Cognitive, Computational and Social Neurosciences

Basic Neuro-Linguistics

Language springs from distributed, basic as well as higher sensory and cognitive functions. The course will explore the evolutionary and neural bases of language development, from the low-level perceptual-motor stage to the combinatory, attentive, mnemonic processes driving morphonsyntax and eventually, semantics and conceptualization.

Stochastic Processes and Stochastic Calculus

This course aims at introducing some important stochastic processes and Ito stochastic calculus. Some proofs are sketched or omitted in order to have more time for examples, applications and exercises.
In particular, the course deals with the following topics:

- Markov chains (definitions and basic properties, classification of states, invariant measure, stationary distribution, some convergence results and applications, passage problems, random walks, urn models, introduction to the Markov chain Monte Carlo method),

Principles of Brain Anatomy and Physiology

The course aims at introducing the fundamentals of brain anatomy and physiology. In the first part of the course we will revise the basics of neuron structure and function, as well as synaptic mechanisms and cytoarchitectonic properties of the cortical mantle, with particular regards to visual, auditory, somatosensory and motor systems.

Philosophical and Ethical Themes in Neuroscience

Since its formal establishment as a self-standing field, neuroethics has been divided into two subdefinitions: the neuroscience of ethics and the ethics of neuroscience. While the neuroscience of ethics aims at explaining the way our brain works in relation to moral judgement, the ethics of neuroscience is a further expansion of bioethics: a discipline that wants to assess the moral dilemmas specifically raised by recent biotechnological advancements.

Numerical Methods for the Solution of Partial Differential Equations

The course introduces numerical methods for the approximate solution of initial and boundary value problems governed by linear partial differential equations (PDEs) ubiquitous in physics, engineering, and quantitative finance. The fundamentals of the finite difference method and of the finite element method are introduced step-by-step in reference to exemplary model problems related to heat conduction, linear elasticity, and pricing of stock options in finance. Notions on numerical differentiation, numerical integration, interpolation, and time integration schemes are provided.

Neural Bases of Consciousness and Sleep

The course will provide an introduction to fundamental concepts and current experimental approaches related to the study of the functional and anatomical basis of consciousness in humans. In particular, the course deals with the following topics:

a) Definition of consciousness and identification of its fundamental properties;
b) The neuroanatomical basis of consciousness;
c) Altered states of consciousness: sleep, anesthesia, seizures, coma and related conditions;
d) Main experimental paradigms and methodological approaches to the study of consciousness;