An intuitive method for distributing N points on a manifold A ⊂ Rd is to consider minimal s-energy arrangements of points that interact through a power law (Riesz) potential V = 1/r, where s > 0 and r is Euclidean distance in R 0 . Under what conditions will these points be “uniformly” distributed on A for large N? In this talk I will present recent results characterizing asymptotic properties ...

Let ν ∈ M([0,∞[) be a xed probability measure. For each dimension p ∈ N, let (X n)n≥1 be i.i.d. R-valued random variables with radially symmetric distributions and radial distribution ν. We investigate the distribution of the euclidean length of S n := X p 1 + . . . + X p n for large parameters n and p. Depending on the growth of the dimension p = pn on the number of steps n we derive by the me...

The mean of data on the unit circle is defined as the minimizer of the average squared Euclidean distance to the data. Based on Hoeffding’s mass concentration inequalities, non-asymptotic confidence sets for circular means are constructed which are universal in the sense that they require no distributional assumptions. These are then compared with asymptotic confidence sets in simulations and f...

A bstract-In this paper, we propose a coded modulationi scheme with interblock memory. The proposed scheme has a multi-stage coding structure. However, at some coding stage, the coding designs for every two adjacent blocks are related. Compared to coded modulation schemes for which each block is independent of the others, the introduction of interblock coding provides us with additional flexibi...

Abstract: Motivated by problems related to quasi-local mass in general relativity, we study the static metric extension conjecture proposed by R. Bartnik [4]. We show that, for any metric on B̄1 that is close enough to the Euclidean metric and has reflection invariant boundary data, there always exists an asymptotically flat and scalar flat static metric extension in M = R \B1 such that it satis...

We examine the impact of three factors on the ability to predict political coalitions of spatial coalition formation models: (1) inclusion of issue saliences, (2) choice of distance function and (3) choice of solution method. Issue saliences quantify the relative importance that parties attribute to different policy dimensions. The second factor is the distance function that is used to calculat...

Si Li and the fourth listed author (2008) considered unitary graphs attached to the vector spaces over finite rings using an analogue of the Euclidean distance. These graphs are shown to be integral when the cardinality of the ring is odd or the dimension is even. In this paper, we show that the statement also holds for the remaining case: the cardinality of the ring is even and the dimension i...

For the last two decades, matrix factorization has become one of the fundamental methods for tackling recommendation problems. Recent studies demonstrate that the interaction function dot product used in MF can limit its expressiveness and lead to sub-optimal solutions. In this work, we propose modelling user-item interaction paŠerns in an alternative way by considering positions and distances ...

Abstract The issue of how to find the best acoustical fit to a set of anisotropic elastic constants is addressed. The optimal moduli are determined which minimize the orientation averaged squared-norm of the difference in the acoustical tensors. The optimal moduli are derived explicitly and turn out to be identical to those obtained by minimizing the Euclidean distance function, or equivalently...

We study a variant of the Falconer distance problem for perturbations of the Euclidean and related metrics. We prove that Mattila’s criterion, expressed in terms of circular averages, which would imply the Falconer conjecture, holds on average. We also use a diophantine conversion mechanism to prove that well-distributed case of the Erdos Distance Conjecture holds for almost every appropriate p...