The hydrodynamic limit of a kinetic Cucker-Smale flocking model is investigated. The starting point is the model considered in [17], which in addition to free-transport of individuals and a standard Cucker-Smale alignment operator, includes Brownian noise and strong local alignment. The latter was derived in [18] as the singular limit of an alignment operator first introduced by Motsch and Tadm...

Given any half-sided modular inclusion of standard subspaces, we show that the entropy function associated with decreasing one-parameter family translated subspaces is convex for given (not necessarily smooth) vector in underlying Hilbert space. In second quantisation, this infers convexity vacuum relative respect to translation parameter tunnel von Neumann algebras. This result allows us study...

A selfadjoint involutive matrix J endows Cn with an indefinite inner product [·, ·] given by [x,y] = 〈Jx,y〉 , x,y ∈ Cn. Characterizations of the J -chaotic order Log(A) J Log(B) are presented for J -selfadjoint matrices A,B with positive eigenvalues, in terms of operator functions involving the α -power mean and the J -relative entropy. An indefinite complete form of the Furuta inequality and s...

We study the asymptotic behaviour of the following linear growthfragmentation equation B Btupt, xq ` B Bx ` xupt, xq ̆ `Bpxqupt, xq “ 4Bp2xqupt, 2xq, and prove that under fairly general assumptions on the division rate Bpxq, its solution converges towards an oscillatory function, explicitely given by the projection of the initial state on the space generated by the countable set of the dominant ...

We show that the derivative of the relative entropy with respect to its parameters is lower and upper bounded. We characterize the conditions under which this derivative can reach zero. We use these results to explain when the minimum relative entropy and the maximum log likelihood approaches can be valid. We show that these approaches naturally activate in the presence of large data sets and t...

PURPOSE: To propose a method for Parametric Statistical Weights (PSW) estimations and analyze its statistical impact in Computer-Aided Diagnosis Imaging Systems based on a Relative Similarity (CADIRS) classification approach. MATERIALS AND METHODS: A Multifactor statistical method was developed and applied for Parametric Statistical Weights calculations in CADIRS. The implemented PSW method was...