Innovation Heuristics: Experiments on Sequential Creativity in Intellectual Property

All creativity and innovation build on existing ideas. Authors and inventors copy, adapt, improve, interpret, and refine the ideas that have come before them. The central task of intellectual property (IP) law is regulating this sequential innovation to ensure that initial creators and subsequent creators receive the appropriate sets of incentives. Although many scholars have applied the tools of economic analysis to consider whether IP law is successful in encouraging cumulative innovation, that work has rested on a set of untested assumptions about creators’ behavior. This Article reports four novel creativity experiments that begin to test those assumptions. In particular, we study how creators decide whether to copy, or “borrow,” from existing ideas or to innovate around them

Lie theory and coverings of finite groups

We introduce the notion of an `inverse property' (IP) quandle C which we propose as the right notion of `Lie algebra' in the category of sets. To any IP quandle we construct an associated group G_C. For a class of IP quandles which we call `locally skew' and when G_C is finite we show that the noncommutative de Rham cohomology H^1(G_C) is trivial aside from a single generator \theta that has no classical analogue. If we start with a group G then any subset C\subseteq G\setminus {e} which is ad-stable and inversion-stable naturally has the structure of an IP quandle. If C also generates G then we show that G_C \twoheadrightarrow G with central kernel, in analogy with the similar result for the simply-connected covering group of a Lie group. We prove that G_C\twoheadrightarrow G is an isomorphism for all finite crystallographic reflection groups W with C the set of reflections, and that C is locally skew precisely in the simply laced case. This implies that H^1(W)=k when W is simply laced, proving in particular a previous conjecture for S_n. We obtain similar results for the dihedral groups D_{6m}. We also consider C=Z P^1\cup Z P^1 as a locally skew IP-quandle `Lie algebra' of SL_2(Z) and show that G_C\cong B_3, the braid group on 3 strands. The map B_3\twoheadrightarrow SL_2(Z) which arises naturally as a covering map in our theory, coincides with the restriction of the universal covering map \widetilde {SL_2(R)}\to SL_2(R) to the inverse image of SL_2(Z).Comment: 14 pages, one pdf graphic (minor improvements

Interannual variability in the summertime hydrological cycle over European regions

A variety of observations-based hydrological variables from different data sets are used to investigate interannual variability and changes in the summertime hydrological cycle over four European regions—Iberian Peninsula (IP), British Isles (BI), Central Europe (CE), and European Russia (ER). An analysis performed on seasonal means (June, July, and August) suggests that soil moisture variability is impacted almost equally by precipitation and air temperature in BI and ER regions. However, stronger links between soil moisture and precipitation are revealed for CE region and between soil moisture and air temperature for IP region. In all except IP regions summertime interannual variability of column-integrated water vapor is strongly linked to air temperature consistent with the dominating influence of the Clausius-Clapeyron equation. In BI, CE, and ER interannual variability of regional precipitation is driven by variations in atmospheric moisture transport into these regions. In IP the link between precipitation and moisture transport is relatively weak. Based on monthly data, analysis of the lag-lead correlations revealed specific regional relationships between different hydrological variables. In particular, it is shown that in some regions (and months) interannual variability of soil moisture is linked more strongly to precipitation and air temperature anomalies in the previous month, rather than in the coinciding month. An analysis of the vertical structure of regional atmospheric moisture transport has revealed that the more continental the climate of the region is, the larger deviation from the mean (i.e., climatological) profile might be observed during anomalously dry/wet summers

Solvability of Rado systems in D-sets

Rado's Theorem characterizes the systems of homogenous linear equations having the property that for any finite partition of the positive integers one cell contains a solution to these equations. Furstenberg and Weiss proved that solutions to those systems can in fact be found in every central set. (Since one cell of any finite partition is central, this generalizes Rado's Theorem.) We show that the same holds true for the larger class of $D$-sets. Moreover we will see that the conclusion of Furstenberg's Central Sets Theorem is true for all sets in this class

Central sets and substitutive dynamical systems

In this paper we establish a new connection between central sets and the strong coincidence conjecture for fixed points of irreducible primitive substitutions of Pisot type. Central sets, first introduced by Furstenberg using notions from topological dynamics, constitute a special class of subsets of \nats possessing strong combinatorial properties: Each central set contains arbitrarily long arithmetic progressions, and solutions to all partition regular systems of homogeneous linear equations. We give an equivalent reformulation of the strong coincidence condition in terms of central sets and minimal idempotent ultrafilters in the Stone-\v{C}ech compactification \beta \nats . This provides a new arithmetical approach to an outstanding conjecture in tiling theory, the Pisot substitution conjecture. The results in this paper rely on interactions between different areas of mathematics, some of which had not previously been directly linked: They include the general theory of combinatorics on words, abstract numeration systems, tilings, topological dynamics and the algebraic/topological properties of Stone-\v{C}ech compactification of \nats.Comment: arXiv admin note: substantial text overlap with arXiv:1110.4225, arXiv:1301.511

New polynomial and multidimensional extensions of classical partition results

In the 1970s Deuber introduced the notion of $(m,p,c)$-sets in $\mathbb{N}$ and showed that these sets are partition regular and contain all linear partition regular configurations in $\mathbb{N}$. In this paper we obtain enhancements and extensions of classical results on $(m,p,c)$-sets in two directions. First, we show, with the help of ultrafilter techniques, that Deuber's results extend to polynomial configurations in abelian groups. In particular, we obtain new partition regular polynomial configurations in $\mathbb{Z}^d$. Second, we give two proofs of a generalization of Deuber's results to general commutative semigroups. We also obtain a polynomial version of the central sets theorem of Furstenberg, extend the theory of $(m,p,c)$-systems of Deuber, Hindman and Lefmann and generalize a classical theorem of Rado regarding partition regularity of linear systems of equations over $\mathbb{N}$ to commutative semigroups.Comment: Some typos, including a terminology confusion involving the words `clique' and `shape', were fixe