News
Dr Andreas Klingler
Andreas gave a clear and beautiful account of his (very technical) PhD work. Congratulations! And all the best for your Postdoc!
Visiting the Perimeter Institute
Tobias, Johannes and Gemma are visiting the wonderful Perimeter Institute and sharing our recent work on emulations of spin models and epistemic horizons. It is so inspiring to be here!
Emulations of spin models preserve all properties, are modular and allow for universality
We present a framework to study and construct emulations of spin models in arXiv:2407.13428
Tensors inspired us to study polynomial decompositions
Just published in Linear Algebra and its Applications 698, 537 (2024). This is one of DAL·LE’s renderings.
An epistemic horizon in a deterministic theory
The world from inside can look quite different from the world from outside, as we show in arXiv:2406.17581
An invitation to the framework for universality
To be found at arXiv:2406.16607. The image is DAL·LE’s rendering of the title.
Stefan Kremminger defended his Master Thesis on Quantum conditional independence
Congratulations, Stefan!
Our framework for universality will be published in Compositionality
Our framework for universality (arXiv:2307.06851) will be published in Compositionality soon
Positivity of Matrix Moments
In this paper, we examine the moment membership problem, investigating both its decidability and undecidability.
Mechanistic and emergent universality in natural languages
We examine notions of universality and recursion in grammars, writing systems and the occurence of words, and find that they come in two main flavours: mechanistic and emergent. Preprints:202402.1330
From the whole to the parts: Symmetry and positivity
If a vector (whole) is symmetric and/or positive, can these properties be pushed to the local tensors (parts)? We investigated this question in “Tensor decompositions on simplicial complexes with invariance” just published in Journal of Symbolic Computation 124, 102299 (2024) (The image is DALL·E’s rendering of this short explanation)
Beautiful skiing day
We had a wonderful day on the snow with views on the Kalkkoegel and Innsbruck
Beyond operator systems
Operator systems are based on the cone of positive semidefinite matrices. What happens if we generalize this to other convex cones? We introduce general conic systems and show that many important theorems still hold. (arXiv:2312.13983)
A framework for universality in physics, computer science and beyond
What do universal Turing machines, universal spin models, NP completeness, top of a preorder and denseness of a subset have in common? They are all universal in a certain (precise) sense.
arXiv:2307.06851
Many bounded versions of undecidable problems are NP-hard
Being undecidable and NP-hard are two ways of being hard - the former for machines with unbounded time, the latter for machines with poly-bounded time.
Does bounding an undecidable problem result in an NP-hard problem? Quite often. SciPost Phys. 14, 173 (2023)