The course covers the theory and modeling of the ways in which the brain processes information, from the neuron to high-level cognitive functions. Knowledge and Understanding: The student will gain a basic understanding of the theory and applications of models used to describe the behavior of single neurons or sets of neurons, and perceptual-cognitive phenomena. Making judgments: Students will develop the ability to critically assess and interpret complex data and research findings in computational neuroscience. They will be skilled in evaluating the validity and reliability of different computational models and methodologies, making informed decisions about their application. Students will be encouraged to form independent opinions and make judgments about the most appropriate approaches to addressing specific neuroscience problems, considering ethical implications and the broader context of their work. Application of Knowledge: The student will be able to develop and test from scratch simple models, including those inspired by biologically based machine learning with applications to neuroscience. Communication Skills: The student will acquire the ability to present the results of model applications and provide an explanation of the motivations behind the chosen approach. Learning Skills: The student will navigate the literature related to the course themes and will be capable of comparing and improving the chosen modeling strategy.

Knowledge from Elementi di Fisica, Algebra Lineare e i corsi di Analisi Matematica e di probabilità di base). Knowledge of Python and scientific Python. Basic knowledge of Physics, of linear algebra, of elementary Calculus and of applied differential equations

1) Biophysical Models of Single Neuron and of basic biological neural networks 2) The Importance of Noise in Information Encoding in Neurons. 3) Introduction to the Visual Cortex 4) Bottom-Up Approach: Biologically Inspired Neural Networks and Visual Cortex 5) Top-.Down Approach: theories of mind.

1. N Brunel and V Hakim “Neuronal Dynamics” in B. Chakraborty (Editor) “Statistical and Nonlinear Physics - A Volume in the Encyclopedia of Complexity and Systems Science”, Second Edition, Springer (2022) pages 495-516 2. Alexander N. Pisarchik and Alexander E. Hramov "Multistability in Physical and Living Systems" Springer (2022) 3. Ermentrout, B., & Terman, D. H. (2010). Foundations of mathematical neuroscience. Springer. 4. “Visual Cortex and Deep Networks: Learning Invariant Representations”. Tomaso Poggio, Anselmi Fabio, MIT press. 5. Hanspeter A. Mallot - Computational Neuroscience_ An Essential Guide to Membrane Potentials, Receptive Fields, and Neural Networks-Springer (2025).

1) Introduction to Biological Neurons 2) The Hodgkin–Huxley model: Neural Dynamics and main simplified models 3) Neural Oscillators and the kuramoto model 4) Elements of modeling of Biological Neural Networks 5) Stochastic Models in Neurosciences 6) Neural Fields Models 7) Modeling human perception 8) Intro to computational neuroscience and visual cortex 9) Models of visual cortex and machine learning 10) Invariance and equivariance in image representations and biologically plausible models 11)Applications: specialized modules in the brain,mirror symmetry, whole and parts (with coding). 12) Theories of mind and the high level cognitive phenomena.

Frontal lectures and hands on sessions (the latter both individual and in groups). Ideally, each lecture will have a part of frontal teaching and a part of hands-on training. This may range from getting used to new libraries and tools to analyze complex datasets in groups.

Bring your own laptop.

The exam will consist of two parts: 1. Each student will propose a final project for the exam, typically analyzing a topic chosen freely by the student or from a list suggested by the instructor. The project will be briefly presented (10 minutes) at the beginning of the exam using slides. 2. an interview where few questions will be asked to assess the preparation on the topics of the course. The final mark is obtained by averaging the score for the project (max 12) and the oral part, max (18) to reach a maximum of 30. In the portal part we will ask 3 questions of increasing difficulty.

The course introduces students to modern techniques of analysis and modeling of neuroscience data. It is widely believed that understanding how the brain functions is one of the foundations for sustainable development, and all the techniques learned in this course can be applied in this context;