Median inverse problem and approximating the number of kk-median inverses of a permutation

We introduce the "Median Inverse Problem" for metric spaces. In particular, having a permutation $\pi$ in the symmetric group $S_n$ (endowed with the breakpoint distance), we study the set of all $k$-subsets $\{x_1,...,x_k\}\subset S_n$ for which $\pi$ is a breakpoint median. The set of all $k$-tuples $(x_1,...,x_k)$ with this property is called the $k$-median inverse of $\pi$. Finding an upper bound for the cardinality of this set, we provide an asymptotic upper bound for the probability that $\pi$ is a breakpoint median of $k$ permutations $\xi_1^{(n)},...,\xi_k^{(n)}$ chosen uniformly and independently at random from $S_n$

Rewriting the Canadian Charter of Rights and Freedoms: Four Suggestions Designed to Promote a Fairer Trial and Evidentiary Process

The Canadian Charter of Rights and Freedoms has secured a vital place at the core of Canadian criminal justice, and its substantive and remedial provisions have helped to secure a much fairer trial and evidentiary process for criminal defendants than was available in 1982. Still, the Charter is hardly a perfect document. The wording of many of the clauses was the product of compromise, and difficulties in interpretation and application have arisen over the years. This paper attempts to consider what a “new” Charter would look like if it were actually possible to re-draft certain clauses in a different manner. Focusing upon the Charter provisions directly affecting the law of evidence and the trial process, four significant changes are recommended. The Charter’s evidentiary clause — section 24(2) — is especially targeted, with two alterations suggested. First, the section should be made available to any accused challenging violations against “third parties” where evidence secured from those parties is admitted in a criminal trial. Second, the “fair trial” aspect of the exclusionary analysis is questioned as being counter-productive and rationally inconsistent. In addition, the paper recommends a change to section 11(f) — the right to a jury trial — contending that it should be extended to include the right not to choose a trial by jury. Finally, the paper suggests enacting a new Charter right — the right of an accused person not to be confronted with unreliable evidence

The where and wherefore of evolutionary breakpoints

The 'action' in genome-level evolution lies not in the large gene-containing segments that are conserved among related species, but in the breakpoint regions between these segments. Two recent papers in BMC Genomics detail the pattern of repetitive elements associated with breakpoints and the epigenetic conditions under which breakage occurs