What majority decisions are possible with possible abstaining

Suppose we are given a family of choice functions on pairs from a given finite set. The set is considered as a set of alternatives (say candidates for an office) and the functions as potential "voters". The question is, what choice functions agree, on every pair, with the majority of some finite subfamily of the voters? For the problem as stated, a complete characterization was given in \citet{shelah2009mdp}, but here we allow each voter to abstain. There are four cases.Comment: 23 page

On the descriptional complexity of iterative arrays

The descriptional complexity of iterative arrays (lAs) is studied. Iterative arrays are a parallel computational model with a sequential processing of the input. It is shown that lAs when compared to deterministic finite automata or pushdown automata may provide savings in size which are not bounded by any recursive function, so-called non-recursive trade-offs. Additional non-recursive trade-offs are proven to exist between lAs working in linear time and lAs working in real time. Furthermore, the descriptional complexity of lAs is compared with cellular automata (CAs) and non-recursive trade-offs are proven between two restricted classes. Finally, it is shown that many decidability questions for lAs are undecidable and not semidecidable

On the Sensitivity of Partial Redistribution Scattering Polarization Profiles to Various Atmospheric Parameters

This paper presents a detailed study of the scattering polarization profiles formed under partial frequency redistribution (PRD) in two thermal models of the solar atmosphere. Particular attention is given to understanding the influence of several atmospheric parameters on the emergent fractional linear polarization profiles. The shapes of these $Q/I$ profiles are interpreted in terms of the anisotropy of the radiation field, which in turn depends on the source function gradient that sets the angular variation of the specific intensity. We define a suitable frequency integrated anisotropy factor for PRD that can be directly related to the emergent linear polarization. We show that complete frequency redistribution is a good approximation to model weak resonance lines. We also show that the emergent linear polarization profiles can be very sensitive to the thermal structure of the solar atmosphere and, in particular, to spatial variations of the damping parameter.Comment: 45 pages, 16 figures, accepted for publication in the Astrophysical Journal (2010

Minimizing Running Costs in Consumption Systems

A standard approach to optimizing long-run running costs of discrete systems is based on minimizing the mean-payoff, i.e., the long-run average amount of resources ("energy") consumed per transition. However, this approach inherently assumes that the energy source has an unbounded capacity, which is not always realistic. For example, an autonomous robotic device has a battery of finite capacity that has to be recharged periodically, and the total amount of energy consumed between two successive charging cycles is bounded by the capacity. Hence, a controller minimizing the mean-payoff must obey this restriction. In this paper we study the controller synthesis problem for consumption systems with a finite battery capacity, where the task of the controller is to minimize the mean-payoff while preserving the functionality of the system encoded by a given linear-time property. We show that an optimal controller always exists, and it may either need only finite memory or require infinite memory (it is decidable in polynomial time which of the two cases holds). Further, we show how to compute an effective description of an optimal controller in polynomial time. Finally, we consider the limit values achievable by larger and larger battery capacity, show that these values are computable in polynomial time, and we also analyze the corresponding rate of convergence. To the best of our knowledge, these are the first results about optimizing the long-run running costs in systems with bounded energy stores.Comment: 32 pages, corrections of typos and minor omission

The Relation between the Radial Temperature Profile in the Chromosphere and the Solar Spectrum at Centimeter, Millimeter, Sub-millimeter, and Infrared Wavelengths

Solar observations from millimeter to ultraviolet wavelengths show that there is a temperature minimum between photosphere and chromosphere. Analysis based on semi-empirical models locate this point at about 500 km over the photosphere. The consistency of these models has been tested by means of millimeter to infrared observations. In the present work, we show that variations of the theoretical radial temperature profile near the temperature minimum impacts the brightness temperature at centimeter, submillimeter, and infrared wavelengths, but the millimeter wavelength emission remains unchanged. We found a region between 500 and 1000 km over the photosphere that remains hidden to observations at the frequencies under study in this work.Comment: Accepted in Solar Physic