Monoidal categories for the physics of integrable models

Scopo di questa tesi é di evidenziare le connessioni tra le categorie monoidali, l'equazione di Yang-Baxter e l’integrabilità di alcuni modelli. Oggetto prinacipale del nostro lavoro é stato il monoide di Frobenius e come sia connesso alle C∗-algebre. In questo contesto la totalità delle dimostrazioni sfruttano la strumentazione dell'algebra diagrammatica. Nel corso del lavoro di tesi sono state riprodotte tali dimostrazioni tramite il più familiare linguaggio dell’algebra multilineare allo scopo di rendere più fruibili questi risultati ad un raggio più ampio di potenziali lettori.

Deep learning for computer vision: a comparison between convolutional neural networks and hierarchical temporal memories on object recognition tasks

In recent years, Deep Learning techniques have shown to perform well on a large variety of problems both in Computer Vision and Natural Language Processing, reaching and often surpassing the state of the art on many tasks. The rise of deep learning is also revolutionizing the entire field of Machine Learning and Pattern Recognition pushing forward the concepts of automatic feature extraction and unsupervised learning in general. However, despite the strong success both in science and business, deep learning has its own limitations. It is often questioned if such techniques are only some kind of brute-force statistical approaches and if they can only work in the context of High Performance Computing with tons of data. Another important question is whether they are really biologically inspired, as claimed in certain cases, and if they can scale well in terms of "intelligence". The dissertation is focused on trying to answer these key questions in the context of Computer Vision and, in particular, Object Recognition, a task that has been heavily revolutionized by recent advances in the field. Practically speaking, these answers are based on an exhaustive comparison between two, very different, deep learning techniques on the aforementioned task: Convolutional Neural Network (CNN) and Hierarchical Temporal memory (HTM). They stand for two different approaches and points of view within the big hat of deep learning and are the best choices to understand and point out strengths and weaknesses of each of them. CNN is considered one of the most classic and powerful supervised methods used today in machine learning and pattern recognition, especially in object recognition. CNNs are well received and accepted by the scientific community and are already deployed in large corporation like Google and Facebook for solving face recognition and image auto-tagging problems. HTM, on the other hand, is known as a new emerging paradigm and a new meanly-unsupervised method, that is more biologically inspired. It tries to gain more insights from the computational neuroscience community in order to incorporate concepts like time, context and attention during the learning process which are typical of the human brain. In the end, the thesis is supposed to prove that in certain cases, with a lower quantity of data, HTM can outperform CNN.

Model categories

The purpose of this thesis is to present some fundamental results about model categories, and to give some examples of categories that can be equipped with a model structure.

Regular and exact categories

Lo scopo del lavoro è quello di presentare alcune proprietà di base delle categorie regolari ed esatte nel contesto della teoria delle categoria algebrica.

Tor network forensics and hidden service deanonymization

The cybernetics revolution of the last years improved a lot our lives, having an immediate access to services and a huge amount of information over the Internet. Nowadays the user is increasingly asked to insert his sensitive information on the Internet, leaving its traces everywhere. But there are some categories of people that cannot risk to reveal their identities on the Internet. Even if born to protect U.S. intelligence communications online, nowadays Tor is the most famous low-latency network, that guarantees both anonymity and privacy of its users. The aim of this thesis project is to well understand how the Tor protocol works, not only studying its theory, but also implementing those concepts in practice, having a particular attention for security topics. In order to run a Tor private network, that emulates the real one, a virtual testing environment has been configured. This behavior allows to conduct experiments without putting at risk anonymity and privacy of real users. We used a Tor patch, that stores TLS and circuit keys, to be given as inputs to a Tor dissector for Wireshark, in order to obtain decrypted and decoded traffic. Observing clear traffic allowed us to well check the protocol outline and to have a proof of the format of each cell. Besides, these tools allowed to identify a traffic pattern, used to conduct a traffic correlation attack to passively deanonymize hidden service clients. The attacker, controlling two nodes of the Tor network, is able to link a request for a given hidden server to the client who did it, deanonymizing him. The robustness of the traffic pattern and the statistics, such as the true positive rate, and the false positive rate, of the attack are object of a potential future work.