Dispersion relations and subtractions in hard exclusive processes

We study analytical properties of the hard exclusive processes amplitudes. We found that QCD factorization for deeply virtual Compton scattering and hard exclusive vector meson production results in the subtracted dispersion relation with the subtraction constant determined by the Polyakov-Weiss $D$-term. The relation of this constant to the fixed pole contribution found by Brodsky, Close and Gunion and defined by parton distributions is proved, while its manifestation is spoiled by the small $x$ divergence. The continuation to the real photons limit is considered and the numerical correspondence between lattice simulations of $D$-term and low energy Thomson amplitude is found.Comment: 4 pages, journal versio

Intertwining and commutation relations for birth-death processes

Given a birth-death process on $\mathbb {N}$ with semigroup $(P_t)_{t\geq0}$ and a discrete gradient ${\partial}_u$ depending on a positive weight $u$, we establish intertwining relations of the form ${\partial}_uP_t=Q_t\,{\partial}_u$, where $(Q_t)_{t\geq0}$ is the Feynman-Kac semigroup with potential $V_u$ of another birth-death process. We provide applications when $V_u$ is nonnegative and uniformly bounded from below, including Lipschitz contraction and Wasserstein curvature, various functional inequalities, and stochastic orderings. Our analysis is naturally connected to the previous works of Caputo-Dai Pra-Posta and of Chen on birth-death processes. The proofs are remarkably simple and rely on interpolation, commutation, and convexity.Comment: Published in at http://dx.doi.org/10.3150/12-BEJ433 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Relations between Communities of Practice and Innovation Processes

The paper makes an empirical and theoretical contribution to the innovation literature by both examining case study evidence from a number of technological innovation projects, and reflecting on the relationship between innovation processes and communities of practice. It is concluded that this relationship is not unidirectional. Not only did the communities of practice influence the innovation processes, for example through shaping important knowledge sharing processes, but the innovations also impinged on organizational communities of practice in important ways. The paper also proposes ways in which the analytical utility of the community of practice concept can be improved, for example by taking greater account of potential negative effects that communities of practice can have for innovation processes.innovation, community of practice

Network geography: relations, interactions, scaling and spatial processes in GIS

This chapter argues that the representational basis of GIS largely avoidseven the most rudimentary distortions of Euclidean space as reflected, forexample, in the notion of the network. Processes acting on networks whichinvolve both short and longer term dynamics are often absent from GIscience. However a sea change is taking place in the way we view thegeography of natural and man-made systems. This is emphasising theirdynamics and the way they evolve from the bottom up, with networks anessential constituent of this decentralized paradigm. Here we will sketchthese developments, showing how ideas about graphs in terms of the waythey evolve as connected, self-organised structures reflected in theirscaling, are generating new and important views of geographical space.We argue that GI science must respond to such developments and needs tofind new forms of representation which enable both theory andapplications through software to be extended to embrace this new scienceof networks

Description of Complex Systems in terms of Self-Organization Processes of Prime Integer Relations

In the paper we present a description of complex systems in terms of self-organization processes of prime integer relations. A prime integer relation is an indivisible element made up of integers as the basic constituents following a single organizing principle. The prime integer relations control correlation structures of complex systems and may describe complex systems in a strong scale covariant form. It is possible to geometrize the prime integer relations as two-dimensional patterns and isomorphically express the self-organization processes through transformations of the geometric patterns. As a result, prime integer relations can be measured by corresponding geometric patterns specifying the dynamics of complex systems. Determined by arithmetic only, the self-organization processes of prime integer relations can describe complex systems by information not requiring further explanations. This gives the possibility to develop an irreducible theory of complex systems.Comment: 8 pages, 4 figures, index corrected, minor changes mainly of stylistic characte