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Classical methods for processing and analysis of multidimensional signals – such as color videos and hyperspectral images – do not exploit full information contained in inner their factors. On the other hand, recently developed tensor based methods allow for data representation and analysis which directly account for data multidimensionality. Examples can be found in many applications such as face recognition, image synthesis, video analysis, surveillance systems, sensor networks, data stream analysis, marketing and medical data analysis, to name a few.

In this presentation, I will discuss a number of issues related to the problem of selecting a group of candidates (referred to as the committee). Committee elections have applications ranging from shortlisting, through the issue of finding items to present on a store's website, to parliamentary elections (or, on a smaller scale, the problem of choosing the electors at a university). I will show simulation results for a number of multiwinner rules and discuss these rules' computational complexity and axiomatic properties.

During the presentation I will introduce the formalism of tensor networks and introduce their relevance to describe the basic states of many-body systems. Then I will introduce the simplest model with topological order presented by Alexei Kitaev, known as the toric code. On his example, I will construct a Projected Entangled Pair States (PEPS) tensor network that describes the basic state of the model and will present the purpose of my project, ie, investigating anion excitation statistics.

Quantum walks are quantum counterparts of classical random walks.
They have been useful for designing quantum algorithms that outperform their classical versions for a variety of search problems.
Most of the results, however, consider a search space containing a single marked element only.
We show that if the search space contains more than one marked element the quantum speed-up may disappear.

The seminar will be devoted to results of http://www.nature.com/articles/ncomms7908. A major application of quantum communication is the distribution of entangled particles for use in quantum key distribution.