Related papers: Union of n Disks: Remote Centers, Common Origin
We introduce a new formalism for computing expectations of functionals of arbitrary random vectors, by using generalised integration by parts formulae. In doing so we extend recent representation formulae for the score function introduced…
To complete a previous work, the probability density functions for the errors in the center-of-gravity as positioning algorithm are derived with the usual methods of the cumulative distribution functions. These methods introduce substantial…
Anderson's theorem states that if the numerical range W(A) of an n-by-n matrix A is contained in the unit disk and intersects with the unit circle at more than n points, then it coincides with the (closed) unit dissk. An analogue of this…
By using the method in [5], the aim of the present note is to generalize the Riemann integral in probability introduced in [7], to Kurzweil-Henstock integral in probability. Properties of the new integral are proved.
This paper is devoted to rejective sampling. We provide an expansion of joint inclusion probabilities of any order in terms of the inclusion probabilities of order one, extending previous results by H\'ajek (1964) and H\'ajek (1981) and…
We consider MAP estimators for structured prediction with exponential family models. In particular, we concentrate on the case that efficient algorithms for uniform sampling from the output space exist. We show that under this assumption…
In this article we derive some explicit decay estimates for the dual system of a basis of functions polynomially localized in space.
The "expansion by regions" is a method of asymptotic expansion developed by Beneke and Smirnov in 1997. It expands the integrand according to the scaling prescriptions of a set of regions and integrates all expanded terms over the whole…
This paper proposes new formulas for the probabilities of causation difined by Pearl (2000). Tian and Pearl (2000a, 2000b) showed how to bound the quantities of the probabilities of causation from experimental and observational data, under…
In this paper, we derive some formulae involving coefficients of polynomials which occur quite naturally in the study of restricted partitions. Our method involves a recently discovered sieve technique by Li and Wan (Sci. China. Math.…
In 2002 Zhi-Wei Sun [Integers 2(2002)] published a curious identity involving binomial coefficients. In this paper we present a generalization of the identity.
A conformal map from a Riemann surface to the Euclidean four-space is explained in terms of its twistor lift. A local factorization of a differential of a conformal map is obtained. As an application, the factorization of a differential…
As observers of the universe we are physical systems within it. If the universe is very large in space and/or time, the probability becomes significant that the data on which we base predictions is replicated at other locations in…
A famous conjecture of Littlewood (c. 1930) concerns approximating two real numbers by rationals of the same denominator, multiplying the errors. In a lesser-known paper, Wang and Yu (1981) established an asymptotic formula for the number…
Let each of n particles starting at the origin in Z^2 perform simple random walk until reaching a site with no other particles. Lawler, Bramson, and Griffeath proved that the resulting random set A(n) of n occupied sites is (with high…
Separating active regions that are quiet from potentially eruptive ones is a key issue in Space Weather applications. Traditional classification schemes such as Mount Wilson and McIntosh have been effective in relating an active region…
Using results from theory of operators on a Hilbert space, we prove approximation results for matrix-valued holomorphic functions on the unit disc and the unit bidisc. The essential tools are the theory of unitary dilation of a contraction…
Consider the empirical spectral distribution of complex random $n\times n$ matrix whose entries are independent and identically distributed random variables with mean zero and variance $1/n$. In this paper, via applying potential theory in…
In this paper we generalize the classical theorem of Thue about the optimal circular disc packing in the plane. We are given a family of circular discs, not necessarily of equal radii, with the property that the inflation of every disc by a…
Recent approaches to the problem of inferring a continuous probability distribution from a finite set of data have used a scalar field theory for the form of the prior probability distribution. This letter presents a more general form for…