All maximal-pairs in step-leap representation of melodic sequence

This paper proposes an efficient pattern extraction algorithm that can be applied on melodic sequences that are represented as strings of abstract intervallic symbols; the melodic representation introduces special “binary don’t care” symbols for intervals that may belong to two partially overlapping intervallic categories. As a special case the well established “step–leap” representation is examined. In the step–leap representation, each melodic diatonic interval is classified as a step (±s), a leap (±l) or a unison (u). Binary don’t care symbols are used to represent the possible overlapping between the various abstract categories e.g. *=s, *=l and #=-s, #=-l. We propose an O(n+d(n-d)+z)-time algorithm for computing all maximal-pairs in a given sequence x=x[1..n], where x contains d occurrences of binary don’t cares and z is the number of reported maximal-pairs.

Contingent Edis: a new contractual framework for minimizing the risk of incentive failures

Granting economic development incentives (or “EDIs”) has become commonplace throughout the United States, but the efficiency of these mechanisms is generally unwarranted. Both the politicians granting, and the companies seeking, EDIs have incentives to overestimate the EDIs benefits. For politicians, ribbon–cutting ceremonies can be the highly desirable opportunity to please political allies and financiers, and the same time that they demonstrate to the population that they are successful in promoting economic growth – even when the population would be better off otherwise. In turn, businesses are naturally prone to seek governmental aid. This explains in part why EDIs often “fail” (i.e. don’t pay–off). To increase transparency and mitigate the risk of EDI failure, local and state governments across the country have created a number of accountability mechanisms. The general trait of these accountability mechanisms is that they apply controls to some of the sub–risks that underlie the risk of EDI failure. These sub–risks include the companies receiving EDIs not generating the expected number of jobs, not investing enough in their local facilities, not attracting the expected additional businesses investments to the jurisdiction, etc. The problem with such schemes is that they tackle the problem of EDI failure very loosely. They are too narrow and leave multiplier effects uncontrolled. I propose novel contractual framework for implementing accountability mechanisms. My suggestion is to establish controls on the risk of EDI failure itself, leaving its underlying sub–risks uncontrolled. I call this mechanism “Contingent EDIs”, because the EDIs are made contingent on the government achieving a preset target that benchmarks the risk of EDI failure. If the target is met, the EDIs will ex post kick in; if not, then the EDIs never kick in.