If f is a positive definite form, Reznick’s Positivstellensatz states that there exists [Formula: see text] such sum of squares polynomials. Assuming can be written as forms text], where each l depends on subset the initial variables, and assuming these subsets satisfy so-called running intersection property, we provide sparse version Positivstellensatz. Namely, σ polynomials, H uniform polynom...

O. Mandelstam's poem Like chiaroscuro Martyr Rembrandt combines ekphrasis, testament of the poet, and declaration social position: this combination has posed difficulties for interpreters. A number obscure images, such as imprisonment, wealth, or a tribe associates, are convincingly interpreted Mandelstams deduction his own biography from circumstances Rembrandts life, but explain neither expre...

Optimal mass transportation can be traced back to Gaspard Monge’s famous paper of 1781: ‘Mémoire sur la théorie des déblais et des remblais’. The problem there is to minimize the cost of transporting a given distribution of mass from one location to another. Since then, it has become a classical subject in probability theory, economics and optimization. At the end of the 80’s, the seminal work ...

*Correspondence: Rachel Honnert, Centre National de Recherches Météorologiques, Groupe d’Etudes de l’Atmophère Météorologique, Météo France/CNRS, GMAP 42, avenue Gaspard Coriolis, 31100 Toulouse, France e-mail: [email protected] In numerical weather prediction (NWP) models, at mesoscale, the sub-grid convective boundary-layer turbulence is dominated by the uni-dimensional (1D) vertical th...

The mammalian cerebral neocortex is a complex six-layered structure containing multiple types of neurons. Pyramidal neurons of the neocortex are formed during development in an inside-out manner, by which deep layer (DL) neurons are generated first, and upper layer (UL) neurons are generated last. Neurons within the six-layered neocortex express unique markers for their position, showing whethe...

Wallenberg syndrome was initially described by Gaspard Vieusseaux of Geneva in 1810. It was characterized by vertigo, unilateral facial numbness, loss of pain and temperature appreciation in the opposite limbs, dysphagia and hoarseness, minor tongue involvement, hiccups and a dropped eyelid [1]. Wallenberg described in his case reports from 1895-1922 how the patients could not swallow solids at...