We show that if a strictly positive joint probability distribution for a set of binary random variables factors according to a tree, then vertex separation represents all and only the independence relations encoded in the distribution. The same result is shown to hold also for multivariate strictly positive normal distributions. Our proof uses a new property of conditional independence that hol...

We show that if a strictly positive joint probability distribution for a set of binary random variables factors according to a tree, then vertex separation represents all and only the independence relations encoded in the distribution. The same result is shown to hold also for multivariate strictly positive normal distributions. Our proof uses a new conditional independence property that holds ...

For the two sixth-order polynomials a(s) and b(s), Hurwitz stability of their convex combination is necessary and sufficient for the existence of a polynomial c(s) such that c(s)/a(s) and c(s)/b(s) are both strictly positive real. Our reasoning method is constructive, and is insightful and helpful in solving the general robust strictly positive real synthesis problem.

We show that strictly positive inductive types, constructed from polynomial functors, constant exponentiation and arbitrarily nested inductive types exist in any Martin-Löf category (extensive locally cartesian closed category with W-types) by exploiting our work on container types. This generalises a result by Dybjer (1997) who showed that non-nested strictly positive inductive types can be re...

We show how conditionally negative deenite functions on spheres coupled with strictly completely monotone functions (or functions whose derivative is strictly completely monotone) can be used for Hermite interpolation. The classes of functions thus obtained have the advantage over the strictly positive deenite functions studied in 17] that closed form representations (as opposed to series expan...

Theorem 1. Let p(x,θ) be a strictly positive, continuous probability distribution over continuous or discrete states xn and continuous parameters θ = (θ1, . . . , θM ), twice continuously differentiable with respect to θ. Let b(θ) be a strictly positive, twice continuously differentiable function. Then the set of stochastic differential equations (S1) leaves the distribution p∗(θ) invariant. Fu...

For every positive integer n, consider the linear operator Un on polynomials of degree at most d with integer coefficients defined as follows: if we write h(t) (1−t)d+1 = P m≥0 g(m) t , for some polynomial g(m) with rational coefficients, then Un h(t) (1−t)d+1 = P m≥0 g(nm) t . We show that there exists a positive integer nd, depending only on d, such that if h(t) is a polynomial of degree at m...

We consider global bounded solutions of fully nonlinear parabolic equations on bounded reflectionally symmetric domains, under nonhomogeneous Dirichlet boundary condition. We assume that, as t→∞, the equation is asymptotically symmetric, the boundary condition is asymptotically homogeneous, and the solution is asymptotically strictly positive in the sense that all its limit profiles are strictl...

Background: Dengue fever is a mosquito-borne disease which is not known to be endemic in Iran. Case Report: In October 2015, a 32-year-old Iranian woman was admitted with acute unexplained high-grade fever, headache, pain, rash, diarrhea, leukopenia and elevated liver enzymes after returning from India. Serological and molecular analysis for Dengue virus (DENV) infection revealed positive ...