This paper is composed of two complementary parts. The first part is a formal investigation into the interplay of properties of reciprocal relations, how monotonicity relates to some natural and intuitive properties, including stochastic transitivity. The goal is to aggregate monotone reciprocal relations on a given set of alternatives. Monotonicity is expressed w.r.t. a linear order on the set...

An example of reversed reciprocal rhythm is presented with associated 2:I heart block and other abnormalities of conduction. The electrocardiograms have been analysed and compared with an earlier electrocardiogram in which sinus rhythm was present. Despite dramatic electrocardiographic abnormalities, evidence is offered which suggests that there may have been only a small alteration in activity...

The present paper introduces a principal-agent model in which the principal pays wages that exceed agents’ resevations values, and agents voluntarily comply with his directives even though no formal mechanisms exist to enforce these directives. We view the agency relationship as a reciprocal exchange where the principal pays rents to reduce the probability of a collective challenge. These rents...

Abstract-Any basis function of a generalized Fourier series takes on many values in an interval. In contrast, the binary nature of the basis functions of Walsh-Fourier series (WFS) allows them to be considered self-reciprocall except for a finite number of discontinuities. Hence, quotients of linear combinations of Walsh functions may be used to generate series representations of reciprocals of...

Biologists rely extensively on the iterated Prisoner's Dilemma game to model reciprocal altruism. After examining the informal conditions necessary for reciprocal altruism, I argue that formal games besides the standard iterated Prisoner's Dilemma meet these conditions. One alternate representation, the modified^Prisoner's Dilemma game, removes a standard but unnecessary condition; the other ga...

Reciprocal collision avoidance has become a popular area of research over recent years. Approaches have been developed for a variety of dynamic systems ranging from single integrators to car-like, differential-drive, and arbitrary, linear equations of motion. In this paper, we present two contributions. First, we provide a unification of these previous approaches under a single, generalized rep...

Let Ψn(x) be the monic polynomial having precisely all non-primitive nth roots of unity as its simple zeros. One has Ψn(x) = (x n − 1)/Φn(x), with Φn(x) the nth cyclotomic polynomial. The coefficients of Ψn(x) are integers that like the coefficients of Φn(x) tend to be surprisingly small in absolute value, e.g. for n < 561 all coefficients of Ψn(x) are ≤ 1 in absolute value. We establish variou...

On the positive half-line, there are two natural, and complementary, analogues of the single notion of symmetry of distributions on the real line. One is the R-symmetry recently proposed and investigated by Mudholkar and Wang (2007); the other is the ‘log-symmetry’ investigated here. Log-symmetry can be thought of either in terms of a random variable having the same distribution as its reciproc...

In virtually every semantic account of reciprocity it is assumed that reciprocal sentences are distributive. However, it turns out that the distributivity must be of very local nature since it shows no effect on the predicate or other arguments in reciprocal sentences. I present a semantic analysis of reciprocals that treats reciprocal sentences as distributive but captures the local nature of ...

T RADITIONALLY, reciprocal rhythms have been classified as atrial and ventricular on the basis of the site to which the impulse returns.1) While the ventricular reciprocal rhythm is not uncommon, the atrial rhythm is exceedingly rare, clinically.2) We experienced an example of atrial reciprocal rhythm following electrical conversion for atrial flutter. To our knowledge, no case of atrial recipr...