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Probabilistic programming is related to a compositional approach to stochastic modeling by switching from discrete to continuous time dynamics. In continuous time, an operator-algebra semantics is available in which processes proceeding in…
We show that under natural and quite general assumptions, a large part of a matrix for a bounded linear operator on a Hilbert space can be preassigned. The result is obtained in a more general setting of operator tuples leading to…
This paper presents a new approach to generate samples from conditional belief functions for a restricted but non trivial subset of conditional belief functions. It assumes the factorization (decomposition) of a belief function along a…
We study the problem of extending a state on an abelian $C^*$- subalgebra to a tracial state on the ambient $C^*$-algebra. We propose an approach that is well-suited to the case of regular inclusions, in which there is a large supply of…
We provide mathematicaly rigorous justification of using term "probability" in connection to the so called non-signalling theories,known also as Popescu's and Rohrlich's box worlds. No only do we prove correctness of these models (in the…
In 2000, Voiculescu proved an algebraic characterization of cyclic gradients of noncommutative polynomials. We extend this remarkable result in two different directions: first, we obtain an analogous characterization of free gradients;…
This is a continuation of our earlier paper \cite{PT3}. We consider here operator-valued functions (or infinite matrix functions) on the unit circle $\T$ and study the problem of approximation by bounded analytic operator functions. We…
Conditional Monte Carlo refers to sampling from the conditional distribution of a random vector X given the value T(X) = t for a function T(X). Classical conditional Monte Carlo methods were designed for estimating conditional expectations…
Conformal prediction provides prediction sets with finite-sample marginal coverage, but many applications require coverage guarantees that adapt to individual test points, a subpopulation, or a structural component of the data. Existing…
In multiple criteria decision aiding, very often the alternatives are compared by means of a value function compatible with the preferences expressed by the Decision Maker. The problem is that, in general, there is a plurality of compatible…
We discuss conditionalisation for Accept-Desirability models in an abstract decision-making framework, where uncertain rewards live in a general linear space, and events are special projection operators on that linear space. This abstract…
When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp.\ functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by…
In this paper, we introduce and investigate two new subclasses of analytic functions in the open unit disk in the complex plane. Several interesting properties of the functions belonging to these classes are examined. Here, sufficient, and…
The use of function contracts to specify the behavior of functions often remains limited to the scope of a single function call. Relational properties link several function calls together within a single specification. They can express more…
We study the problem of conditional expectations in free random variables and provide closed formulas for the conditional expectation of resolvents of arbitrary non-commutative polynomials in free random variables onto the subalgebra of an…
Sublinear expectations for uncertain processes have received a lot of attention recently, particularly methods to extend a downward-continuous sublinear expectation on the bounded finitary functions to one on the non-finitary functions. In…
New proofs are given of the existence of the compensator (or dual predictable projection) of a locally integrable c\'adl\'ag adapted process of finite variation and of the existence of the quadratic variation process for a c\'adl\'ag local…
We consider approximation by functions with finite support and characterize its approximation spaces in terms of interpolation spaces and Lorentz spaces.
We explain how to formulate Voiculescu's non-commutative Riemann sphere framework for fully matricial functions \cite{v10} within the theory of nc functions developed by Vinnikov and Kaliuzhnyi-Verbovetskyi \cite{kvv14}. We then extend this…
The paper studies complementary choice functions, i.e. monotonic and consistent choice functions. Such choice functions were introduced and used in the work \cite{RY} for investigation of matchings with complementary contracts. Three…