This study investigated the levels of irrationality reported by a clinical sample of anxiety disorder patients, including simple and social phobics, panic disorder patients, agoraphobics, and obssessive compulsive patients. The levels of irrationality were compared between these groups and a group of normal control subjects, using the Rational Behavior Inventory (RBI). Agoraphobic patients were...

In this work, we study the Gross-Pitaevskii hierarchy on general –rational and irrational– rectangular tori of dimension two and three. This is a system of infinitely many linear partial differential equations which arises in the rigorous derivation of the nonlinear Schrödinger equation. We prove a conditional uniqueness result for the hierarchy. In two dimensions, this result allows us to obta...

A utility maximizing model of allocating limited attention between adopting new behaviors and adapting current behaviors generates an optimal policy that resembles commonly observed, and apparently irrational, behavioral rules. The ability to update current behaviors implies an endogenous opportunity cost of adopting a new behavior. If this cost is sufficiently high, then behaviors are less tha...

Let α be an irrational number with bounded partial quotients of the continued fraction ak. It is well known that symmetrizations of the irrational lattice {( μ/N,{μα}N−1 μ=0 have optimal order of L2 discrepancy, √ logN. The same is true for their rational approximations Ln(α) = {( μ/qn,{μ pn/qn} )}qn−1 μ=0 , where pn/qn is the nth convergent of α . However, the question whether and when the sym...

α is algebraic if there exists p ∈ Z[x], p 6= 0 with p(α) = 0, otherwise α is called transcendental . Cantor: Algebraic numbers are countable, so transcendental numbers exist, and are a measure 1 set in [0, 1], but it is hard to prove transcendence for any particular number. Examples of (proported) transcendental numbers: e, π, γ, e, √ 2 √ 2 , ζ(3), ζ(5) . . . Know: e, π, e, √ 2 √ 2 are transce...

We present a game-theoretic account of irrational agent behavior and define conditions under which irrational behavior may be considered quasi-rational. To do so, we use a 2-player, zero-sum strategic game, parameterize the reward structure and study how the value of the game changes with this parameter. We argue that for any “underdog” agent, there is a point at which the asymmetry of the game...