Related papers: Effective subfactor theory

We exhibit a way of "forcing a functional to be an effective operation" for arbitrary partial combinatory algebras (pcas). This gives a method of defining new pcas from old ones for some fixed functional, where the new partial functions can…

First, we construct the Jones tower and tunnel of the central sequence subfactor arising from a hyperfinite type II_1 subfactor with finite index and finite depth, and prove each algebra has the double commutant property in the ultraproduct…

We consider MAP estimators for structured prediction with exponential family models. In particular, we concentrate on the case that efficient algorithms for uniform sampling from the output space exist. We show that under this assumption…

While there is a well-established notion of what a computable ordinal is, the question which functions on the countable ordinals ought to be computable has received less attention so far. We propose a notion of computability on the space of…

We describe the subfactor planar algebra of an intermediate subfactor $N\subset Q \subset M$ of an extremal subfactor $N\subset M$ of finite Jones index which is not necessarily irreducible.

A theorem is derived which (i) provides a new class of subfactors which may be interpreted as generalized asymptotic subfactors, and which (ii) ensures the existence of two-dimensional local quantum field theories associated with certain…

For any class of operators which transform unary total functions in the set of natural numbers into functions of the same kind, we define what it means for a real function to be uniformly computable or conditionally computable with respect…

We study computable topological spaces and semicomputable and computable sets in these spaces. In particular, we investigate conditions under which semicomputable sets are computable. We prove that a semicomputable compact manifold $M$ is…

Although there is a somewhat standard formalization of computability on countable sets given by Turing machines, the same cannot be said about uncountable sets. Among the approaches to define computability in these sets, order-theoretic…

Let $\RR_S$ denote the expansion of the real ordered field by a family of real-valued functions $S$, where each function in $S$ is defined on a compact box and is a member of some quasianalytic class which is closed under the operations of…

Any function can be constructed using a hierarchy of simpler functions through compositions. Such a hierarchy can be characterized by a binary rooted tree. Each node of this tree is associated with a function which takes as inputs two…

Improving the explainability of the results from machine learning methods has become an important research goal. Here, we study the problem of making clusters more interpretable by extending a recent approach of [Davidson et al., NeurIPS…

We define a class of computable functions over real numbers using functional schemes similar to the class of primitive and partial recursive functions defined by G\"odel and Kleene. We show that this class of functions can also be…

Compactness is one of the core notions of analysis: it connects local properties to global ones and makes limits well-behaved. We study the computational properties of the compactness of Cantor space $2^{\mathbb{N}}$ for uncountable covers.…

An approach to the description of subdynamics inside non-relativistic quantum field theory is presented, in which the notions of relevant observable, time scale and complete positivity of the time evolution are stressed. A scattering theory…

We develop synthetic notions of oracle computability and Turing reducibility in the Calculus of Inductive Constructions (CIC), the constructive type theory underlying the Coq proof assistant. As usual in synthetic approaches, we employ a…

Physical processes are computations only when we use them to externalize thought. Computation is the performance of one or more fixed processes within a contingent environment. We reformulate the Church-Turing thesis so that it applies to…

There is a natural construction which associates to a finitely generated, countable, discrete group $G$ and a 3-cocycle $\omega$ of $G$ an inclusion of II$_1$ factors, the so-called diagonal subfactors (with cocycle). In the case when the…

There are a variety of results in the literature proving forms of computability for topological entropy and pressure on subshifts. In this work, we prove two quite general results, showing that topological pressure is always computable from…

In existing literature, while approximate approaches based on Monte-Carlo simulation technique have been proposed to compute the semantics of probabilistic argumentation, how to improve the efficiency of computation without using simulation…