Related papers: Elementary Complexity and von Neumann Algebras
We apply the machinery of projection lattices and von Neumann algebras to analyze the question of how modal interpretations can (and do) circumvent von Neumann's infamous 'no-hidden-variables' theorem.
In this vision paper, we explore the challenges and opportunities of a form of computation that employs an empirical (rather than a formal) approach, where the solution of a computational problem is returned as empirically most likely…
We construct a large family of quantum mechanical systems that give rise to an emergent type III$_1$ von Neumann algebra in the large $N$ limit. Their partition functions are matrix integrals that appear in the study of various gauge…
The Euler characteristic of a very affine variety encodes the algebraic complexity of solving likelihood (or scattering) equations on this variety. We study this quantity for the Grassmannian with $d$ hyperplane sections removed. We provide…
Topological complexity for spaces was introduced by M. Farber as a minimal number of continuity domains for motion planning algorithms. It turns out that this notion can be extended to the case of not necessarily commutative C*-algebras.…
Circular (or cyclic) proofs have received increasing attention in recent years, and have been proposed as an alternative setting for studying (co)inductive reasoning. In particular, now several type systems based on circular reasoning have…
This paper studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs), a.k.a. (Ordinary) Difference Equations. It presents a new framework using these equations as a central tool for computation and…
In this talk, I will survey recent progress made on the classification of von Neumann algebras arising from countable groups and their actions on probability spaces. In particular, I will present the first results which provide classes of…
We investigate bicomplex analogues of fundamental notions from classical algebraic number theory. In particular, we show that the primitive element theorem admits a natural generalization to bicomplex extensions, giving rise to two distinct…
We extend the semiclassical study of the Neumann model down to the deep quantum regime. A detailed study of connection formulae at the turning points allows to get good matching with the exact results for the whole range of parameters.
This article addresses a fundamental problem faced by the ab initio community: the lack of an effective formalism for the rapid exploration and exchange of new methods. To rectify this, we introduce a novel, basis-set independent,…
We investigate the end extendibility of models of arithmetic with restricted elementarity. By utilizing the restricted ultrapower construction in the second-order context, for each $n\in\mathbb{N}$ and any countable model of…
What is computable with limited resources? How can we verify the correctness of computations? How to measure computational power with precision? Despite the immense scientific and engineering progress in computing, we still have only…
These lecture notes present a computation driven pathway from classical complex analysis to the theory of compact Riemann surfaces and their connections to algebraic geometry. The exposition follows a compute first then abstract philosophy,…
Extending the idea of Even and Lehrer [3], we discuss a general approach to integration based on a given decomposition system equipped with a weighting function, and a decomposition of the integrated function. We distinguish two type of…
Let $\M$ be a hyperfinite finite von Nemann algebra and $(\M_k)_{k\geq 1}$ be an increasing filtration of finite dimensional von Neumann subalgebras of $\M$. We investigate abstract fractional integrals associated to the filtration…
Many proposed applications of neural networks in machine learning, cognitive/brain science, and society hinge on the feasibility of inner interpretability via circuit discovery. This calls for empirical and theoretical explorations of…
In the rapidly growing area of quantum information, the Deutsch algorithm is ubiquitous and, in most cases, the first one to be introduced to any student of this relatively new field of research. The reason for this historical relevance…
We assume that every element of a matrix has a small, individual error, and model it by an external number, which is the sum of a nonstandard real number and a neutrix, the latter being a convex (external) set having the group property. The…
Operator systems are the unital self-adjoint subspaces of the bounded operators on a Hilbert space. Complex operator systems are an important category containing the C*-algebras and von Neumann algebras, which is increasingly of interest in…