Methods for integrating machine learning and constrained optimization

In the framework of industrial problems, the application of Constrained Optimization is known to have overall very good modeling capability and performance and stands as one of the most powerful, explored, and exploited tool to address prescriptive tasks. The number of applications is huge, ranging from logistics to transportation, packing, production, telecommunication, scheduling, and much more. The main reason behind this success is to be found in the remarkable effort put in the last decades by the OR community to develop realistic models and devise exact or approximate methods to solve the largest variety of constrained or combinatorial optimization problems, together with the spread of computational power and easily accessible OR software and resources. On the other hand, the technological advancements lead to a data wealth never seen before and increasingly push towards methods able to extract useful knowledge from them; among the data-driven methods, Machine Learning techniques appear to be one of the most promising, thanks to its successes in domains like Image Recognition, Natural Language Processes and playing games, but also the amount of research involved. The purpose of the present research is to study how Machine Learning and Constrained Optimization can be used together to achieve systems able to leverage the strengths of both methods: this would open the way to exploiting decades of research on resolution techniques for COPs and constructing models able to adapt and learn from available data. In the first part of this work, we survey the existing techniques and classify them according to the type, method, or scope of the integration; subsequently, we introduce a novel and general algorithm devised to inject knowledge into learning models through constraints, Moving Target. In the last part of the thesis, two applications stemming from real-world projects and done in collaboration with Optit will be presented.

Mathematical methods to analyze and interpret calcium signals of astrocytes

Astrocytes are the most numerous glial cell type in the mammalian brain and permeate the entire CNS interacting with neurons, vasculature, and other glial cells. Astrocytes display intracellular calcium signals that encode information about local synaptic function, distributed network activity, and high-level cognitive functions. Several studies have investigated the calcium dynamics of astrocytes in sensory areas and have shown that these cells can encode sensory stimuli. Nevertheless, only recently the neuro-scientific community has focused its attention on the role and functions of astrocytes in associative areas such as the hippocampus. In our first study, we used the information theory formalism to show that astrocytes in the CA1 area of the hippocampus recorded with 2-photon fluorescence microscopy during spatial navigation encode spatial information that is complementary and synergistic to information encoded by nearby "place cell" neurons. In our second study, we investigated various computational aspects of applying the information theory formalism to astrocytic calcium data. For this reason, we generated realistic simulations of calcium signals in astrocytes to determine optimal hyperparameters and procedures of information measures and applied them to real astrocytic calcium imaging data. Calcium signals of astrocytes are characterized by complex spatiotemporal dynamics occurring in subcellular parcels of the astrocytic domain which makes studying these cells in 2-photon calcium imaging recordings difficult. However, current analytical tools which identify the astrocytic subcellular regions are time consuming and extensively rely on user-defined parameters. Here, we present Rapid Astrocytic calcium Spatio-Temporal Analysis (RASTA), a novel machine learning algorithm for spatiotemporal semantic segmentation of 2-photon calcium imaging recordings of astrocytes which operates without human intervention. We found that RASTA provided fast and accurate identification of astrocytic cell somata, processes, and cellular domains, extracting calcium signals from identified regions of interest across individual cells and populations of hundreds of astrocytes recorded in awake mice.

Data-driven and data-oriented methods for materials science and technologies

The discovery of new materials and their functions has always been a fundamental component of technological progress. Nowadays, the quest for new materials is stronger than ever: sustainability, medicine, robotics and electronics are all key assets which depend on the ability to create specifically tailored materials. However, designing materials with desired properties is a difficult task, and the complexity of the discipline makes it difficult to identify general criteria. While scientists developed a set of best practices (often based on experience and expertise), this is still a trial-and-error process. This becomes even more complex when dealing with advanced functional materials. Their properties depend on structural and morphological features, which in turn depend on fabrication procedures and environment, and subtle alterations leads to dramatically different results. Because of this, materials modeling and design is one of the most prolific research fields. Many techniques and instruments are continuously developed to enable new possibilities, both in the experimental and computational realms. Scientists strive to enforce cutting-edge technologies in order to make progress. However, the field is strongly affected by unorganized file management, proliferation of custom data formats and storage procedures, both in experimental and computational research. Results are difficult to find, interpret and re-use, and a huge amount of time is spent interpreting and re-organizing data. This also strongly limit the application of data-driven and machine learning techniques. This work introduces possible solutions to the problems described above. Specifically, it talks about developing features for specific classes of advanced materials and use them to train machine learning models and accelerate computational predictions for molecular compounds; developing method for organizing non homogeneous materials data; automate the process of using devices simulations to train machine learning models; dealing with scattered experimental data and use them to discover new patterns.