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Interventional causal models describe several joint distributions over some variables used to describe a system, one for each intervention setting. They provide a formal recipe for how to move between the different joint distributions and…

A few observations concerning topological string theories at the string-tree level are presented: (1) The tree-level, large phase space solution of an arbitrary model is expressed in terms of a variational problem, with an ``action'' equal,…

We develop a purely set-theoretic formalism for binary trees and binary graphs. We define a category of binary automata, and display it as a fibred category over the category of binary graphs. We also relate the notion of binary graphs to…

Tree-child networks are a recently-described class of directed acyclic graphs that have risen to prominence in phylogenetics (the study of evolutionary trees and networks). Although these networks have a number of attractive mathematical…

Motivated by chemical applications, we revisit and extend a family of positive definite kernels for graphs based on the detection of common subtrees, initially proposed by Ramon et al. (2003). We propose new kernels with a parameter to…

We show that contrary to appearances, Multimodal Type Theory (MTT) over a 2-category M can be interpreted in any M-shaped diagram of categories having, and functors preserving, M-sized limits, without the need for extra left adjoints. This…

Source code comes in different shapes and forms. Previous research has already shown code to be more predictable than natural language as well as highlighted its statistical predictability at the token level: source code can be natural.…

The concept of derivative coordinate functions proved useful in the formulation of analytic fractal functions to represent smooth symmetric binary fractal trees [1]. In this paper we introduce a new geometry that defines the fractal space…

We consider actions of completely metrisable groups on simplicial trees in the context of the Bass--Serre theory. Our main result characterises continuity of the amplitude function corresponding to a given action. Under fairly mild…

Let $G=$ $\left( V,E\right) $ be a simple graph.\ A non-empty set $S \subseteq V$ is called a global offensive alliance if $S$ is a dominating set and for every vertex $v$ in $V-S$, at least half of the vertices from the closed neighborhood…

Controllable Automatic Text Simplification (CATS) produces user-tailored outputs, yet controllability is often treated as a decoding problem and evaluated with metrics that are not reflective to the measure of control. We observe that…

Dynamic fault trees (DFTs) have emerged as an important tool for capturing the dynamic behavior of system failure. These DFTs are then analyzed qualitatively and quantitatively using stochastic or algebraic methods to judge the failure…

The recently introduced graph parameter tree-cut width plays a similar role with respect to immersions as the graph parameter treewidth plays with respect to minors. In this paper, we provide the first algorithmic applications of tree-cut…

This work introduces a novel interpretable machine learning method called Mixture of Decision Trees (MoDT). It constitutes a special case of the Mixture of Experts ensemble architecture, which utilizes a linear model as gating function and…

Presentations of categories are a well-known algebraic tool to provide descriptions of categories by means of generators, for objects and morphisms, and relations on morphisms. We generalize here this notion, in order to consider situations…

Evaluating the security of multi-agent systems (MASs) powered by large language models (LLMs) is challenging, primarily because of the systems' complex internal dynamics and the evolving nature of LLM vulnerabilities. Traditional attack…

Human cognition can leverage fundamental conceptual knowledge, like geometric and kinematic ones, to appropriately perceive, comprehend and interact with novel objects. Motivated by this finding, we aim to endow machine intelligence with an…

Embedded Systems (ES) development has been historically focused on functionality rather than security, and today it still applies in many sectors and applications. However, there is an increasing number of security threats over ES, and a…

This paper introduces TACTIC-GRAPHS, a system that combines spectral graph theory and multimodal graph neural reasoning for semantic understanding and threat detection in tactical video under high noise and weak structure. The framework…

We study the problem of efficient adversarial attacks on tree based ensembles such as gradient boosting decision trees (GBDTs) and random forests (RFs). Since these models are non-continuous step functions and gradient does not exist, most…