Abstract. We introduce an algorithm based on semidefinite programming that yields increasing (resp., decreasing) sequences of lower (resp., upper) bounds on polynomial stationary averages of di↵usions with polynomial drift vector and di↵usion coe cients. The bounds are obtained by optimizing an objective, determined by the stationary average of interest, over the set of real vectors defined by ...

Di usion magnetic resonance imaging (dMRI) is the reference in vivo modality to study the connectivity of the brain white matter. Images obtained through dMRI are indeed related to the probability density function (pdf) of displacement of water molecules subject to restricted di usion in the brain white matter. The knowledge of this di usion pdf is therefore of primary importance. Several metho...

The paper deals with a special problem concerning the transport of electrically charged species via di usion, drift, and reaction mechanisms. We prove for a variety of models that without knowing any a priori estimate for the chemical potentials one can estimate the free energy from above by the corresponding dissipation rate. The inequality presented here can be interpreted as a nonlinear anal...

Existing state-of-the-art schemes for dynamic repartitioning of adaptive meshes can be classi ed as either di usion-based schemes or scratch-remap schemes. We present a new scratch-remap scheme called Locally-Matched Multilevel Scratch-Remap (or simply LMSR). The LMSR scheme tries to compute a partitioning that has a high overlap with the existing partitioning. We show that LMSR decreases the a...

We explore the determinants of research specialization and examine the e ects of technology di usion and trade on the incentives for innovation. To some extent, di usion substitutes for trade. If trade costs are low relative to di erences in comparative advantage in doing research, rapid di usion implies specialization in research activity. Country size has an ambiguous e ect on specialization ...

This study aims to explain what drives innovation di€usion in management accounting during its various phases. Based on Abrahamson [Abrahamson, E. (1991). Managerial fads and fashions: the di€usion and rejection of innovations. Academy of Management Review, 16, 586±612], four perspectives with potential to explain the di€usion of accounting innovations are identi®ed: the ecient-choice, forced ...

Linear di¬usion is an established model for spatial spread in biological systems, including movement of cell populations. However, for interacting, closely packed cell populations, simple di¬usion is inappropriate, because di¬erent cell populations will not move through one another: rather, a cell will stop moving when it encounters another cell. In this paper, I introduce a nonlinear di¬usion ...

We derive time-asymptotic decay rates in L for large disturbances to some important classes of solutions of the Cauchy problem for a number of uniformly parabolic equations, provided only that the disturbances belong to appropriate L spaces at initial time. Examples considered include the scalar nonlinear advection–di usion equation ut + f(u)x =(b(u)ux)x and the parabolic system ut + (u’(|u|))x...

This special issue is an outgrowth of a minisyposium titled “Mathematics of Social Systems” held at the 9th AIMS Conference on Dynamical Systems, Di↵erential Equations and Applications, held in Orlando, FL in July 2012. Presenters from that session were invited to submit papers that were reviewed using the usual procedures of the DCDS journals, along with additional authors from the field. Math...

We compare two load balancing techniques for Cayley graphs based on information and load exchange between neighboring vertices. In the rst scheme, called natural di usion, each vertex gives (or receives) a xed part of the load di erence to (from) its direct neighbors. In the second scheme, called Cayley di usion, each vertex successively gives (or receives) a part of the load di erence to (or f...