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

• the probability calculus (“Bayesian probability theory”) $$\quad\mathrm{P}(A \land B \rvert I) = \mathrm{P}(A \rvert B \land I)\; \mathrm{P}(B \rvert I)$$

• continuum thermomechanics, including subfields such as fluid dynamics, thermodynamics, and particle mechanics $$\quad\pmb{b} + \nabla\pmb{T} =0$$

• general relativity $$\quad\pmb{G}=\smash{\frac{8\pi\kappa}{c^{2}}} \pmb{T}$$

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

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

• formal logic $$\quad\frac{I\;\vdash\; B \quad I\land B\; \vdash\; A}{I \;\vdash\; A \land B}$$

• 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 below.

Here’s my present address, in case you want to send me a postcard or your latest manuscript:

Kavli Institute for Systems Neuroscience
NTNU Norwegian University of Science and Technology
NO-7030 Trondheim, Norway

You can take a look at my page at NTNU or at my previous pages at Oxford University and the Perimeter Institute. There’s also a personal page (an exercise in self-indulgence).

#### Projects – progressed and in progress!

The works I authored and co-authored can be found for free at Open Science Framework. Some are also on arXiv, although I’m feeling increasingly uneasy about arXiv, since it doesn’t seem to use any scientific criteria to screen papers. I strongly believe that all research papers should be free and that it’s ludicrous that we pay to read research we fund.

Here is a list of my past and ongoing research projects. Some links to papers, others to sort of blog posts.

Dimensional analysis in general relativity and differential geometry

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

Sampling on the simplex

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

“Eppur ruota”: modelling the ocean as a fluid with spin

Force, inertia, metric in Newtonian relativity and general relativity

Quantum theory within the probability calculus: a there-you-go theorem and partially exchangeable models

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

Geometry of maximum-entropy proofs: stationary points, convexity, Legendre transforms, exponential families

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

Conjectures and questions in convex geometry: of interest for quantum theory and other physical statistical theories

Affine and convex spaces: blending the analytic and geometric viewpoints

In favour of the time variable in classical thermo-dynamics

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: Schr"odinger-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?

Consistency of the Shannon entropy in quantum experiments

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