Topological ManifoldsMarzio De Corato
03 / Blog & ideas

Blog & ideas.

Here I bring together essays and readings through which I explore information, knowledge and decisions, following the questions that arise when scientific problems meet their historical and cultural implications.

Julia set
Essays / 2026-11-12

The War of False Perceptions

Alerts in European schools show how an unfounded threat can consume resources, change decisions and prolong its effects. This essay examines that pressure through cognitive overload, orientation and the OODA loop in John Boyd’s thinking.

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Essays / 2026-11-07

Striking the Nerves of the System

Starting from altered commands and false alarms, the essay follows the checks, decisions and shifts of resources that a signal can provoke, drawing on Liddell Hart and John Boyd to examine how disrupted information affects an organisation’s freedom of action and cohesion.

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Graph theory and cyber-attacks

Unaffected nodeCompromised node

When devices, services and identities are described through their relationships, system security can be studied as a structural problem in which both a vulnerability and the paths through which it could expose other resources matter.

From connections to attack paths

A graph G = (V, E) consists of vertices V and edges E. In an asset network, vertices may represent devices or services, while edges describe connections, dependencies or trust relationships. An attack graph instead represents conditions, actions or system states, depending on the model, to examine how several steps can combine into a compromise.

G = (V, E)

The analogy with an epidemic helps illustrate how a compromise can spread between nodes, provided that the conditions for each transition are considered. Credentials, permissions, vulnerabilities and configurations determine which paths are feasible; a connection alone describes a possibility of communication.

How this supports defence

Path analysis helps identify the resources reachable from an initial position and the connections that form critical passages. Comparing the graph before and after a change shows how network segmentation, reduced privileges or a vulnerability fix can interrupt particular sequences. A node’s importance depends on its role and context, so its number of connections gives only a partial account of risk.

Reading this figure

Red nodes marked with a cross represent compromised systems in the scenario; green nodes remain unaffected, while pale pulses follow the propagation paths. The map provides a conventional geographical layout for an illustrative network whose links and timing are constructed to clarify the phenomenon. It does not show observed attacks or estimate compromise probabilities.

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Relations, assumptions and study references. These are not empirical results from the author’s research.

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