We study nearest-neighbors walks on the two-dimensional square lattice, that is, models of walks on Z defined by a fixed step set that is a subset of the non-zero vectors with coordinates 0, 1 or −1. We concern ourselves with the enumeration of such walks starting at the origin and constrained to remain in the quarter plane N, counted by their length and by the position of their ending point. B...

Let C[[z]] be the ring of power series over an effective ring C. In Brent and Kung (1978), it was first shown that differential equations over C[[z]] may be solved in an asymptotically efficient way using Newton’s method. More precisely, if M(n) denotes the complexity for multiplying two polynomials of degree < n over C, then the first n coefficients of the solution can be computed in time O(M(...

The term cardiac amyloidosis refers to the involvement of the heart as a result of amyloid deposition in heart tissue either in the context of a systemic disease or as a localized form. Several proamyloid proteins can produce amyloid deposits in the heart. Each of these amyloidoses has characteristic clinical (cardiac and extracardiac) features, its own course, and a specific diagnosis and trea...