We introduce non-Abelian Kuramoto model on \begin{document}$ S^3 $\end{document} in the most general form. Following an analogy with the classical Kuramoto model (on the circle \begin{document}$ S^1 $\end{document} ), we study some interesting variations of the model on \begin{document}$ S^3 $\end{document} that are obtained for particular coupling functions. As a partial case, by choosing "standard" coupling function one obtains a previously known model, that is referred to as Kuramoto-Lohe model on \begin{document}$ S^3 $\end{document} . We briefly address two particular models: Kuramoto models on \begin{document}$ S^3 $\end{document} with frustration and with external forcing. These models on higher dimensional manifolds have not been studied so far. By choosing suitable values of parameters we observe different nontrivial dynamical regimes even in the simplest setup of globally coupled homogeneous population. Although non-Abelian Kuramoto models can be introduced on various symmetric spaces, we restrict our analysis to the case when underlying manifold is the 3-sphere. Due to geometric and algebraic properties of this specific manifold, variations of this model are meaningful and geometrically well justified.

Extracurricular activities as a variety of organizational forms of students gathering in free extracurricular time at elementary school have predominantly cultural, artistic, sporting, technical, recreational or scientific character (Cindrić, 1992). Through them, students meet their needs and develop the culture of using their leisure time. Thanks to its pedagogic potential, chess is increasingly used as an educational tool and taught in elementary schools around the world. This trend begins to follow Croatia, where chess in many schools is carried out as an extracurricular and/or extracurricular activity. In this paper we will present and analyze the advantages that chess has for the elementary school students and empirically determine the occurrence of chess as an extracurricular activity in the schools in the City of Zagreb. Also, based on the results of the qualitative research, the views of the chess teachers regarding advantages of chess implementation, ways of determining the interests of students, and teaching methods used in chess teaching will be presented.

Izvannastavne aktivnosti kao različiti organizacijski oblici okupljanja učenika u slobodno izvannastavno vrijeme u školi imaju pretežito kulturnoumjetničko, športsko, tehničko, rekreacijsko ili znanstveno obilježje (Cindrić, 1992). Kroz njih učenici zadovoljavaju svoje potrebe i razvijaju kulturu korištenja slobodnog vremena. Zahvaljujući svom pedagoškom potencijalu, šah se sve više implementira u kurikulume škola i poučava na svim razinama obrazovanja. Ovaj trend počinje pratiti i Hrvatska, u kojoj se šah u mnogo škola provodi kao izvannastavna i/ili izvanškolska aktivnost. U ovome radu prikazat će se i analizirati prednosti koje bavljenje šahom ima za učenike osnovnih škola te će se empirijskim istraživanjam utvrditi pojavnost izvannastavne aktivnosti šaha u školama Grada Zagreba. Temeljem rezultata kvalitativnog istraživanja prikazat će se stavovi voditelja šaha kao izvannastavne aktivnosti o prednostima njegove implementacije, načinima utvrđivanja interesa te o načinima rada voditelja i polaznika/učenika.

: We construct bijections between certain energetically favorable resonance-like structures in several classes of benzenoid compounds and some well- known combinatorial structures enumerated by Catalan and related numbers. In that way we derive explicit formulas for the n umber of such structures in the considered classes of compounds. We also list some open problems and indicate some possible d irections for future research.

On September 9-12, 2019, I traveled to Beijing, China for the World Congress of Neurosurgery. I was eager to attend the biggest event of my profession for two reasons. One was my nomination for second vice-president of the World Federation of Neurosurgical Societies (WFNS). The second reason was to learn about Chinese culture for the first time in my life. I was honored to be elected for an officer position of the WFNS and I tremendously enjoyed the grandiosity of the Great Wall of China (Figure 1), the Forbidden City, and Summer Palace; I also enjoyed trying authentic Chinese food.

No abstract available.

OBJECTIVE To describe the technical nuances of multimodal transseptal-transsphenoid surgery for pituitary tumors using a combination of microneurosurgery, neuroendoscopy, and electromagnetic neuronavigation. MATERIALS AND METHODS A transnasal approach to the sella is performed endoscopically and widely exposed by an otolaryngologic surgeon. Surgery is next performed by the neurosurgeon with microscope and neuronavigation for microsurgical resection of pituitary tumors. Neuroendoscope is also used at the end of surgery to confirm tumor resection and inspect operative site. During surgery, the patient's head, angle and height of the microscope, and position of the table are repositionable to allow for multiple angle views. Abdominal fat harvested prior to the procedure is used to ensure cerebrospinal fluid seal. RESULTS The senior author (KIA) has used the combined approach with 84 consecutive patients. Radical resection was achieved in 66 patients, subtotal in 11, and partial in 7. There were no perioperative complications. Six patients experienced postoperative transient diabetes insipidus. The pituitary gland and stalk were preserved in all cases. Visual symptoms were improved in 78% and endocrinological symptoms in 56% of cases. CONCLUSION This combined approach is safe and effective. It increases the efficacy and radicality of surgical resection, helps to preserve the pituitary gland, and improves and resolves preoperatively altered patient hormonal function and impaired vision. It also reduces complications, provides less postoperative pain and discomfort, reduces the surgery time, and enables a shorter hospital-stay.

Recent trends in the development of autonomous vehicles focus on real-time processing of vast amounts of data from various sensors. The data can be acquired using multiple cameras, lidars, ultrasonic sensors, and radars to collect useful information about the state of the traffic and the surroundings. Significant computational power is required to process the data fast enough, and this is even more pronounced in vehicles that not only assist the driver but are capable of fully autonomous driving. This article proposes speed and accuracy improvement of traffic sign detection and recognition in high-definition images, based on focusing on different regions of interest in traffic images. These regions are determined with efficient and parallelized preprocessing of every traffic image, after which convolutional neural network is applied for detection and recognition in parallel on graphics processing units. We employed different “You Only Look Once” (YOLO) architectures as baseline detectors, due to their speed, straightforward architecture, and high accuracy in general object detection tasks. Several preprocessing procedures were proposed, to achieve real-time performance requirement. Our experiments using a large-scale traffic sign dataset show that we can achieve real-time detection in high-definition images with high recognition accuracy.