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An introduction to physics of in-medium hadrons with special emphasis towards modification of vector meson properties in dense nuclear matter is given. We start from remarkable analogy between the in-medium behavior of atoms in gases and hadrons in nuclear matter. Modifications of vector meson widths and masses can be registered experimentally in heavy-ion collisions by detecting dilepton spectra from decays of nucleon resonances and light unflavored mesons including $\rho$- and $\omega$-mesons. Theoretical schemes for description of the in-medium hadrons are reviewed and recent experimental results of the NA60 and HADES collaborations on the dilepton production are discussed., Comment: 18 pages WS LaTeX, 9 eps figures. Lecture given at the 42-nd Predeal International Summer School in Nuclear Physics "Collective Motion and Phase Transitions in Nuclear Systems", 28 August - 9 September, Predeal, Romania

The problem with constructing probability density functions (PDFs) of volatility is discussed. The first model we have used represents the simple Gaussian random walk model. The PDF is given in the form of a one-dimensional contour integral. The second model we have used is based on the joint multidimensional Student PDFs of returns. Such distributions are useful for the description of well established deviations from the Gaussian random walk, observed for financial time series, such as an approximate scaling of the PDFs of returns, heavy tails of return distributions, return-volatility correlations and long ranged volatility-volatility correlations. We have fixed free parameters of the Gaussian and modified multidimensional Student PDFs of returns over a short term period by fitting three to eight years of trade-by-trade quotes from the Eurex Bund, Bobl, DAX and EuroSTOXX futures contracts, and over the long term by fitting 100+ years of the DOW Jones 30 Industrial Averages (DJIA) and 50+ years of the Standard & Poors 500 (S&P 500) daily quotes. Two estimators are considered to quantify volatility. These are short-term dynamic and long-term static PDFs that are then constructed. The volatility distributions are compared with the historical ones of the Eurex Bund, Bobl, DAX and EuroSTOXX futures contracts and also with the historical distributions for the DJIA and the S&P 500 indices.