# PGLuca Porta Mana’s page

“It is important for him who wants to discover not to confine himself to one chapter of science, but to keep in touch with various others.”

## Intro

I am a researcher and student interested in all science, and especially in these fields:

general relativity \(\quad\pmb{G}=\smash{\frac{8\pi\kappa}{c^{4}}} \pmb{T}\)

quantum theory \(\quad\mathrm{P}(O_{i} \rvert M_{k} \land S_{j}) = \mathop{\rm tr}(\pmb{M}_{ik}\,\pmb{\rho}_{j})\)

the probability calculus, that is, Bayesian probability theory, including machine learning and statistics \(\quad\mathrm{P}(A \land B \rvert I) = \mathrm{P}(A \rvert B \land I)\; \mathrm{P}(B \rvert I)\)

continuum thermomechanics, including subfields such as fluid dynamics, thermostatics, and particle mechanics \(\quad\pmb{b} + \nabla\pmb{T} =0\)

differential, convex, affine geometry, and Peano spaces \(\quad\mathrm{d}\rho =0\)

formal logic and constructive (computable) analysis \(\quad\frac{I\;\vdash\; B \quad I\land B\; \vdash\; A}{I \;\vdash\; A \land B}\)

quantization of Julio Iglesias

history of science

(statistical mechanics – but that’s just an application of the probability calculus to continuum thermomechanics)

In each of the above fields I’ve done original research or given seminars or lectures. Feel free to take a look at my CV or the projects and contributions below.

Finding and rewriting physical laws is for me a great source of joy and awe. For this reason I’m not interested in algorithms or artificial intelligence that could find such laws for me. They are like algorithms that could look at the stars for me, or read a book for me, or eat for me, or go on holiday for me, or play a game for me. What’s the point?

Presently at *HVL
Western Norway University of Applied Sciences* in Bergen. You
can write to me at pglZZ@portamanaZZ.org,
or on Matrix at pglpmZZ:matrix.sdf.org
(remove all “ZZ” from these addresses, for anti-spam purposes), or on
Mastodon.

There’s also a personal page (an exercise in self-indulgence).

“I don’t know what’s the matter with people: they don’t learn by understanding; they learn by some other way – by rote, or something. Their knowledge is so fragile!”

## Memos, lecture notes, talks

Here are some memos, lecture notes, talks.

Foundations of data science, in collaboration with Steffen Mæland. This is a BSc or MSc course that tries to explain the fundamentals of “Bayesian nonparametric frequency inference” (the part of decision theory which many machine-learning algorithms are a sub-optimal approximation of) with as simple maths as possible, and keeping in mind connections with artificial intelligence and “data science”.

Introduction to probability theory 2: basics of Bayesian theory

Exercise: The Monty Hall problem and some variations, from the point of view of the probability calculus (with solutions)

Cross-validation and early stopping: a Bayesian point of view? (warning: 10 MB file). Invited talk at the 11th Trondheim Symposium in Statistics, Trondheim, Norway.

Uncertainty, information, and entropy: comparison of two definitions. With G. Björk. Invited talk at the Ninth International Conference on Squeezed States and Uncertainty Relations ICSSUR 2005, Besançon, France.

“If what we are discussing were a point of law or of the humanities, in which neither true nor false exists, one might trust in subtlety of mind and readiness of tongue and in the greater experience of the writers, and expect him who excelled in those things to make his reasoning most plausible, and one might judge it to be the best. But in the natural sciences, whose conclusions are true and necessary and have nothing to do with human will, one must take care not to place oneself in the defense of error; for here a thousand Demostheneses and a thousand Aristotles would be left in the lurch by every mediocre wit who happened to hit upon the truth for himself.”

## Scientific research

Most works I authored and co-authored can be found for free at Open Science Framework. Some are also on arXiv, although I find arXiv’s screening policies increasingly shady. I strongly believe that all research papers should be free and that it’s ludicrous that we pay to read research we fund.

See also my GitHub, Orcid, Open Science Framework, Semantic Scholar pages.

Dimensional analysis in relativity and in differential geometry

P.G.L. Porta Mana, I. Rye, A. Vik, M. Kociński, A. J. Lundervold, A. Lundervold, A. S. Lundervold: Personalized prognosis & treatment using Lusted-Jaynes machines: An example study on conversion from Mild Cognitive Impairment to Alzheimer’s Disease

K. Dyrland, A. S. Lundervold, P.G.L. Porta Mana: Don’t guess what’s true: choose what’s optimal. A probability transducer for machine-learning classifiers

K. Dyrland, A. S. Lundervold, P.G.L. Porta Mana: Does the evaluation stand up to evaluation? A first-principle approach to the evaluation of classifiers

A relation between log-likelihood and cross-validation log-scores

P.G.L. Porta Mana, V. Rostami, E. Torre, Y. Roudi: Maximum-entropy and representative samples of neuronal activity: a dilemma

C. Bachmann, H. I. Jacobs, P.G.L. Porta Mana, et al.: On the extraction and analysis of graphs from resting-state fMRI to support a correct and robust diagnostic tool for Alzheimer’s disease

P.G.L. Porta Mana, C. Bachmann, A. Morrison: Inferring health conditions from fMRI-graph data

Force, inertia, metric in Newtonian relativity and general relativity

Unlearning and Seyab’s theorem: a dialogue about updating probability

J. Krishnan, P.G.L. Porta Mana, M. Helias, et al.: Perfect detection of spikes in the linear sub-threshold dynamics of point neurons

V. Rostami, P.G.L. Porta Mana, M. Helias: Pairwise maximum-entropy models and their Glauber dynamics: bimodality, bistability, non-ergodicity problems, and their elimination via inhibition

Maximum-entropy from the probability calculus: exchangeability, sufficiency

L. Zanna, P.G.L. Porta Mana, J. Anstey, et al.: Scale-aware deterministic and stochastic parametrizations of eddy-mean flow interaction

P.G.L. Porta Mana, E. Torre, V. Rostami: Inferences from a network to a subnetwork and vice versa under an assumption of symmetry

P.G.L. Porta Mana, L. Zanna: Toward a stochastic parametrization of ocean mesoscale eddies (also here)

P.G.L. Porta Mana, P. G. Lewis: On two recent conjectures in convex geometry

Affine and convex spaces: blending the analytic and geometric viewpoints

On the relation between plausibility logic and the maximum-entropy principle: a numerical study

G. Brodin, M. Marklund, J. Zamanian, Å. Ericsson, P.G.L. Porta Mana: Effects of the \(g\)-factor in semi-classical kinetic plasma theory

Studies in plausibility theory, with applications to physics

P.G.L. Porta Mana, A. Månsson, G. Björk: The Laplace-Jaynes approach to induction

P.G.L. Porta Mana, A. Månsson, G. Björk: ‘Plausibilities of plausibilities’: an approach through circumstances

A. Månsson, P.G.L. Porta Mana, G. Björk: Numerical Bayesian state assignment for a three-level quantum system. I. Absolute-frequency data, constant and Gaussian-like priors

A. Månsson, P.G.L. Porta Mana, G. Björk: Numerical Bayesian state assignment for a quantum three-level system. II. Average-value data with a constant, a Gaussian-like, and a Slater prior

P.G.L. Porta Mana, A. Månsson, G. Björk: On distinguishability, orthogonality, and violations of the second law: contradictory assumptions, contrasting pieces of knowledge

Distinguishability of non-orthogonal density matrices does not imply violations of the second law

P.G.L. Porta Mana, G. Björk: Schrödinger-cat states: size classification based on evolution or dissipation

Probabilistic properties of non-deterministic physical systems

G. Björk, P.G.L. Porta Mana: A size criterion for macroscopic superposition states

Why can states and measurement outcomes be represented as vectors?

M. Cadoni, P.G.L. Porta Mana: Hamiltonians for a general dilaton gravity theory on a spacetime with a non-orthogonal, timelike or spacelike outer boundary

Asymptotic symmetries of anti-de Sitter space in two and three dimensions

## Informal pedagogic contributions

Answer to

*Stress-energy-momentum tensor and potential energy*Answer to

*Probability density functions for the Bose-Einstein and Fermi-Dirac statistics*Answer to

*Why only orientation-preserving transformations are considered when integrating forms?*Answer to

*If gravity is curvature of space why are more massive objects “heavier”?*Answer to

*What does it mean for thermodynamic entropy to be defined only up to a constant?*Answer to

*How could the ideal gas law be discovered from experiments on real gases?*

*“It was a dream, but it wasn’t a dream!”*