In this paper, we prove that, in dimension one, the Poincaré inequality is equivalent to a new transport-chi-square inequality linking the square of the quadratic Wasserstein distance with the chi-square pseudo-distance. We also check tensorization of this transport-chi-square inequality. For q ≥ 1, the Wasserstein distance with index q between two probability measures µ and ν on R d is denoted...

Recent investigations point to the presence of paracrystalline lattice disorder in the nerve myelin in the swollen, fixed and to some extent also in the native state. This leads to the distortion of the Q-function of the membrane stack and the Q0-function of the unit cell, which can be experimentally isolated through swelling. Representing the distance statistics between neighbouring membranes ...

This report contains a list of some of the more prominent properties and theorems concerning the Kullback-Leibler (KL) discrimination distance. A brief discussion is also provided indicating the type of problems in which the KL distance has been applied. References are provided for the reader’s convenience. 1 Definition For two continuous density functions f1(x), f2(x) the Kullback-Leibler (KL)...

The Reed-Muller (RM) code encoding n-variate degree-d polynomials over Fq for d < q, with its evaluation on Fq , has relative distance 1− d/q and can be list decoded from a 1−O( √ d/q) fraction of errors. In this work, for d ≪ q, we give a length-efficient puncturing of such codes which (almost) retains the distance and list decodability properties of the Reed-Muller code, but has much better r...