Mathematical models for cellular aggregation: the chemotactic instability and clustering formation

In this thesis we present a mathematical formulation of the interaction between microorganisms such as bacteria or amoebae and chemicals, often produced by the organisms themselves. This interaction is called chemotaxis and leads to cellular aggregation. We derive some models to describe chemotaxis. The first is the pioneristic Keller-Segel parabolic-parabolic model and it is derived by two different frameworks: a macroscopic perspective and a microscopic perspective, in which we start with a stochastic differential equation and we perform a mean-field approximation. This parabolic model may be generalized by the introduction of a degenerate diffusion parameter, which depends on the density itself via a power law. Then we derive a model for chemotaxis based on Cattaneo's law of heat propagation with finite speed, which is a hyperbolic model. The last model proposed here is a hydrodynamic model, which takes into account the inertia of the system by a friction force. In the limit of strong friction, the model reduces to the parabolic model, whereas in the limit of weak friction, we recover a hyperbolic model. Finally, we analyze the instability condition, which is the condition that leads to aggregation, and we describe the different kinds of aggregates we may obtain: the parabolic models lead to clusters or peaks whereas the hyperbolic models lead to the formation of network patterns or filaments. Moreover, we discuss the analogy between bacterial colonies and self gravitating systems by comparing the chemotactic collapse and the gravitational collapse (Jeans instability).

Competition between boson condensation and molecule formation in 2D Bose-Fermi mixtures with a pairing interaction

The study of ultra-cold atomic gases is one of the most active field in contemporary physics. The main motivation for the interest in this field consists in the possibility to use ultracold gases to simulate in a controlled way quantum many-body systems of relevance to other fields of physics, or to create novel quantum systems with unusual physical properties. An example of the latter are Bose-Fermi mixtures with a tunable pairing interaction between bosons and fermions. In this work, we study with many-body diagrammatic methods the properties of this kind of mixture in two spatial dimensions, extending previous work for three dimensional Bose-Fermi mixtures. At zero temperature, we focus specifically on the competition between boson condensation and the pairing of bosons and fermions into molecules. By a numerical solution of the main equations resulting by our many-body diagrammatic formalism, we calculate and present results for several thermodynamic quantities of interest. Differences and similarities between the two-dimensional and three-dimensional cases are pointed out. Finally, our new results are applied to discuss a recent proposal for creating a p-wave superfluid in Bose-Fermi mixtures with the fermionic molecules which form for sufficiently strong Bose-Fermi attraction.

Computer vision in aseptic pharmaceutical manufacturing: a deep learning-based approach to vial inspection and pack formation during a lyophilizer loading cycle

Vision systems are powerful tools playing an increasingly important role in modern industry, to detect errors and maintain product standards. With the enlarged availability of affordable industrial cameras, computer vision algorithms have been increasingly applied in industrial manufacturing processes monitoring. Until a few years ago, industrial computer vision applications relied only on ad-hoc algorithms designed for the specific object and acquisition setup being monitored, with a strong focus on co-designing the acquisition and processing pipeline. Deep learning has overcome these limits providing greater flexibility and faster re-configuration. In this work, the process to be inspected consists in vials’ pack formation entering a freeze-dryer, which is a common scenario in pharmaceutical active ingredient packaging lines. To ensure that the machine produces proper packs, a vision system is installed at the entrance of the freeze-dryer to detect eventual anomalies with execution times compatible with the production specifications. Other constraints come from sterility and safety standards required in pharmaceutical manufacturing. This work presents an overview about the production line, with particular focus on the vision system designed, and about all trials conducted to obtain the final performance. Transfer learning, alleviating the requirement for a large number of training data, combined with data augmentation methods, consisting in the generation of synthetic images, were used to effectively increase the performances while reducing the cost of data acquisition and annotation. The proposed vision algorithm is composed by two main subtasks, designed respectively to vials counting and discrepancy detection. The first one was trained on more than 23k vials (about 300 images) and tested on 5k more (about 75 images), whereas 60 training images and 52 testing images were used for the second one.