We study the following interacting particle system. There are ρn particles, ρ<1, moving clockwise (“right”), in discrete time, on n sites arranged a circle. Each site may contain at most one particle. At each move to right-neighbor according rules. If its is occupied by another particle, does not move. has unoccupied (“holes”) as neighbors both sides, it moves right with probability 1. hole and...

We investigate the limit behaviour of the spectral measures of matrices following the Gibbs measure for the Ising model on random graphs, Potts model on random graphs, matrices coupled in a chain model or induced QCD model. For most of these models, we prove that the spectral measures converge almost surely and describe their limit via solutions to an Euler equation for isentropic flow with neg...

We consider the problem of reconstructing an N-dimensional continuous vector x from P constraints which are generated by its linear transformation under the assumption that the number of non-zero elements of x is typically limited to ρN (0 ≤ ρ ≤ 1). Problems of this type can be solved by minimizing a cost function with respect to the L p-norm ||x|| p = lim ǫ→+0 N i=1 |x i | p+ǫ , subject to the...

We consider the problem of reconstructing an N-dimensional continuous vector x from P constraints which are generated by its linear transformation under the assumption that the number of non-zero elements of x is typically limited to ρN (0 ≤ ρ ≤ 1). Problems of this type can be solved by minimizing a cost function with respect to the L p-norm ||x|| p = lim ǫ→+0 N i=1 |x i | p+ǫ , subject to the...

Transmembrane α-Klotho (TM-Klotho), mainly expressed in renal distal tubules, is a co-factor for FGF23 receptor. Circulating soluble α-Klotho (s-Klotho) results from shedding of the ecto-domain of TM-Klotho and has specific effects on urinary Phosphate (P) and Calcium (Ca) transport. The possibility exists that a decrease in TM-Klotho, described in experimental chronic kidney disease (CKD), may...