Matematički kolokvij

Balanced truncation is a classical approach to model reduction that has long been the ”gold standard” for high fidelity reduced order modeling for large scale linear dynamical systems. I will discuss a novel data-driven reformulation of this approach that does not require intrusive access to internal system dynamics, that is, knowledge of an original system realization is unnecessary. Instead, observations are accumulated of the system response - either sampling the transfer function evaluated at complex driving frequencies, or sampling (in time) the system’s impulse response. Notably, we do not require access to state-space trajectory snapshots as would be found in POD-type methods, nor do we approximate any system Grammians. A variety of numerical experiments are provided that verify the effectiveness of this approach.

Kooperativni heterogeni roboti, robotska manipulacija različitim objektima, umreženi sustavi upravljanja, planiranje putanja heterogenih robota u dinamičnim okruženjima primjeri su sustava u kojima se adaptivno optimalno upravljanje uspješno koristi. U sklopu ovog predavanja predstavit će se problemi i rezultati algoritama koji omogućuju sustavima prilagodbu u promjenjivim okruženjima uz zadržavanje suboptimalnosti. Također će se prezentirati trenutne istraživačke aktivnosti povezane s navedenim temama.

In this talk we will present a survey of the main topics and results from the recently published research monograph "Fractal Zeta Functions and Fractal Drums: Higher-Dimensional Theory of Complex Dimensions" by the coauthors Michel L. Lapidus, Goran Radunović and Darko Žubrinić. In the monograph, a new theory of fractal zeta functions and complex dimensions valid for arbitrary subsets of Euclidean spaces has been developed. This theory provides a significant extension of the existing theory of zeta functions for fractal strings, i.e., "fractal" subsets of the real line. Two new classes of fractal zeta functions,
namely, the distance and the tube zeta function, are introduced and their properties are investigated. In fact, for a given subset, its complex dimensions are defined as poles or even more general singularities of the corresponding fractal zeta function. The complex dimensions themselves, although defined analytically, have a deep connection with the fractal geometry of the given set.

Računalna kaznena djela su kaznena djela koja se događaju gotovo svakodnevno i zbog toga valja znati kako ih tretira nacionalno kazneno zakonodavstvo. Naravno, tretira ih kao i ostala kaznena djela, a kažnjava ih onako kako je to propisano Kaznenim zakonom. Da bi se računalno kazneno djelo (i ostala kaznena djela propisana Kaznenim zakonom) smatralo ostvarenim, moraju biti ispunjene određene pretpostavke, a kada su one ispunjene, kazneni postupak može početi.