Sam Gonzalez

Structural type theory is an extension of simple type theory that incorporates types for any kind of mathematical structure and allows isomorphic structures to be identified within them. In order to guarantee consistency, the system incorporates several syntactic restrictions. Modelling structural type theory in Tarski–Grothendieck set theory and extending the definition of transport functions, we show that some of these restrictions can be lifted, thus improving the expressive power of the system. In addition, we show how to treat axiomatic theories as first-class objects in our reformulation of structural type theory, and we state and prove within it a result analogous to the morphism theorem by Farmer.

In this work, we introduce families of multimodal maps based on logistic map, i.e., families of m-modal maps are defined on an interval I ⊂ ℝ, which is partitioned into non-uniform subdomains, with m ∈ ℕ. Because the subdomains of the partition are not uniform, each subdomain contains a unimodal map, given by the logistic map, that can have different heights. Therefore, we give the necessary and sufficient conditions for these modal maps present a multimodal family of m-modal maps, i.e., a bifurcation parameter can set a unimodal map, a bimodal map, up to a m -modal map. Some numerical examples are given according to the developed theory. Some numerical examples are given in accordance with the developed theory.

The Secure Shell Protocol (SSH) is a well-known standard protocol, mainly used for remotely accessing shell accounts on Unix-like operating systems to perform administrative tasks. As a result, the SSH service has been an appealing target for attackers, aiming to guess root passwords performing dictionary attacks or to directly exploit the service itself. To identify such situations, this article addresses the detection of SSH anomalous connections from an intrusion detection perspective. The main idea is to compare several strategies and approaches for a better detection of SSH-based attacks. To test the classification performance of different classifiers and combinations of them, SSH data coming from a real-world honeynet are gathered and analysed. For comparison purposes and to draw conclusions about data collection, both packet-based and flow data are analysed. A wide range of classifiers and ensembles are applied to these data, as well as different validation schemes for better analysis of the obtained results. The high-rate classification results lead to positive conclusions about the identification of malicious SSH connections.