Related papers: Analytic Subordination for Free Compression
It is well known that conditional independence can be used to factorize a joint probability into a multiplication of conditional probabilities. This paper proposes a constructive definition of inter-causal independence, which can be used to…
We provide a construction of free factorization algebras in algebraic geometry and link factorization homology of a scheme with coefficients in a free factorization algebra to the homology of its (unordered) configuration spaces. As an…
Free probability provides a framework for describing correlations between non-commuting observables in complex quantum systems whose Hilbert-space states follow maximum-entropy distributions. We examine the robustness of this framework…
As an instance of a linear action of a Hopf algebra on a free associative algebra, we consider finite group gradings of a free algebra induced by gradings on the space spanned by the free generators. The homogeneous component corresponding…
This paper develops and analyzes a stochastic derivative-free optimization strategy. A key feature is the state-dependent adaptive variance. We prove global convergence in probability with algebraic rate and give the quantitative results in…
In the paper, I consider properties and mappings of free algebra with unit. I consider also conjugation of free algebra with unit.
This paper shows how to build a formal analytical solution for a differential equation of arbitrary order and with variable coefficients. It proofs that the most known approximated solutions for such a problem can be derived from the…
Lifted probabilistic inference exploits symmetries in a probabilistic model to allow for tractable probabilistic inference with respect to domain sizes. To apply lifted inference, a lifted representation has to be obtained, and to do so,…
Wick polynomials and Wick products are studied in the context of non-commutative probability theory. It is shown that free, boolean and conditionally free Wick polynomials can be defined and related through the action of the group of…
Amortized analysis is a cost analysis technique for data structures in which cost is studied in aggregate: rather than considering the maximum cost of a single operation, one bounds the total cost encountered throughout a session.…
The subsumption problem with respect to terminologies in the description logic ALC is EXPTIME-complete. We investigate the computational complexity of fragments of this problem by means of allowed Boolean operators. Hereto we make use of…
This is an introduction to some of the most probabilistic aspects of free probability theory.
In this brief note we would like to give the construction of a free commutative unital associative Nijenhuis algebra on a commutative unital associative algebra based on an augmented modified quasi-shuffle product.
We investigate commutator operations on compatible uniformities of an algebra. We present a commutator operation for compatible uniformities of an algebra in a congruence-modular variety which extends the commutator on congruences, and…
The free algebra adjunction, between the category of algebras of a monad and the underlying category, induces a comonad on the category of algebras. The coalgebras of this comonad are the topic of study in this paper (following earlier…
A compression function is a map that slims down an observational set into a subset of reduced size, while preserving its informational content. In multiple applications, the condition that one new observation makes the compressed set change…
We consider the problem of estimating assortment probabilities, which is common in operations management applications, including product bundling, advertising, etc. Existing approaches typically model each assortment as a category and apply…
The paper presents conditions on entry permutations that induce asymptotic freeness when acting on Gaussian random matrices. The class of permutations described includes the matrix transpose, as well as entry permutations relevant in…
Factors $\frac{X}{Y}$ in a free group $F$ with $Y$ normal in $X$ are considered. Precise results on the free structure of ${Y}$ relative to the free structure of ${X}$ when $\frac{X}{Y}$ is abelian are obtained. Some extensions and…
We develop a least-squares method for computing the analytic capacity of compact plane sets with piecewise-analytic boundary. The method furnishes rigorous upper and lower bounds which converge to the true value of the capacity. Several…