A broadcast channel given by p(y 1 , y 2 |x) is said to be (physically degraded) if p(y 1 , y 2 |x) = p(y 1 |x)p(y 2 |y 1), ∀x ∈ X , ∀y 1 ∈ Y 1 , ∀y 2 ∈ Y 2. A broadcast channel given by p(y 1 , y 2 |x) is said to be (stochastic degraded) if its conditional marginal distributions p(y 1 |x) and p(y 2 |x) are the same as that of a physically degraded broadcast channel; that is, if there exists a ...

In this appendix we present the proofs omitted in “Dynamic Free Riding with Irreversible Investments” by Marco Battaglini, Salvatore Nunnari and Thomas Palfrey. Marco Battaglini Department of Economics Princeton University Princeton NJ 08544 [email protected] Salvatore Nunnari Department of Political Science Columbia University New York, NY 10027 [email protected] Thomas Palfrey Divisi...

On the behavior of solutions of the system of rational difference equations x n+1 = x n−1 y n x n−1 − 1 , y n+1 = y n−1 x n y n−1 − 1 , z n+1 = 1 y n z n Abstract In this article, we investigate the solutions of the system of difference equations y n+1 = y n−1 x n y n−1 − 1 , y n+1 = y n−1 x n y n−1 − 1 , z n+1 = 1 y n z n where x 0 , x-1 , y 0 , y-1 , z 0 , z-1 real numbers such that y 0 x-1 ≠...

Neuropeptide Y (NPY) is an inhibitory neuromodulator expressed abundantly in the central nervous system that is suspected of being an endogenous antiepileptic agent that can control propagation of limbic seizures. Electrophysiological and pharmacological data suggest that these actions of NPY are mediated by G protein-coupled NPY Y2 and NPY Y5 receptors. To determine whether the NPY Y5 receptor...

We begin with three technical lemmas. Lemma 2 Let y ̸ = 0 and 0 < λ 1 ≤ ∥X T y∥ ∞. We have ⟨ y λ 1 − θ * 1 , θ * 1 ⟩ ≥ 0. Proof Since the Euclidean projection of y λ1 onto {θ : ∥X T θ∥ ∞ ≤ 1} is θ * 1 , it follows from Lemma 1 that ⟨θ * 1 − y λ 1 , θ − θ * 1 ⟩ ≥ 0, ∀θ : ∥X T θ∥ ∞ ≤ 1. (46) As 0 ∈ {θ : ∥X T θ∥ ∞ ≤ 1}, we have Eq. (45). Lemma 3 Let y ̸ = 0 and 0 < λ 1 ≤ ∥X T y∥ ∞. If θ * 1 parallel...