This note studies the bias arises from the MLE estimate of the rate parameter and the mean parameter of an exponential distribution. 1 Motivation Although maximum likelihood estimation (MLE) methods provide estimates that are useful, the estimates themselves are not guaranteed to be unbiased. Nevertheless, MLE methods are still highly regarded in practice due to several of their properties, not...

The symmetries of the wavefunction for identical particles, including anyons, are given a rigorous non-relativistic derivation within pilot-wave formulations of quantum mechanics. In particular, parastatistics are excluded. The result has a rigorous generalisation to n particles and to spinorial wavefunctions. The relation to other non-relativistic approaches is briefly discussed. 1 Quantum ind...

The problem of ballistically controlled annihilation is revisited for general initial velocity distributions and an arbitrary dimension. An analytical derivation of the hierarchy equations obeyed by the reduced distributions is given, and a scaling analysis of the corresponding spatially homogeneous system is performed. This approach points to the relevance of the nonlinear Boltzmann equation f...

using fixed pointmethods, we investigate approximately higher ternary jordan derivations in banach ternaty algebras via the cauchy functional equation$$f(lambda_{1}x+lambda_{2}y+lambda_3z)=lambda_1f(x)+lambda_2f(y)+lambda_3f(z)~.$$

The basic Schema Theorem for genetic algorithms is modiied for a grammatically-based learning system. A context-free grammar is used to deene a language in which each sentence is mapped to a tness value. The derivation trees associated with these sentences are used to deene the structure of schemata. The eeect of crossover and mutation on schemata is described. A schema theorem is developed whi...

In this paper, we study a coupled system of nonlinear fractional differential equations with multi-point boundary condi- tions. The differential operator is taken in the Riemann-Liouville sense. Applying the Schauder fixed-point theorem and the contrac- tion mapping principle, two existence results are obtained for the following system D^{alpha}_{0+}x(t)=fleft(t,y(t),D^{p}_{0+}y(t)right), t in (0,...

where α = max(|D(ui)|, |D(uj)|)+ ; is a small positive number. For notational simplicity, we denoteD(xi) = D(ui)xi, V (xi, xj) = V (ui, uj)xixj , V̂ (xi, xj) = V̂ (ui, uj)xixj , andR(xi, xj) = R(ui, uj)xixj . Lemma 1. If X∗ is the global optimum of E(X),R(xi, xj) < To,∀ xi ∼ xj , xi, xj ∈ X∗. Proof. If there exists a pair xi ∼ xj , xi, xj ∈ X∗ such thatR(xi, xj) ≥ To, then E(X∗) > 0 = E(0) (5) wh...

Solving constrained combinatorial optimization problems via MAP inference is often achieved by introducing extra potential functions for each constraint. This can result in very high order potentials, e.g. a 2-order objective with pairwise potentials and a quadratic constraint over all N variables would correspond to an unconstrained objective with an order-N potential. This limits the practica...