Anomalous diffusion with absorption: Exact time-dependent solutions

Recently, analytical solutions of a nonlinear Fokker-Planck equation describing anomalous diffusion with an external linear force were found using a non extensive thermostatistical Ansatz. We have extended these solutions to the case when an homogeneous absorption process is also present. Some peculiar aspects of the interrelation between the deterministic force, the nonlinear diffusion and the absorption process are discussed.Comment: RevTex, 16 pgs, 4 figures. Accepted in Physical Review

Normal Cones and Thompson Metric

The aim of this paper is to study the basic properties of the Thompson metric $d_T$ in the general case of a real linear space $X$ ordered by a cone $K$. We show that $d_T$ has monotonicity properties which make it compatible with the linear structure. We also prove several convexity properties of $d_T$ and some results concerning the topology of $d_T$, including a brief study of the $d_T$-convergence of monotone sequences. It is shown most of the results are true without any assumption of an Archimedean-type property for $K$. One considers various completeness properties and one studies the relations between them. Since $d_T$ is defined in the context of a generic ordered linear space, with no need of an underlying topological structure, one expects to express its completeness in terms of properties of the ordering, with respect to the linear structure. This is done in this paper and, to the best of our knowledge, this has not been done yet. The Thompson metric $d_T$ and order-unit (semi)norms $|\cdot|_u$ are strongly related and share important properties, as both are defined in terms of the ordered linear structure. Although $d_T$ and $|\cdot|_u$ are only topological (and not metrical) equivalent on $K_u$, we prove that the completeness is a common feature. One proves the completeness of the Thompson metric on a sequentially complete normal cone in a locally convex space. At the end of the paper, it is shown that, in the case of a Banach space, the normality of the cone is also necessary for the completeness of the Thompson metric.Comment: 36 page

Myeloid SLC2a1-deficient murine model revealed macrophage activation and metabolic phenotype are fueled by GLUT1

Macrophages (MFs) are heterogeneous and metabolically flexible, with metabolism strongly affecting immune activation. A classic response to proinflammatory activation is increased flux through glycolysis with a downregulation of oxidative metabolism, whereas alternative activation is primarily oxidative, which begs the question of whether targeting glucose metabolism is a viable approach to control MF activation. We created a murine model of myeloid-specific glucose transporter GLUT1 (Slc2a1) deletion. Bone marrow-derived MFs (BMDM) from Slc2a1 M -/ - mice failed to uptake glucose and demonstrated reduced glycolysis and pentose phosphate pathway activity. Activated BMDMs displayed elevated metabolism of oleate and glutamine, yet maximal respiratory capacity was blunted in MF lacking GLUT1, demonstrating an incomplete metabolic reprogramming. Slc2a1 M -/ - BMDMs displayed a mixed inflammatory phenotype with reductions of the classically activated pro- and anti-inflammatory markers, yet less oxidative stress. Slc2a1 M -/ - BMDMs had reduced proinflammatory metabolites, whereas metabolites indicative of alternative activation-such as ornithine and polyamines-were greatly elevated in the absence of GLUT1. Adipose tissue MFs of lean Slc2a1 M -/ - mice had increased alternative M2-like activation marker mannose receptor CD206, yet lack of GLUT1 was not a critical mediator in the development of obesity-associated metabolic dysregulation. However, Ldlr-/ - mice lacking myeloid GLUT1 developed unstable atherosclerotic lesions. Defective phagocytic capacity in Slc2a1 M -/ - BMDMs may have contributed to unstable atheroma formation. Together, our findings suggest that although lack of GLUT1 blunted glycolysis and the pentose phosphate pathway, MF were metabolically flexible enough that inflammatory cytokine release was not dramatically regulated, yet phagocytic defects hindered MF function in chronic diseases

A tale of two conformally invariant metrics

AbstractThe Harnack metric is a conformally invariant metric defined in quite general domains that coincides with the hyperbolic metric in the disk. We prove that the Harnack distance is never greater than the hyperbolic distance and if the two distances agree for one pair of distinct points, then either the domain is simply connected or it is conformally equivalent to the punctured disk