1 Bayesian Interpretation of Mutual Information Recall that the mutual information I(θ; X) between two random variables θ and X is defined as the Kullback-Leibler divergence between their joint distribution and the product of their marginal distributions. The following Bayesian interpretation of I(θ; X) well captures its intuitive interpretation as the amount of information that X contains abou...

Given (M,Ω) a calibrated Riemannian manifold with a parallel calibration of rank m, and M an immersed orientable submanifold with parallel mean curvature H we prove that if cos θ is bounded away from zero, where θ is the Ω-angle of M , and if M has zero Cheeger constant, then M is minimal. In the particular case M is complete with Ricc ≥ 0 we may replace the boundedness condition on cos θ by co...

Let X,Y be locally compact Hausdorff spaces and M,N be Banach algebras. Let θ : C0(X,M) → C0(Y,N ) be a zero-product preserving bounded linear map with dense range. We show that θ is given by a continuous field of algebra homomorphisms from M into N if N is irreducible. As corollaries, such a surjective θ arises from an algebra homomorphism, provided thatM is a W*-algebra and N is a semi-simple...

Let βi, i = 1, . . . , k, denote parameters whose values must be determined by deformation measurements. The results of measurements are given by a realization y of an n-dimensional random vector Y . The class of distribution functions connected with Y is F = {F (·, β, θ) : β ∈ R, θ ∈ θ}, where β = (β1, . . . , βk) (′ denotes the transposition of a matrix) ∈ R (k-dimensional Euclidean space), θ...

Every mode of a quantized boson (photon) field is described as a quantum harmonic oscillator. In this description one meets the quantum phase problem, which has been reviewed in the paper [1]. Using the photon annihilation and creation operators â and â†, respectively, which obey the boson commutation relation [â, â†] = 1̂, with 1̂ an identity operator, the number operator is expressed as n̂ = â†â...

We show that the application of Regge phenomenology to SU(4) meson multiplets leads to a new Gell-Mann–Okubo mass-mixing angle formula in the SU(3) sector, 3m 2 1 + cos 2 θ m 2 0 + sin 2 θ m 2 0 ′ + √ 2 sin 2θ m 2 0 − m 2 0 ′ = 4m 2 1/2 , where m 1 , m 1/2 , m 0 , m 0 ′ are the masses of the isovector, isodoublet, isoscalar mostly octet and isoscalar mostly singlet states, respectively, and θ i...

We study a model of "elastic" lattice polymer in which a fixed number of monomers m is hosted by a self-avoiding walk with fluctuating length l . We show that the stored length density ρm≡1-/m scales asymptotically for large m as ρm=ρ∞(1-θ/m+…) , where θ is the polymer entropic exponent, so that θ can be determined from the analysis of ρm. We perform simulations for elastic lattice polymer l...

We developed a genetic algorithm (GA) in the Heisenberg model that combines a triadic crossover and a parameter-free genetic algorithm. Using the algorithm, we examined the ground-state stiffness of the ±J Heisenberg model in three dimensions up to a moderate size range. Results showed the stiffness constant of θ = 0 in the periodic-antiperiodic boundary condition method and that of θ ∼ 0.62 in...

Write Θ for the stable character associated to a finite dimensional representation E of a connected real reductive group G. Let M be the centralizer of a maximal torus T , and denote by ΦM (γ,Θ ) Arthur’s extension of |D M (γ)| 1 2Θ(γ) to T (R). In this paper we give a simple explicit expression for ΦM (γ,Θ ), when γ is elliptic in G.