Tales of ghosts, sweets, and photons

Tales of spirits who return from the dead are present in the folklore of many cultures. Halloween gives out the perfect context to introduce a probabilistic model, which entails an element of randomness. This word does not have to be understood as its typical mathematical definition. It should be understood as a probabilistic model that can display random behavior of certain events occurring in intervals of time (or space). Ghostly apparitions are rare events occurring independently in time. Do not co-occur at the same instant. …

Rating of players (or teams) is a topic of interest in sports analytics and, in general, in competitive games (e.g., video gaming). The rating in sports and video gaming consists of assigning a numerical value to a player or team using the past games’ results. The estimation of player (team) skills uses statistical models to match players or teams for tournaments and matches. In general, the rating dynamics (how the players’ skills evolve) is a hot topic in competitive games.

🎮 In gaming, a ranking is a numerical ordering of players (ordinal number), and rating is the numerical approximation of…

Every day we experiment the reality of the world, a network of networks, a system of systems: transportation, energy, water, waste, logistics, telecommunications, economy, services, government, institutions, businesses, and social communities. There is a chaotic equation to describe any apparent randomness in real world. Fractals are just something more to add to our descriptive shapes. Networks can be seen or studied as fractals. Sales route planning, power networks, social networks, communication networks, traffic networks, river networks, tourism route planning, etc. can be modeled as fractals.

While Euclidean geometry is a description of lines, planes, circles, triangles, and so on, fractal…