Topological ManifoldsMarzio De Corato
Topological ManifoldsTime series, quantitative methods and financial modelling
02 / Time series, quantitative methods and financial modelling

Time series, quantitative methods and financial modelling.

Data analysis and applied interests

Covariance ellipsoid
Research problem

How can a forecast be evaluated when data change over time?

Time-series analysis includes the evaluation of forecasting methods and the translation of numerical procedures between programming languages, through experience involving COVID-19 data and, in Data Science 4Citizens, climate series used to teach data-analysis techniques.

Approach and tools

This experience includes statistical models and computational tools in Python and R. His training in Data Science and Economics, together with teaching in mathematical methods for finance, connects with his interest in probabilistic market modelling and risk assessment. These subjects form an applied area of interest, while the main publication record concerns cybersecurity and nanostructure physics.

Time seriesForecast evaluationProbabilistic modellingPython and R

Related activities

Data Science Assistant, University of Milan: COVID-19 time series and forecast evaluation (2020–2021).

Data Science 4Citizens: analysis of climate time series with R (2021–2022).

Teaching support in Mathematical Methods for Finance (2023 and 2024); adjunct teaching in Advanced Calculus and Stochastic Processes (since 2024/2025, ongoing).

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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.

References

Sheyner et al. — Automated Generation and Analysis of Attack Graphs, Carnegie Mellon University

NIST IR 7788 — Security Risk Analysis of Enterprise Networks Using Probabilistic Attack Graphs

Natural Earth cartography — public-domain data

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