Prolific inventors and their mobility: scale, impact and significance. What the literature tells us and some hypotheses

In this paper we survey the literature dealing with the category of prolific inventor. We set out some elements regarding nature, scale, significance and impact of the mobility of this population of prolific inventors. In particular the paper suggests an analysis that measures the effects on mobility on individual inventive productivity and the value of invention. We call “prolificness” the capacity to accumulate knowledge and experience through mobility (that is to say through their capital of contacts and interactions).Prolific inventor ; patent ; mobility ; performance ; corporation ; research and development

Maximal theorems and square functions for analytic operators on Lp-spaces

Let T : Lp --> Lp be a contraction, with p strictly between 1 and infinity, and assume that T is analytic, that is, there exists a constant K such that n\norm{T^n-T^{n-1}} < K for any positive integer n. Under the assumption that T is positive (or contractively regular), we establish the boundedness of various Littlewood-Paley square functions associated with T. As a consequence we show maximal inequalities of the form \norm{\sup_{n\geq 0}\, (n+1)^m\bigl |T^n(T-I)^m(x) \bigr |}_p\,\lesssim\, \norm{x}_p, for any nonnegative integer m. We prove similar results in the context of noncommutative Lp-spaces. We also give analogs of these maximal inequalities for bounded analytic semigroups, as well as applications to R-boundedness properties

SLE on doubly-connected domains and the winding of loop-erased random walks

Two-dimensional loop-erased random walks (LERWs) are random planar curves whose scaling limit is known to be a Schramm-Loewner evolution SLE_k with parameter k = 2. In this note, some properties of an SLE_k trace on doubly-connected domains are studied and a connection to passive scalar diffusion in a Burgers flow is emphasised. In particular, the endpoint probability distribution and winding probabilities for SLE_2 on a cylinder, starting from one boundary component and stopped when hitting the other, are found. A relation of the result to conditioned one-dimensional Brownian motion is pointed out. Moreover, this result permits to study the statistics of the winding number for SLE_2 with fixed endpoints. A solution for the endpoint distribution of SLE_4 on the cylinder is obtained and a relation to reflected Brownian motion pointed out.Comment: 22 pages, 4 figure

Strong q-variation inequalities for analytic semigroups

Let T : Lp --> Lp be a positive contraction, with p strictly between 1 and infinity. Assume that T is analytic, that is, there exists a constant K such that \norm{T^n-T^{n-1}} < K/n for any positive integer n. Let q strictly betweeen 2 and infinity and let v^q be the space of all complex sequences with a finite strong q-variation. We show that for any x in Lp, the sequence ([T^n(x)](\lambda))_{n\geq 0} belongs to v^q for almost every \lambda, with an estimate \norm{(T^n(x))_{n\geq 0}}_{Lp(v^q)}\leq C\norm{x}_p. If we remove the analyticity assumption, we obtain a similar estimate for the ergodic averages of T instead of the powers of T. We also obtain similar results for strongly continuous semigroups of positive contractions on Lp-spaces