Register automata with linear arithmetic

We propose a novel automata model over the alphabet of rational numbers, which we call register automata over the rationals (RA-Q). It reads a sequence of rational numbers and outputs another rational number. RA-Q is an extension of the well-known register automata (RA) over infinite alphabets, which are finite automata equipped with a finite number of registers/variables for storing values. Like in the standard RA, the RA-Q model allows both equality and ordering tests between values. It, moreover, allows to perform linear arithmetic between certain variables. The model is quite expressive: in addition to the standard RA, it also generalizes other well-known models such as affine programs and arithmetic circuits. The main feature of RA-Q is that despite the use of linear arithmetic, the so-called invariant problem---a generalization of the standard non-emptiness problem---is decidable. We also investigate other natural decision problems, namely, commutativity, equivalence, and reachability. For deterministic RA-Q, commutativity and equivalence are polynomial-time inter-reducible with the invariant problem

Brownian motion of a charged test particle near a reflecting boundary at finite temperature

We discuss the random motion of charged test particles driven by quantum electromagnetic fluctuations at finite temperature in both the unbounded flat space and flat spacetime with a reflecting boundary and calculate the mean squared fluctuations in the velocity and position of the test particle. We show that typically the random motion driven by the quantum fluctuations is one order of magnitude less significant than that driven by thermal noise in the unbounded flat space. However, in the flat space with a reflecting plane boundary, the random motion of quantum origin can become much more significant than that of thermal origin at very low temperature.Comment: 11 pages,no figures, Revtex

Weighted allocations, their concomitant-based estimators, and asymptotics

Various members of the class of weighted insurance premiums and risk capital allocation rules have been researched from a number of perspectives. Corresponding formulas in the case of parametric families of distributions have been derived, and they have played a pivotal role when establishing parametric statistical inference in the area. Non-parametric inference results have also been derived in special cases such as the tail conditional expectation, distortion risk measure, and several members of the class of weighted premiums. For weighted allocation rules, however, non-parametric inference results have not yet been adequately developed. In the present paper, therefore, we put forward empirical estimators for the weighted allocation rules and establish their consistency and asymptotic normality under practically sound conditions. Intricate statistical considerations rely on the theory of induced order statistics, known as concomitants.Comment: 20 page