Our future is shaped by many factors, including chance. It’s worth having a vision of where we want our lives to go. First, we will introduce participants to some interesting opportunities for personal and professional growth. Then, we will reflect together on the dilemmas that influence our careers, how they can be addressed, and what the consequences of those choices might be.

No matter the occupation, we all have to present the results of our work at some point. It is essential to be able to do so effectively and to be able to clearly communicate our message to the audience. During the workshop, we will recall the basic rules of good presenting. Afterwards, there will be try-outs with feedback for everyone interested.

Ca2+ plays an important role as an intracellular messenger in multiple biochemical processes. Developing an effective method to measure intracellular concentration of Ca2+ will help to explain these pathways. This lecture gives a recipe for development of genetically modified cells for measuring of Ca2+ concentration.

This lecture will show that complex geometric problems can turn out to be easy if we look at them from the right perspective. First, I will introduce the concepts of projective geometry, and then we will try to prove some beautiful but difficult to synthetically prove lemmas using projective methods.

One of the most widely used models of handheld radios is the Baofeng UV-5R. We'll look at the basics of its operation and talk about common findings on the available radio frequencies. Not to be missed are the basics of etiquette for ham radio operators and neccessary precautions.

The author will present the most important results that he came to during the preparation of his master's thesis and will elaborate on the ones that can help the audience the most to orient themselves in the given area of pedagogical research. The lecture will develop the epistemological background of the audience and can facilitate their navigation among scientific theories in any field. It will also summarize selected social research concepts that aid in the modernization of the science curriculum, necessary for the education of the new generation of scientists. The author will be happy to share what he learned from the journey.

As every year, we will open with a lecture containing a selection of recent discoveries in various fields of natural science. In addition, listeners will be encouraged to share insights from recent conferences they have attended.

This paper proposes a novel quantum optimization framework that inverts the conventional input-to-output paradigm by fixing a desired final state and systematically eliminating incompatible initial states. Unlike traditional approaches such as QAOA or adiabatic quantum computing, which evolve systems toward energy minima, our method evaluates which Hamiltonian subsystems – derived from historical data – can evolve into the target state using time as the sole free variable. This exclusionary dynamic mirrors constraint satisfaction logic but is governed by continuous quantum evolution. Designed for hybrid quantum-classical systems, this method leverages classical resources for Hamiltonian encoding and quantum hardware for time evolution, offering a promising solution for complex, outcome-driven decision-making tasks.

The Dirac equation offers a profound relativistic framework for modeling spin-½ particles, uniting internal spinor structure with spacetime dynamics through gamma matrices. This seminar explores its extension to systems under external potentials and its natural evolution into quantum field theory (QFT), where particles emerge as excitations of underlying fields and interactions are shaped by symmetry principles. We conclude by illustrating how these foundational ideas inform modern quantum technologies – particularly the manipulation of trapped ions via laser pulses – bridging fundamental physics with quantum information processing.

Perturbation theory provides a systematic framework for deriving approximate solutions to problems involving a small parameter, particularly in ordinary differential equations (ODEs). In this talk, we will establish the foundational concepts and key methodologies of this field. We will begin by examining the Poincaré-Lindstedt method for periodic oscillators, using Duffing's equation to illustrate how secular terms are eliminated to yield uniformly valid approximations for oscillatory behavior. We will then explore the two-scale method for analyzing damped oscillators, with examples such as Cole's and the van der Pol's oscillator, focusing on systems with multiple time scales. Finally, a core focus will be placed on boundary layer problems, where we will introduce the method of matched asymptotic expansions. Using Friedrichs' equation, we will detail the construction of inner and outer solutions and their matching to form a composite solution. This presentation aims to provide a clear understanding of these powerful perturbation techniques and their wide applicability in applied mathematics and engineering.

Stochastic Differential Equations (SDEs) are a powerful mathematical framework for modeling systems evolving under random influences. In this talk, we will establish the foundational concepts of SDEs, beginning with Martingale, Wiener, and Itô processes, and introduce Itô's Lemma. We will then examine the Fokker-Planck equation and its derivation, which describes the evolution of probability density functions for stochastic processes. A core focus will be placed on the precise computation of hitting probabilities and expected stopping times, exploring general solutions and specific cases like decaying processes. Finally, we will apply these concepts to "Limit Laws for Critical Dispersion on Complete Graphs." This section will illustrate how the Central Limit Theorem can be utilized to analyze the dispersion of particles on a complete graph, framing the system as a Harris chain (a continuous Markov chain), and conclude with a discussion on the mean time to reach a specific state and boundary layer behavior.

Active look at phenomena distinguishing its properties especially ones which somehow are emerging from the perception and close observation. This activity could lead to new point of views and new question could come. We will look at different phenomena and try this process, we will try to be integral in our description and try not to loose connection between the human and the phenomenon. The practical philosophy will be helping us.

The current trend is to simplify difficult computational problems with useful approximate methods that are able to go to an accuracy that is more than sufficient. In this case, we are concerned with a general problem of quantum chemistry, namely the solution of the Schrödinger equation for a quantum system, namely the Endohedral fullerene He@C60. From the resulting solution we are able to obtain all the necessary properties to describe the system. Machine learning – in this respect – helps to speed up the computations by four orders of magnitude and thus allows completely new possibilities for simulations of quantum systems as needed.

Overview of the state of radar technology. There are many devices which we can call radars. We will show the principles of several of them – passive radar for emitter localization using multilateration ("Tamara"); airplane detection using non-cooperative illuminators; modern primary radar used for weather detection and target classification; the future with active electronically scanned antennas (AESA). We believe it is within the means of a motivated individual or a small group to create working prototypes of all of the presented devices – and we have done so with several of them. Therefore, the talk will mention lessons from actually building and running such devices and will be oriented a bit in a ”do it yourself“ fashion. An older version of this talk has actually already been given once, and the slides can be found at https://jenda.hrach.eu/talks/2024-radarova-technika.pdf and the recording at https://www.youtube.com/watch?v=RV_i5bNcJ0A

Reichenbach's Common Cause Principle (RCCP) posits that correlations arise either from direct causal links or common causes. We investigate its mathematical structure under four foundational axioms. Focusing first on countably additive states, we show that RCCP is meaningful only for positively correlated events and compare the classical Boolean and quantum settings, highlighting key differences in maximal correlation. A counterexample is constructed using a free orthomodular lattice, resolving an open question. We then relate RCCP to the Darboux property and prove that atomless countable complete quantum logics are common-cause complete. Additionally, we demonstrate that certain incomplete quantum logics can be embedded into complete ones. Finally, we explore RCCP under finitely additive states, constructing countable Boolean and quantum logics with states that are common-cause complete, thus uncovering novel examples within this broader framework.

Metal-oxide based nanostructures have a potential to become accessible, efficient, and stable catalysts for future applications in energy storage [1]. In particular, the Ce/CoOx structure is significant for its thermal stability [2] and its catalytic activity towards redox reactions [3]. In the present study, we characterised the Ce/CoOx structure by means of X-ray photoelectron spectroscopy (XPS), energy-dependent low energy electron diffraction (IV-LEED) and scanning tunneling microscopy (STM) over temperature range from 323 K to 923 K. We identified three temperature intervals with distinct behaviours of various structural properties. In the interval from 323 K to 473 K the Ce/Co3O4 system is thermally stable, and the Ce layer is amorphous. Between 473 K and 773 K the Ce forms an ordered structure and gradually becomes partially oxidised as CeOx upon annealing, while the system is still stable. In the last interval, above 773 K, the spinel structure begins to collapse, the CeOx becomes fully oxidised and the Co3O4 is gradually reduced.

On mathematical axiomatization in abstract algebra.

The author will present basics of light and biological tissue interactions and their applications in medical field. Theoretical basics will be followed by presentation of authors' experiments and their results aimed at harvesting the information to build diagnostical optical medical tools on.

Explanation and implementation of basic building blocks of neural network training and inference. Goal: To be able to understand how simple neural networks are trained (or to implement one from scratch including simple training). Without parentheses it would be more like a lecture. For the goal in parentheses each participant would have a computer and code for themselves so it would require a computer for each participant and at least some basic programming skills. We will decide the course according to the situation on the spot.