate ↘ 1↓→↘ 1↓→↘ 3↓→↘ 6↓→↘ 15↓→↘ −1 ≈ 1 →↘ 1↓→↘ 2↓→↘ 4↓→↘ 9↓...

To leave or not to leave.

Lies, damned lies and Brexit statistics. It's not been a good month for anyone espousing evidence-based policy and politics after the chair of the Commons health committee switched from Leave to Remain, citing misuse of data by the Leave campaign.

The Leave - one - out

Has Family Leave Legislation Increased Leave-Taking?

In 1993, the federal government passed the Family and Medical Leave Act (FMLA), which gives eligible employees twelve weeks of job-protected unpaid leave from work per year to address family issues. Employees are eligible for family leave under the FMLA if they have worked for their employer for at least a year, accumulating at least 1,250 work hours. Employers are covered if they employ at lea...