Thermodynamics is a funny subject. The first time you go through it, you don't understand it at all. The second time you go through it, you think you understand it, except for one or two small points. The third time you go through it, you know you don't understand it, but by that

Oldies but goldies: Hopfield, Neural networks and physical systems with emergent collective computational abilities, 1982. Hopfield networks are recurrent networks minimizing an Ising-type energy parameterized by its weights. en.wikipedia.org/wiki/Hopfield_…

Bertrand Russell on the excellence of Mathematics ✍️ It seems to me now that mathematics is capable of an artistic excellence as great as that of any music, perhaps greater; not because the pleasure it gives (although very pure) is comparable, either in intensity or in the

The Fiedler vector of a graph is the second eigenvector of the Laplacian. It is the lowest « Fourier » mode and is useful to order the nodes (clustering, dimensionality reduction, etc).  en.wikipedia.org/wiki/Algebraic…

Ernst G. Strauss on 'the friendship of A. EInstein and Kurt Gödel ✍️ The one man who was, during the last years, certainly by far Einstein's best friend, and in some ways strangely resembled him most, was Kurt Gödel, The great logician. They were very different in almost every

"Only a few know, how much one must know to know how little one knows." -- Werner Heisenberg (1901 - 1976)

The Ising model is one of the most celebrated model from statistical physics exhibiting a phase transition at a critical temperature in dimension 2 and higher. Models variety of phenomena from ferromagnet to neural networks. en.wikipedia.org/wiki/Square_la…

This was a pioneering result! Have a look at how I use it to obtain a priori error estimates for PINNs in a Galerkin least-square framework in doi.org/10.1016/j.ifac… . I'll be presenting this work in Siena at #YAMC2023 , tommorow.

Larga parte degli israeliani sta vivendo quanto sta accadendo come una minaccia esistenziale. Non so dire se lo sia effettivamente, ma che sia avvertito così è molto chiaro ed è bene che, ragionando della situazione, di questo teniamo conto, insieme a tutto il resto.

Oldies but goldies: Luigi Ambrosio, Nicola Gigli, Giuseppe Savare, Gradient Flows In Metric Spaces and in the Space of Probability Measures, 2005. Formalize the notion of descent methods on non-Euclidean domains without using a gradient. springer.com/la/book/978376…

What a fascinating PDE !

Singapore isn’t just rich, it’s #GPU-rich About 15% or $2.7 billion of @Nvidia's revenue for the quarter ended October came from Singapore #AI #HPC

The Origin

Ricordo ancora quando sono entrata per la prima volta nel Collegio Ghislieri nell’autunno del 1993 da giovane matricola di matematica. Ricordo in modo nitido l’incontro con il Professor Belvedere, i dialoghi nel suo ufficio, il suo sostegno alle iniziative che portavano avanti

Oldies but goldies: J. Crank, P. Nicolson, A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type, 1947. Introduced a celebrated implicit finite difference method to solve PDEs. en.wikipedia.org/wiki/Crank%E2%…

Oldies but goldies: Arnold Emch, On some properties of the medians of closed continuous curves formed by analytic arcs, 1916. Showed that Toeplitz' inscribed square conjecture is true for piecewise smooth curves. en.wikipedia.org/wiki/Inscribed…

Fokker-Planck equation equivalently describes the movement of a random particle with a drift (as a stochastic ODE) and the evolution of its density (as a PDE). en.wikipedia.org/wiki/Fokker%E2…

The Fast Marching algorithm is a generalization of Dijkstra’s algorithm. Computes the geodesic distance in O(n*log(n)) operation. Equivalently solves the non-linear Eikonal equation in a non-iterative way by front propagation. en.wikipedia.org/wiki/Fast_marc… nbviewer.jupyter.org/github/gpeyre/…

Professor IRL

Should you ask a question during seminar?