Related papers: Interval Effect Algebras and Holevo Instruments
Dimension effect algebras were introduced in (A. Jencova, S. Pulmannova, Rep. Math. Phys. 62 (2008), 205-218), and it was proved that they are unit intervals in dimension groups. We prove that the effect algebra tensor product of dimension…
Markov processes on the lattices with arbitrary dimension are omnipresent in statistical mechanics; however their algebraic description is complete only in dimension 1, for which linear algebra provides many tools complementary to the…
Founding our analysis on the Geneva-Brussels approach to the foundations of physics, we provide a clarification and classification of the key concept of observation. An entity can be observed with or without a scope. In the second case, the…
We introduce the notion of stochastic product as a binary operation on the convex set of quantum states (the density operators) that preserves the convex structure, and we investigate its main consequences. We consider, in particular,…
In order to study quantum measurement theory, sequential product defined for any two quantum effects is introduced. Physically motivated conditions ask the sequential product to be continuous with respect to the strong operator topology. In…
The use of instrumental variables for estimating the effect of an exposure on an outcome is popular in econometrics, and increasingly so in epidemiology. This increasing popularity may be attributed to the natural occurrence of instrumental…
Quantum statistics is defined by Hilbert space products between the eigenstates associated with state preparation and measurement. The same Hilbert space products also describe the dynamics generated by a Hamiltonian when one of the states…
The Hilbert space effect algebra is a fundamental mathematical structure which is used to describe unsharp quantum measurements in Ludwig's formulation of quantum mechanics. Each effect represents a quantum (fuzzy) event. The relation of…
In observational studies, treatments are typically not randomized and therefore estimated treatment effects may be subject to confounding bias. The instrumental variable (IV) design plays the role of a quasi-experimental handle since the IV…
Convolution is a ubiquitous operation in mathematics and computing. The Kripke semantics for substructural and interval logics motivates its study for quantale-valued functions relative to ternary relations. The resulting notion of…
This chapter uses categorical techniques to describe relations between various sets of operators on a Hilbert space, such as self-adjoint, positive, density, effect and projection operators. These relations, including various…
In this paper we present the set of intervals as a normed vector space. We define also a four-dimensional associative algebra whose product gives the product of intervals in any cases. This approach allows to give a notion of divisibility…
The partial (ceteris paribus) effects of interest in nonlinear and interactive linear models are heterogeneous as they can vary dramatically with the underlying observed or unobserved covariates. Despite the apparent importance of…
This paper presents a systematic study of the calculus of interval-valued functions and its application to interval differential equations. To this end, first, we introduce new interval arithmetic operations. Under new operations, the space…
Exogenous heterogeneity, for example, in the form of instrumental variables can help us learn a system's underlying causal structure and predict the outcome of unseen intervention experiments. In this paper, we consider linear models in…
Instrumental variables are a popular study design for the estimation of treatment effects in the presence of unobserved confounders. In the canonical instrumental variables design, the instrument is a binary variable. In many settings,…
We consider iterated function systems (finite or countable), together with linear and continuous operators on Hilbert spaces, which enable us to construct Markov-type operators. Under suitable conditions, these Markov-type operators have…
Instrumental variables (IVs) are widely used for estimating causal effects in the presence of unmeasured confounding. Under the standard IV model, however, the average treatment effect (ATE) is only partially identifiable. To address this,…
Algebraic effects & handlers have become a standard approach for side-effects in functional programming. Their modular composition with other effects and clean separation of syntax and semantics make them attractive to a wide audience.…
Studying sequential measurements is of the utmost importance to both the foundational aspects of quantum theory and the practical implementations of quantum technologies, with both of these applications being abstractly described by the…