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

Two groups of Pinus cembra forest communities in the Tatras

A syntaxonomical statistical analysis of 110 phytocoenological relevés of the Western Carpathians Norway spruce-Arolla pine and Arolla pine phytocoenoses was performed. Resulting six relevé aggregates were evaluated at the rank of association. Two major groups of Arolla pine woodlands were distinguished following strong floristical differences and classified at the rank of alliances: non-carbonate group – Homogyno alpinae-Pinion cembrae (associations: Homogyno alpinae-Pinetum cembrae, Mylio taylorii-Pinetum cembrae, Prenantho purpureae-Pinetum cembrae, Cembro-Piceetum) and carbonate group – Calamagrostio variae-Pinion cembrae (associations: Seslerio tatrae-Pinetum cembrae, Cystopterido montanae-Pinetum cembrae)

Arithmetic complexity via effective names for random sequences

We investigate enumerability properties for classes of sets which permit recursive, lexicographically increasing approximations, or left-r.e. sets. In addition to pinpointing the complexity of left-r.e. Martin-L\"{o}f, computably, Schnorr, and Kurtz random sets, weakly 1-generics and their complementary classes, we find that there exist characterizations of the third and fourth levels of the arithmetic hierarchy purely in terms of these notions. More generally, there exists an equivalence between arithmetic complexity and existence of numberings for classes of left-r.e. sets with shift-persistent elements. While some classes (such as Martin-L\"{o}f randoms and Kurtz non-randoms) have left-r.e. numberings, there is no canonical, or acceptable, left-r.e. numbering for any class of left-r.e. randoms. Finally, we note some fundamental differences between left-r.e. numberings for sets and reals

Mechanical and structural response of AISI 4135 steel after controlled cooling process

AISI 4135 steel is a commonly used material for high strength applications such as shafts, forgings and high pressure steel cylinders. The mentioned steel is used in a variety of microalloying by Nb, Ti, V, N, respectively of those elements combinations. In this presented paper, three different microalloyed (by N and V) heats of mentioned steel were studied. Three heat treatment modes were applied. The first mode was based on heating at 700 °C, subsequent quenching and tempering at 470 °C. In the second and the third mode the material was heated at 890 °C and subsequently different controlled cooling process followed in both modes. Microstructural and microfractographic analyses compared with found mechanical properties were part of the solution

Universal fluctuations in subdiffusive transport

Subdiffusive transport in tilted washboard potentials is studied within the fractional Fokker-Planck equation approach, using the associated continuous time random walk (CTRW) framework. The scaled subvelocity is shown to obey a universal law, assuming the form of a stationary Levy-stable distribution. The latter is defined by the index of subdiffusion alpha and the mean subvelocity only, but interestingly depends neither on the bias strength nor on the specific form of the potential. These scaled, universal subvelocity fluctuations emerge due to the weak ergodicity breaking and are vanishing in the limit of normal diffusion. The results of the analytical heuristic theory are corroborated by Monte Carlo simulations of the underlying CTRW