We investigate global dynamics of the equation\begin{equation*}x_{n+1}=\frac{x_{n-1}+F}{ax_{n}^2+f},\text{ \ }n=0,1,2,...,\end{equation*}where the parameters $a,F$ and $f$ are positive numbers and the initial conditions $x_{-1},x_{0}$ are arbitrary nonnegative numbers such that $x_{-1}+x_{0}>0$. The existence and local stability of the unique positive equilibrium are analyzed algebraically. We characterize the global dynamics of this equation with the basins of attraction of its equilibrium point and periodic solutions.

European plum cultivars (Prunus domestica L.) are hexaploid and partially self-fertile or self-sterile requiring compatible pollinizers with overlapping bloom times. Therefore, inter-planting of different pollinizer cultivars is recommended. In order to identify successful pollinizers of the plum cultivars ‘Edda’, ‘Opal’ (self-fertile), ‘Jubileum’, ‘Reeves’, ‘Mallard’, ‘Avalon’, ‘Cacanska Lepotica’ (self-fertile), and ‘Valor’, 60 fruits per cultivar were collected from nine orchards in 2017 and 2018, all of which were located in Ullensvang, western Norway. DNA extraction was subsequently conducted from the obtained embryos, followed by genetic characterization using seven microsatellite markers. Tissue samples from all possible pollinizers were collected during the summer of 2017 and the same DNA approach was conducted. Results showed that ‘Opal’ was the most successful pollinizer among the investigated plum cultivars. The main exception was ‘Cacanska Lepotica’, which consistently displayed very high level of self-pollination. The most successful foreign pollinizer of ‘Opal’ was ‘Mallard’. However, in more than two thirds of embryos extracted from ‘Opal’ fruits self-fertilization was determined. ‘Reeves’ was identified as the most successful pollinizer among embryos collected from ‘Valor’. Among the five cultivars (‘Edda’, ‘Jubileum’, ‘Reeves’, ‘Mallard’, and ‘Avalon’) that did not display self-pollination, the pollinizer success rate of ‘Opal’, ranged from 36.5% (‘Mallard’) to 93.5% (‘Edda’) in 2017, while in 2018 this rate ranged from 43.5% (‘Jubileum’ and ‘Reeves’) up to 96.5% (‘Edda’). Overall, genotyping embryos using SSRs (simple sequence repeats) proved an effective method in determining the success rate of individual pollinizers among European plum cultivars.

We investigate the global dynamics of the following rational difference equation of second order\begin{equation*}x_{n+1}=\frac{Ax_{n}^{2}+Ex_{n-1}}{x_{n}^{2}+f},\quad n=0,1,\ldots ,\end{equation*}where the parameters $A$ and $E$ are positive real numbers and the initial conditions $x_{-1}$ and $x_{0}$ are arbitrary non-negative real numbers such that $x_{-1}+x_{0}>0$. The transition function associated with the right-hand side of this equation is always increasing in the second variable and can be either increasing or decreasing in the first variable depending on the parametric values. The unique feature of this equation is that the second iterate of the map associated with this transition function changes from strongly competitive to strongly cooperative. Our main tool for studying the global dynamics of this equation is the theory of monotone maps while the local stability is determined by using center manifold theory in the case of the nonhyperbolic equilibrium point.

Before choosing an intersection project design, an important step is to examine the justification of the construction on the basis of defined criteria. One of the key criteria is the analysis of capacity. Large numbers of roundabout capacity models are present in the world, most of them adapted to the conditions of the country they originate from and they need to be calibrated for local conditions. Key parameters for calibration are critical headway and follow-up headway. Follow-up headway can be measured directly in the field, while critical headway cannot be measured, but is estimated. Many critical headway estimation methods exist (over 30) and each of them provides different values. Different values of critical headway result in different capacity estimation values. This raises the question which method provides more realistic estimations under certain conditions. In this paper, four most frequently used critical headway estimation methods (Raff, Maximum likelihood method, Wu, Logit) were selected to be tested by comparison of theoretical capacity models and actual measured capacity at a small urban roundabout.

Purpose: Youth represents the most vulnerable population, mainly due to their lifestyle derived from risky sexual behaviours. The aim of the study was to identify specific HPV genotypes correlating with cervical smear cytologic abnormalities, well as sociodemographic/behavioural characteristics and history of sexually transmitted diseases in Bosnian women age up to 30 years. Methods: The longitudinal study was performed at the Department of Microbiology School of Medicine University of Sarajevo and Institute for Public Health dr. Andrija Stampar, Zagreb, Croatia from June 2017 to January 2018. Thirty (30) cervical smears were taken from tested females were screened using COBAS assay for HPV DNA testing. Routine Pap screening was performed in the Public Institution Department for Health Care of Women and Maternity of Sarajevo Canton. A self-administered questionnaire was applied. Results: A total of 30 sexually active women with abnormal cytological reports were enrolled in the study. The mean age was 26 IQR (20.75, 29.0) year. The overall prevalence of HR HPV was 66.7 %. Women age of ≤25 years had a positive association with positive results of HPV testing, OR=1.91. Consummation of alcohol, cigarettes had a strong positive association with positive HPV testing. Conclusions: The data obtained from this study indicate that HPV 16 is the most common HPV type found in the cervical specimens among young Bosnian women, followed by HPV 18. HPV DNA testing using as a screening test should be considered in the development of cervical cancer prevention programs in Bosnia and Herzegovina.

In order for a tourist to visit a location, it has to be attractive. Destination attractiveness can be examined in several ways. One of them is offered by this study, which has examined destination attractiveness based on resources available in certain rural settlements. Based on a case study carried out in the Brčko District of Bosnia and Herzegovina (Brčko District), a model will be developed to test for rural tourism destination attractiveness. Examination of tourist destination attractiveness in the area of the Brčko District was conducted with a decision model based on the Decision EXpert method and expert decision-making. For that purpose, six rural settlements in the area of the Brčko District were examined with respect to destination attractiveness. Results obtained using this model showed that rural settlement Bijela has a “very good” attractiveness, rural settlements Brezik, Brezovo Polje, and Gornji Zovik have “good” attractiveness, while rural settlements Ražljevo and Maoča have “middle” attractiveness. The results obtained by applying this model have shown the need for improvement of touristic offer in order to make it more attractive. In order to improve attractiveness of a tourist destination, we need to strengthen human potential in this area and improve tourist infrastructure and make more effort to preserve the environment. The application of the used model has given good results in examination of tourist destination attractiveness and it should be applied for other branches of tourism in the future studies.

For certain industrial control applications an explicit function capturing the non-trivial trade-off between competing objectives in closed loop performance is not available. In such scenarios it is common practice to use the human innate ability to implicitly learn such a relationship and manually tune the corresponding controller to achieve the desirable closed loop performance. This approach has its deficiencies because of individual variations due to experience levels and preferences in the absence of an explicit calibration metric. Moreover, as the complexity of the underlying system and/or the controller increase, in the effort to achieve better performance, so does the tuning time and the associated tuning cost. To reduce the overall tuning cost, a tuning framework is proposed herein, whereby a supervised machine learning is used to extract the human-learned cost function and an optimisation algorithm that can efficiently deal with a large number of variables, is used for optimising the extracted cost function. Given the interest in the implementation across many industrial domains and the associated high degree of freedom present in the corresponding tuning process, a Model Predictive Controller applied to air path control in a diesel engine is tuned for the purpose of demonstrating the potential of the framework.

Abstract Let R be an S-graded ring inducing S, that is, a ring which is the direct sum of a family of its additive subgroups indexed by a nonempty set S, under the assumption that the product of homogeneous elements is again homogeneous. We introduce a graded version of the subring and discuss its homogeneity, where U(R) denotes the group of units of R. Communicated by Pavel Kolesnikov

Abstract We study the graded isoradical of a ring graded by a group. In particular, we compare the graded isoradical and the classical isoradical of a graded ring, examine the question of how the (graded) isoradical of a graded ring depends on the classical isoradical of a ring which corresponds to the identity element of the grading group, and we also give some sufficient conditions under which the classical isoradical of a graded ring is homogeneous.

Motivation Recent advances in single cell sequencing (SCS) offer an unprecedented insight into tumor emergence and evolution. Principled approaches to tumor phylogeny reconstruction via SCS data are typically based on general computational methods for solving an integer linear program (ILP), or a constraint satisfaction program (CSP), which, although guaranteeing convergence to the most likely solution, are very slow. Others based on Monte Carlo Markov Chain (MCMC) or alternative heuristics not only offer no such guarantee, but also are not faster in practice. As a result, novel methods that can scale up to handle the size and noise characteristics of emerging SCS data are highly desirable to fully utilize this technology. Results We introduce PhISCS-BnB, a Branch and Bound algorithm to compute the most likely perfect phylogeny (PP) on an input genotype matrix extracted from a SCS data set. PhISCS-BnB not only offers an optimality guarantee, but is also 10 to 100 times faster than the best available methods on simulated tumor SCS data. We also applied PhISCS-BnB on a large melanoma data set derived from the sub-lineages of a cell line involving 24 clones with 3574 mutations, which returned the optimal tumor phylogeny in less than 2 hours. The resulting phylogeny also agrees with bulk exome sequencing data obtained from in vivo tumors growing out from the same cell line. Availability https://github.com/algo-cancer/PhISCS-BnB