• Count data are often modeled using a Poisson model. • If y ∼ Poisson(μ) then E(y) = var(y) = μ. • When counts are assumed exchangeable given μ and the rates μ can also be assumed to be exchangeable, a Gamma population model for the rates is often chosen. • The hierarchical model is then yi ∼ Poisson(μi) μi ∼ Gamma(α, β). • Priors for the hyperparameters are often taken to be Gamma (or exponen...

We present results on the QCD phase diagram for μB ≤ πT . Our simulations are performed with an imaginary chemical potential μI for which the fermion determinant is positive. On an 83 × 4 lattice with 2 flavors of staggered quarks, we map out the phase diagram and identify the pseudo-critical temperature Tc(μI). For μI/T ≤ π/3, this is an analytic function, whose Taylor expansion is found to co...

For each type of classical Lie algebra, we list the dominant highest weights ζ for which (ζ;μi) is not a primitive pair and the weight space Vμi has dimension one where μi are the highest long and short roots in each case. These dimension one weight spaces lead to examples of nilmanifolds for which we cannot prove or disprove the density of closed geodesics.

We show how we can linearize probabilistic linear constraints with binary variables when all coefficients are distributed according to either N (μi, λμi), for some λ > 0 and μi > 0, or Γ(ki, θ) for some θ > 0 and ki > 0. The constraint can also be linearized when the coefficients are independent and identically distributed if they are, besides, either positive or strictly stable random variables.

Proof. ‖∇F (δ)‖∞ ≤ guarantees that μ = μ(δ) are -consistent in the sense that |μi(xi) − μc(xi)| ≤ for all c, i ∈ c and xi. Algorithm 1 maps any such -consistent μ to locally consistent marginals μ̃ such that |μi(xi)− μ̃i(xi)| ≤ 3 Nmax, |μc(xc)− μ̃c(xc)| ≤ 2 N max, (3) for all i, xi, c, and xc, where Nmax = max{maxiNi,maxcNc}. In other words, ‖μ− μ̃‖∞ ≤ K . This can be easily derived from the update...

and Applied Analysis 3 for all f ∈ C∞ 0 Ω . Since Aμ A μI is positive for sufficiently large μ it has a positive self-adjoint Friedrichs extension Aμ F such that D (( Aμ ) F ) ⊂ ◦ W m 2 Ω . 1.9 We define the Friedrichs extension of A Aμ − μI to be AF Aμ F − μI such that D AF ⊂ ◦ W m 2 Ω . 1.10 The domain of AF is given by D AF { f ∈ ◦ W m 2 Ω | Af ∈ L2 Ω } . 1.11 It is also well known that this...

Nuclear matter has finite baryon number density, finite (negative) isospin density and, under certain conditions, finite (negative) strangeness density. Since having a finite chemical potential for baryon number makes the fermion determinant complex and simulations intractable, we restrict ourselves to zero baryon-number chemical potential. QCD at finite chemical potential μI for isospin (I3) a...

and Applied Analysis 3 conditions on masses and location of singularities for the minimum to be achieved. In 9 , both the case of the whole R and bounded domains are taken into account. To proceed, wemake somemotivations of the present paper. In 6 , the authors studied more general problem than problem 1.5 with μ ∈ 0, μ , s 0, and they proved that there exists Λ > 0 such that problem 1.5 has at...