In a Galton-Watson branching process with o spring distribution (p0; p1; : : :) started with k individuals, the distribution of the total progeny is identical to the distribution of the rst passage time to k for a random walk started at 0 which takes steps of size j with probability pj+1 for j 1. The formula for this distribution is a probabilistic expression of the Lagrange inversion formula f...

We present a new cone beam inversion formula based on a general weighting function n. The formula is theoretically exact and is represented by a 2D integral. If the source trajectory C is complete (and satisfies two other very mild assumptions), then the simplest uniform weight gives a convolution-based FBP algorithm. This choice is not always optimal from the practical point of view. The unifo...

Let (M, deg) be a cancellative monoid M equipped with a discrete degree map deg :M →R≥0, and let PM,deg(t) := ∑ u∈M/∼t deg(u) be its generating series, called the growth function of M . We show the inversion formula PM,deg(t) ·NM,deg(t) = 1 where the second factor of the formula is given by NM,deg(t) := 1 + ∑ T∈Tmcm(M,I0)(−1) #J1+···+#Jn−n+1 ∑ ∆∈|T | t , which we call the skew-growth function o...

We prove the Plancherel formula for spherical Schwartz functions on a reductive symmetric space. Our starting point is an inversion formula for spherical smooth compactly supported functions. The latter formula was earlier obtained from the most continuous part of the Plancherel formula by means of a residue calculus. In the course of the present paper we also obtain new proofs of the uniform t...

Moebius syndrome is a rare, nonprogressive neurological disorder (prevalence is estimated to be 0.002% of births) characterized by unilateral or bilateral facial paralysis and defective extraocular eye movements secondary to congenital paresis of the facial (VII) and abducens (VI) cranial nerves. These classic features of the syndrome are often accompanied by hypoglossal (XII), trigeminal (V), ...

Moebius syndrome consists of congenital complete or partial facial nerve palsy with or without paralysis of other cranial nerves (most commonly an abducens paralysis) and often associated with other malformations of the limbs and orofacial structures. The first description of congenital facial diplegia was given by von Graaefe in 18801 and this was soon followed by other reports. Moebius2 3 dre...

We provide yet another proof of the classical Lagrange-Good multivariable inversion formula using the techniques of quantum field theory.

In this paper, we give a weakly stable algorithm to solve a block Toeplitz system of linear equations. If the \look-ahead" steps taken to compute the parameters of the inversion formula for the block Toeplitz matrix are small compared to the order n of the matrix, the algorithm requires O(n 2) oating point operations. The parameters of the inversion formula are interpreted and computed in a rec...

Let a and b be two polynomials having numerical coeecients. We consider the question: when are a and b relatively prime? Since the coeecients of a and b are approximant, the question is the same as: when are two polynomials relatively prime, even after small perturbations of the coeecients? In this paper we provide a numeric parameter for determining that two polynomials are prime, even under s...