Hours:
20 hours (5 credits)

Room:

Aula Riunioni del Dipartimento di Ingegneria dell’Informazione, Via G. Caruso 16, Pisa - Ground Floor

To register to the course, click here

Short Abstract:

Fabrication of 3D nano- and microstructures has become crucial for developing new sustainable energy solutions. These innovative structures can improve the efficiency of devices for energy production, storage, and conversion, such as batteries, solar cells, and supercapacitors. Microsfabrication techniques enable extreme precision and flexibility, which are essential for optimizing energy performance while reducing material consumption. These advances also promote the development of flexible, energy-efficient electronic devices suited to new technological demands and particularly wearable technologies. By integrating sustainability, these research efforts help reduce the environmental impact of energy technologies. The ability to produce complex nano- and micro-scale structures opens new possibilities for increasing storage capacity and efficient renewable energy storage systems. Moreover, these innovations support the transition to a more environmentally-friendly society by promoting the use of responsible and more effective materials. Mastering these advanced techniques could transform the energy sector, making it more sustainable, flexible, and accessible.Fabrication of 3D nano- and microstructures has become crucial for developing new sustainable energy solutions. These innovative structures can improve the efficiency of devices for energy production, storage, and conversion, such as batteries, solar cells, and supercapacitors. Microsfabrication techniques enable extreme precision and flexibility, which are essential for optimizing energy performance while reducing material consumption. These advances also promote the development of flexible, energy-efficient electronic devices suited to new technological demands and particularly wearable technologies. By integrating sustainability, these research efforts help reduce the environmental impact of energy technologies. The ability to produce complex nano- and micro-scale structures opens new possibilities for increasing storage capacity and efficient renewable energy storage systems. Moreover, these innovations support the transition to a more environmentally-friendly society by promoting the use of responsible and more effective materials. Mastering these advanced techniques could transform the energy sector, making it more sustainable, flexible, and accessible.

This course is dedicated to the principle of electrochemical energy storage for microelectronics. It will be presented recent progress achieved in the field of microbatteries for powering sensors, lab-on-a-chips, e-textiles, medical patches, etc. The principles will be explained in terms of basic electrochemistry and thermodynamics. The relationship between properties at the atomic level with the performance of the power sources will be highlighted. Particularly, an insight into the use of micro-nanostructured materials to improve the storage capacity, rate capability, and cyclability will be given. Advanced manufacturing techniques to realize 3D structures like lithographic techniques and Atomic Layer Deposition (ALD) will be also emphasized.

Course Contents in brief:

• Basics of electrochemistry
  Redox reactions
  Thermodynamics of redox reaction
  Kinetics of redox reaction (activation and diffusion processes)
  The electrochemical interfaces
• Electrochemical analysis techniques for the characterization of energy storage systems
  Potentiodynamic and potentiostatic experiments
  Current and potential transients
  Cyclic voltammetry
  Charge and discharge profiles
  Electrochemical impedance spectroscopy
• From the Lithium-ion technology to the design of microbatteries
  Principle and applications
  The negative electrodes for microbatteries (C, oxydes, Si, …)
  The positive electrodes for microbatteries (spinels, …)
  The different electrolytes for microbatteries
  Towards the next generation of microbatteries
• Microfabrication processes for designing microbatteries
  Optical lithography
  Electron- and ion-beam lithography
  Thin-film deposition of battery components (top down and bottom-up)
  Recent examples dedicated to the fabrication of energy storage microsystems
  Flexible microbatteries
  Beyond Li-ion technology (Na-ion, K-ion, etc.)

 Schedule:

1. Day1 – June 9, 2025, 9:00 -13:00 
2. Day2 – June 10, 2025, 9:00 -13:00
3. Day3 – June 11, 2025, 9:00 -13:00
4. Day4 – June 12, 2025, 9:00 -13:00
5. Day5 – June 13, 2025, 9:00 -13:00

Hours:
16 hours (4 credits)

Room:

Aula Riunioni del Dipartimento di Ingegneria dell’Informazione, Via G. Caruso 16, Pisa - Ground Floor

To register to the course, click here

Short Abstract:

The objective of the course is to provide the students with a comprehensive background on the analysis and control of continuous dynamical systems, using a state variable approach in the time domain. The analysis will overview nonlinear dynamics from a qualitative geometric point of view, and advantages/disadvantages of linearization. The full systemic solution of linear systems is addressed, using linear algebra background. Control approaches are based on full state as well as output (static and dynamic) feedback in the deterministic domain. A brief introduction of optimal control is included. Numerical worked examples will accompany the mathematical material.

Course Contents in brief:

1. Part 1: Motivation, main definitions, examples of nonlinear systems (fixed point computation, vector fields), linearization (review of Taylor series and power series).
2. Part 2: Linear systems solution, state transition matrix, Cayley-Hamilton theorem, role of eigenvalues and eigenvectors. Structural properties. Numerical examples
3. Part 3: Full state feedback (regulation, servomechanism), eigensystem assignment, static and dynamic output feedback state reconstruction.
4. Part 4: Optimal control generalities, linear quadratic regulator, Riccati equation and its relationship with Lyapunov stability, robustness of the closed loop system.

Schedule:

1. Day1 – June 10, 2025, 14:00 -18:00
2. Day2 – June 11, 2025, 14:00 -18:00
3. Day3 – June 12, 2025, 14:00 -18:00
4. Day4 – June 13, 2025, 14:00 -18:00

Hours:
16 hours (4 credits)

Room:

Aula Riunioni del Dipartimento di Ingegneria dell’Informazione, Via G. Caruso 16, Pisa - Ground Floor

To register to the course, click here

Short Abstract:

Medical imaging plays a crucial role in the entire spectrum of healthcare, encompassing wellness, screening, early diagnosis, treatment selection, and follow-up. This course will delve deeply into recent advancements in artificial intelligence for medical image analysis, with a specific focus on deep learning approaches for disease screening and detection using medical images. The topics covered in this course include the fundamentals of deep neural networks, the basics of medical imaging, and an exploration of state-of-the-art deep learning models within the context of various medical images. The objective of the course is to equip students from diverse backgrounds with both a conceptual understanding and practical grounding in cutting-edge research on deep learning and medical image analysis.

Course Contents in brief:

1. Day 1:  Research Seminar Introduction.
   • Introduction to AI.
   • Basic Vision Models (classification, Segmentation).
   • Tutorial 1 (Basic Implementation of MLP and CNN) and assigning paper lists to students
2. Day 2:  Advanced 2D Medical Image Analysis Topic (Retinal Images, X-ray)
   • Advanced 2D Medical Image Analysis Topic (Ultrasound Images)
   • Advanced 2D Medical Image Analysis Topic (Pathology Images)
   • Tutorial 2 (Implementation of neural networks for Skin Leision Classification)
3. Day 3:   3D Medical Image Analysis
   • Advanced Medical Image Analysis Topic (Multi-modal Analysis)
   • Tutorial 3 (Implementation of 3D U-Net for MR Image Segmentation)
   • Peer Paper Sharing Topic: Foundation Model for Medical Image Processing
4. Day 4:   Special Topics (Transformer & Vision Foundation Models for MIA)
   • Special Topics (Medical Vision Language Foundation Model)
   • Tutorial 4 (Implementation of CLIP zero-shot transfer to MIA)
   • Peer Paper Sharing Topic: Medical Multi-Modal Diagnostic Foundation Model
   • Final test

Schedule:

1. Day 1 – Monday, 21 July 2025, 9:00-13:00 
2. Day 2 – Tuesday, 22 July 2025, 9:00-13:00
3. Day 3 – Thursday, 23 July 2025, 9:00-13:00
4. Day 4 – Monday, 28 July 2025, 9:00-13:00

ATTENTION: TO BE RESCHEDULED

Hours:
16 hours (4 credits)

Room:

Meeting Room, Dept. of Information Engineering, Largo Lazzarino 1, Pisa, Sixth Floor

To register to the course, click here

Short Abstract:

Cyber-Physical Systems (CPS), comprising Internet of Things (IoT), have a wide variety of applicationsCyber-Physical Systems (CPS), comprising Internet of Things (IoT), have a wide variety of applicationsto smart environments, such as smart grid, smart transportation, smart water distribution networks,smart manufacturing, smart healthcare, and smart agriculture. The aim is to improve human qualityof life and make the society a safer place to live in. However, smart living CPS and IoT domains arevulnerable to a wide variety of unsafe events, threats, adversarial attacks (e.g., false data injection,data poisoning or evasion, deliberate data manipulation or perturbation). Detecting and interpretingsuch threats in real time is vital to proactively respond to the underlying cause and preventimmediate impacts on civilians and the economy. Threats manifest themselves as anomalies in thesensed time series data and machine learning model parameters, and can be formulated as ananomaly detection problem, where we first learn the underlying mathematical structure of benignbehavior and then detect anomalies as deviations from the learned structure.

This research-based Ph.D. course aims to cover a unified theory for detecting anomalies (threats) insmart living CPS in a lightweight, timely, and unsupervised manner. The approach is based on derivinginvariants and latent space that use time series data analytics, machine learning, information theory,and reputation scoring, and ecology models. The proposed unified theory will be validated using realworlddata collected from multiple CPS and IoT domains such as smart grid, smart transportation,and smart water networks. The course will be concluded with future research directions.

Course Contents in brief:

1. Sensors, IoT, CPS and UAV Networks
2. Smart Environments
3. Security Challenges in CPS
4. Machine Learning and Mathematical Models
5. Mobile Crowd Sensing
6. Securing Smart Living CPS
   1. Smart Grid
   2. Smart Transportation
   3. Smart Water Distribution
7. Smart Agriculture and Smart Healthcare
8. Conclusions and Open Problems

Schedule: TO BE RESCHEDULED

1. May 12 – 2:00-6:00 pm
2. May 13 – 10:30-12:30 am; 2:00-4:00 pm
3. May 14 – 10:30-12:30 am; 2:00-4:00 pm
4. May 15 – 10:30-12:30 am; 2:00-4:00 pm

Hours:
16 hours (4 credits)

Room:

Aula Riunioni del Dipartimento di Ingegneria dell’Informazione, Via G. Caruso 16, Pisa - Ground Floor

To register to the course, click here

Short Abstract:

The PhD course is designed to provide students with a comprehensive understanding of in vitro neuroengineering, focusing on the principles, techniques, and applications of engineering approaches for studying and manipulating neuronal systems in vitro. The course will cover fundamental concepts, experimental methodologies, and cutting-edge advancements in the field, with an emphasis on multidisciplinary perspectives. Students will gain practical skills in designing and conducting experiments, and analyzing data.

Course Contents in brief:

The course is divided into four sections:

1. Introduction to In Vitro Neuroengineering
   1. Overview of in vitro neuronal systems
   2. Historical context and significance of in vitro neuroengineering
   3. Ethical considerations in in vitro experiments
2. Neuronal Cell Culture Techniques
   1. Cell culture fundamentals
   2. Primary neuronal culture techniques
   3. Induced pluripotent stem cell-derived neuronal cultures
   4. Co-culture systems and organoids
3. Microelectrode Arrays (MEAs)
   1. Principles of MEAs
   2. Fabrication and design considerations
   3. Signal acquisition and data analysis
   4. Applications in electrophysiology and neural interface development
4. Microfluidics and Brain-on-a-Chip Systems
   1. Microfluidic device fabrication and operation
   2. Integration of neuronal cultures in microfluidic platforms
   3. Advancements in drug delivery and chemical stimulation
   4. Disease modeling and high-throughput screening

Schedule:

1. Day1 – 2nd September 2025- 09:00-13:00 (4 hours)
2. Day2 – 3rd September 2025 – 09:00-13:00 (4 hours)
3. Day3 – 4th September 2025 – 09:00-13:00 (4 hours)
4. Day4 – 5th September 2025 – 09:00- 13:00 (4 hours)

Hours:
20 hours (5 credits)

Room:

Meeting Room, Dept. of Information Engineering, Largo Lazzarino 1, Pisa, Sixth Floor

To register to the course, click here

Short Abstract:

The course aims at allowing PhD students to familiarize with the concept of Privacy, understand its relevance when handling users’ data, and learn some practical techniques that can be employed to anonymize and release the data. Privacy protection has ethical [1], legal [2,3] and economic [4] implications that need to be accounted when developing a system which processes, transmits or handles personal and user’s generated data. Indeed, privacy plays a prominent role in granting cybersecurity in many digital environments, ranging from customers’ data and click logs [5], to medical and genomic data [6,7], to geospatial information [8].
After a brief introduction of the General Data Protection Regulation (GDPR) [2], the major European legal framework that regulates privacy aspects, the course will introduce privacy techniques derived from three major areas: microdata protection, differential privacy, and geomasking.
Microdata are data concerning single individuals. Data used in biological scenarios and generated by sensors typically fall within this category of data. Their use comes with severe risks of reidentification and record linkage [9]. The course will equip the PhD students with statistical techniques to operate securely on such type of data [10]. Furthermore, the course will introduce the main theoretical frameworks to handle this type of information, such as k-Anonymity [11], l-Diversity [12], and t-Closeness [13].
The second module regards Differential Privacy [14]. Differential Privacy is considered the de-facto standard to release privatized data, a paramount task when it comes to digital communications and data publication at large. During the second part of the course, the Phd Students will learn the main basic Differential Privacy mechanisms [14], the building blocks of more advanced solutions, and will be introduced to real world solutions developed by major IT companies, such as Google’s RAPPOR [15],
Apple’s Private CMS [16] and Microsoft’s LDP [17].
The final module will concern geographical data. Due to its volume and sensitivity, this class of data presents additional vulnerabilities and requires proper strategies to be handled in a secure manner. To this end, the students will be introduced to the major Geomasking approaches, including statistical solutions [8] and Metric Differential Privacy [18].
Each module will be followed by a hands-on laboratory where the students can learn how to practically implement the techniques discussed theoretically during the lectures. The implementation will be done in Python, using the major data science packages, such as NumPy, Pandas and Scipy. The students will be able to apply privacy protection approaches to the data they use in their research, or on synthetic or publicly available datasets.

Course Contents in brief:

1. Microdata Protection:
   1. Definition of the concept of microdata and related aspects, such as Personal Identifiable Information (PII), Identifiers, Quasi-Identifiers, and sensitive attributes.
   2. Analysis of the main micro-data protection techniques, including local suppression, recoding, resampling, Post RAndomized Methods (PRAM), micro-aggregation.
   3. Introduction to the main micro-data anonymization frameworks, such as k-Anonymity, l-Diversity, t-Closeness.
2. Differential privacy:
   1. Introduction of the concept of Differential Privacy, with its use cases, application scenarios and limitations.
   2. Introduction to the main differentially private mechanisms, including the randomization mechanism, Laplace mechanism, exponential mechanism.
   3. Introduction of some real-world applications of Differential Privacy, such as Google’s RAPPOR, Apple’s Private Count Mean Sketch, and Microsoft’s LDP.
3. Biosciences:
   1. Understand the criticalities and additional challenges that rise in terms of privacy when handling medical and biological data, including genomic information.
   2. Application of privacy preserving techniques to protect microdata in the medical and biological domains.
   3. Devise approaches to produce aggregated statistics on biological data that can be safely released (i.e., published) by employing differential privacy.
4. Automation Engineering:
   1. Identification of the privacy risks derived from handling data generated through sensors.
   2. Introduction to the privacy risks associated with geospatial information (reverse geocoding) and main approaches to handle geographical data in a privacy preserving manner (geomasking and metric Differential Privacy).
   3. Application of the techniques learned during lecture to protect sensor data and user generated information.
5. Telecommunications:
   1. Analysis of the main approaches studied in the theoretical part of the course explicitly designed for telecommunication data, such as Microsoft’s LDP.
   2. Application of privacy preserving techniques to telecommunication tasks, such as traffic pattern analysis and resource allocation.
   3. Implementation of privacy-preserving solutions specifically tailored towards telecommunication and stream data.

Schedule:

1. 19/5/2025 – 14:30-18:30
2. 20/5/2025 – 9-13    
3. 21/5/2025 – 9-13
4. 21/5/2025 – 14:30-18:30  - new - 
5. 22/5/2025 – 9-13
6. 23/5/2025 – 9-13

Hours:
16 hours (4 credits)

Room:

Aula Riunioni del Dipartimento di Ingegneria dell’Informazione, Via G. Caruso 16, Pisa - Ground Floor

To register to the course, click here

Short Abstract:

ill-posed or ill-conditioned problems are characterized by non-unique solution and/or deleterious noise propagation from the input data to the retrieved solution. This kind of problem arises in a multitude of technical and scientific topics, such as biomedical diagnostic, computational imaging, machine learning, and numerical simulations of physical systems. In particular, ill-posedness and ill-conditioning often arise in the so-called inverse problems, wherein the cause-effect relationship is investigated in the reversed way; an example is given by the CT scan, which aims to reconstruct the structure of a body (the cause) taking as input data the measurements of the scattered X-rays (the effect). Regularization methods pursue the mitigation of the ill-posedness and ill-conditioning, and so they enable the retrieval of solutions of practical interest from problems that would be otherwise untreatable.
The course aims to provide an introduction on regularization methods that can help to deal with, or better understand, problems often met in engineering. The presented regularization methods will be supported by MATLAB trainings.

Course Contents in brief:

1. Introduction to ill-posedness
2. Concept of inverse problem
3. Ill-posedness in inverse linear problems: image deconvolution
4. Discretization of an ill-posed inverse linear problem
5. Ill-conditioning: the condition number
6. MATLAB training: practical issues of inverse filtering of images affected by blurring and noise
7. Solution of inverse linear problem in the sense of minimum least squares and related ill-posedness
8. MATLAB training: practical issues of image deblurring and denoising by means of sparse algebraic linear systems
9. Regularization methods for linear problems: Truncated Singular Value Decomposition (TSVD), Landweber and conjugate gradient methods
10. MATLAB training: application of TSVD, Landweber and conjugate gradient methods for image deblurring and denoising
11. Ill-posedness in inverse linear problems: Electrical Impedance Tomography (EIT) for biomedical applications
12. Finite Elements Methods to discretize the EIT problem
13. MATLAB training: EIT for breath monitoring with the open-source EIDORS toolbox
14. Ill-posedness in machine learning
15. Tikhonov regularization in Support Vector Machine (SVM)
16. Stochastic regularization methods
17. MATLAB training: regularization methods at work to train SVM and neural networks

Schedule:

1. Monday, May 12, h. 9:00-13:00
2. Tuesday, May 13, h. 14:00-17:00
3. Wednesday, May 14, h. 14:00-17:00
4. Thursday, May 15, h. 14:00-17:00
5. Friday, May 16, h. 14:00-17:00

Hours:
16 hours (4 credits)

Room:

Aula Riunioni del Dipartimento di Ingegneria dell’Informazione, Via G. Caruso 16, Pisa - Ground Floor

To register to the course, click here

Short Abstract:

In this course, practical methodologies for marine data analysis and modelling will be presented.

The course will cover specific classes of problems in marine science and their corresponding solutions, adopting state-of-the-art computer science technologies and methodologies. The explained techniques will include:

1. Unsupervised approaches to discover patterns of habitat change and predict fishing vessel activity patterns: Principal Component Analysis and Maximum Entropy for feature selection; KMeans, XMeans, DBScan, and Local Outlier Factor cluster analysis; Singular Spectrum Analysis for time series forecasting;
2. Supervised approaches for species distribution prediction and invasive species monitoring: Feed-Forward Artificial Neural Networks, Support Vector Machines, AquaMaps, Maximum Entropy;
3. Bayesian models to predict fish stock availability in specific fishing areas; 

These methods will be applied to marine data such as vessel transmitted data, species observation records, and catch and vessel time series that fall into the Big Data category. These data are crucial to safeguard food availability and economic welfare, which are fundamental to human life. For example, predicting the impact of climate change on species habitat distribution contributes to avoiding economic and biodiversity collapse due to sudden ecosystem change. Likewise, monitoring the effect of overfishing on fish stocks and marine biodiversity prevents ecosystem and economic collapse.

The explained techniques will address real use cases of the United Nations (FAO, UNESCO, UNEP, and others) for marine food and ecosystem safety and illustrate the new lines of research in this context. They are also general enough to be applied to Big Data of other domains. The analysed data have indeed general characteristics of Big Data such as constantly incrementing volume, vast heterogeneity and complexity, and unreliable content. For this reason, the methodologies will be illustrated in the context of the Open Science paradigm, characterized by the repeatability, reproducibility, and cross-domain reuse of all experimental phases.

The course will be interactive and made up of practical exercises. Attendees will use online environments to parametrize the models, run the experiments, and potentially modify the models.

Course Contents in brief:

1. Big data and marine data
2. Geospatial data
3. Parameter selection techniques for environmental variables
4. Distance and density-based cluster analysis for habitat and vessel pattern recognition
5. Artificial Neural Networks, Support Vector Machines, and Maximum Entropy models for species distribution modelling
6. Techniques for time series forecasting applied to marine data
7. Open Science approaches

Schedule:

1. Day1 – May 6, 2025 – h. 9.00-13.00 Introduction to marine data and Open Science methodologies
2. Day2 – May 7, 2025 – h. 9.00-13.00 Data selection techniques and pattern recognition
3. Day3 – May 8, 2025 – h. 9.00-13.00 Supervised modelling of species distributions and invasions
4. Day4 – May 9, 2025 – h. 9.00-13.00 Data mining techniques for extracting knowledge from biodiversity and vessel data

Hours:
20 hours (5 credits)

Room:

Meeting Room, Dept. of Information Engineering, Largo Lazzarino 1, Pisa, Sixth Floor

To register to the course, click here

Short Abstract:

Recommender Systems have transformed user experiences across industries such as e-commerce, media streaming, and healthcare [1]. This course, tailored for PhD students, offers a comprehensive introduction to RS algorithms, covering foundational concepts like collaborative filtering and matrix factorization, emphasizing how Recommender Systems use user data to generate personalized recommendations. The course will delve into the synergy between AI and Recommender Systems,
teaching machine learning techniques for Recommendation and introducing deep learning for complex user preferences and item relationships [2].
The course will also showcase the power of Recommender Systems in specific fields, demonstrating their practical applications and impact.
In Telecommunications [3,4,5], Recommender Systems can be employed to personalize network resource allocation by analyzing user profiles and traffic patterns, ensuring efficient and userspecific network management.
In Biosciences [6,7,8], Recommender Systems can assist in drug discovery by recommending promising drug candidates based on complex data analyses, or be implemented for personalized medicine, where targeted therapies are suggested according to individual patient profiles, leading to more effective treatments.
In the field of Automation Engineering [9,10,11], Recommender Systems are utilized to analyze sensor data, predicting component degradation and recommending maintenance schedules to ensure optimal performance and longevity of devices.
By the end of the course, students will gain a thorough understanding of Recommender Systems principles and their applications in diverse research domains. They will be equipped with the practical skills and tools necessary to implement and evaluate their own recommender systems using Python libraries such as NumPy, Pandas, Scikit-learn, and TensorFlow/PyTorch for deep learning applications.

Course Contents in brief:

1. Foundational Concepts:
   1. Define Recommender Systems and their impact across various industries.
   2. Explore core algorithms like collaborative filtering, Markov chains, and hybrid approaches.
   3. Discuss scalability challenges and optimization techniques for large-scale implementations.
   4. Analyze case studies of successful implementations from diverse domains.
2. Machine Learning and Neural Networks for Recommendations:
   1. Learn key AI techniques used in Recommendation: matrix factorization, neighborhood methods, and an introduction to deep learning for recommendations.
   2. Understand the role of neural networks in building advanced recommender systems that capture complex user preferences and item relationships.
   3. Explore various neural network architectures commonly used for recommendations, such as Recurrent Neural Networks and Transformers.
3. Telecommunications:
   1. Personalization of network resource allocation based on user profiles and traffic patterns.
   2. Optimization of content delivery with recommendation of appropriate caching strategies.
   3. Development of recommender systems for suggesting network service plans tailored to individual customer needs.
4. Biosciences:
   1. Analyze vast patient data and molecular structures using Recommender Systems for drug discovery, recommending promising drug candidates.
   2. Implement systems for personalized medicine by recommending targeted therapies based on individual patient profiles.
   3. Utilize Recommender Systems to recommend targeted interventions for disease prevention and management.
5. Automation Engineering:
   1. Utilize Recommender Systems to analyze sensor data and recommend maintenance schedules based on predicted component degradation.
   2. Implement Recommender Systems to recommend optimal component sourcing and production strategies based on real-time demand and inventory data.
   3. Design Recommender Systems to recommend product configurations tailored to individual customer needs and specifications.

Schedule:

1. 5/5/2025 – 14:30-18:30
2. 6/5/2025 – 14:30-18:30
3. 7/5/2025 – 14:30-18:30
4. 8/5/2025 – 14:30-18:30
5. 9/5/2025 – 14:30-18:30

Hours:
20 hours (5 credits)

Room:

Aula Riunioni del Dipartimento di Ingegneria dell’Informazione, Via G. Caruso 16, Pisa - Ground Floor

To register to the course, click here

Short Abstract:

Several problems in advanced engineering rely on the manipulation of vectors or matrices that are functions of other vectors or matrices, and their derivatives and differentials. Examples arise in various fields spanning Analytical Mechanics, Robot Control, Deep Neural Networks, Optimization and Computer Vision.
Although the such objects are studied since more than a century, modern theory of matrix algebra and matrix calculus introduced, based the Kronecker product and matrix vectorization, simple yet unambiguous, therefore powerful and flexible, definitions of matrix derivatives and matrix differentials. Those tools have been successfully used to obtain novel theoretical results in the fields of Probability, Psychometrics and Econometrics, by enabling the formal manipulation of complex expressions.
This course will introduce such mathematical instruments in detail and present their application to several relevant problems encountered in the aforementioned engineering fields, to streamline their description and yield more elegant and compact derivations, that will hopefully enable advanced student of those fields to achieve novel and significant results.

Course Contents in brief:

1. Matrix vectorization, Kronecker product, Trace and their properties
2. Definition of Matirx Derivatives and Matrix Differentials and some Notable Results
3. Applications to Analytical Mechanics: Rotation differentials, Robots Jacobian and Stiffness
4. Applications to Robot Control: Lagrange Dynamics, Regressor Form of Robot Dynamics
5. Applications to AI: description of a Deep Neural Network, Computer Vision.

Schedule:

June 23, 2025, 9:00-13.00:

1. Matrix vectorization, Kronecker product, Trace and their properties (2h)
2. Magnus definition of derivatives and their application to matrix calculus (1h)
3. Series expansion of a vector field (1h)

June 24, 2025, 9:00-13:00:

1. Derivative of matrix inverse, matrix determinant and matrix pseudo-inverse (2h)
2. Integration of angular speeds into rotation matrices, definition of angular error (1h)
3. Jacobians: algebraic, geometric, and geometric from algebraic (1h)

June 25, 2025, 9:00-13:00:

1. Jacobians: algebraic, geometric, and geometric from algebraic (1h)
2. Stiffness of a kinematic chain (2h)
3. Second Order and Higher Order Differential Kinematics (1h)

June 26, 2025, 9:00-13:00:

1. Lagrangian dynamics with kron and vec (2h)
2. Robot Kinematics and Dynamics in Regressor Form: either and both (2h)

June 27, 2025, 9:00-13:00:

1. Deep Neural Networks and Back-propagation (2h)
2. Derivative of ReLU, MAX, softMAX, and softReLU (1h)
3. Exercise: Neuromorphic Adaptive control with arbitrary gain matrix (1h)