Quantum Iterated Function Systems

Iterated functions system (IFS) is defined by specifying a set of functions in a classical phase space, which act randomly on an initial point. In an analogous way, we define a quantum iterated functions system (QIFS), where functions act randomly with prescribed probabilities in the Hilbert space. In a more general setting a QIFS consists of completely positive maps acting in the space of density operators. We present exemplary classical IFSs, the invariant measure of which exhibits fractal structure, and study properties of the corresponding QIFSs and their invariant states.Comment: 12 pages, 1 figure include

Monitoring of sessile oak (Quercus petraea Liebl.) autumn phenology using orthomosaics made on a basis of aerial images acquired with drone

Changes to beginning and the length of the growing season and the phenological stages can be of great importance for the individual trees, their populations and the populations of other species. The aim of the research described in this paper is to assess the ability to recognize the autumn phenological phases in single trees of the sessile oak, using UAV images. In our study we have examined if we can on this basis rank the trees according to their preparation for winter dormancy. There were 20 observers involved in the research whose objective was to pass each of 114 trees to one of five classes, based on the dominant color of assimilation apparatus observed on an orthomosaic. Distinguished color classes of oaks were: 1 - green, 2 - greenish-yellow, 3 - yellow, 4 - yellowbrown and 5 - brown. The analysis revealed that only 6 of all trees (5 green and one greenish-yellow) were classified by all observers to the same group. Other trees were classified to different colors, and in the case of 25 trees (22%), the number of the same color indicated was less than or at most equal to 12. The applied color scale did not correspond fully to colors perceived by the participants. After completion of the study, all said they ran out of green-brown color, and the crowns of trees that could be assigned to that color, were therefore classified as greenish-yellow, yellow or yellow-brown. In further research it is necessary to explain the causes of green-brown color observed in some trees, as well as its natural meaning and place in a chain of crown colors changes taking place during autumn, using methods of digital image analysis