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In the quantum-Bayesian approach to quantum foundations, a quantum state is viewed as an expression of an agent's personalist Bayesian degrees of belief, or probabilities, concerning the results of measurements. These probabilities obey the…
This work focuses on a class of functional stochastic Hamiltonian systems with singular coefficients and state-dependent switching, in which the switching process has a countably infinite state space. First, by Girsanov's transformation, we…
Precise rules are developed in order to formalize the reasoning processes involved in standard non-relativistic quantum mechanics, with the help of analogies from classical physics. A classical or quantum description of a mechanical system…
The concepts of superposition and of transition probability, familiar from pure states in quantum physics, are extended to locally normal states on funnels of type I$_\infty$ factors. Such funnels are used in the description of infinite…
Classical results due to Ingham and Paley-Wiener characterize the existence of nonzero functions supported on certain subsets of the real line in terms of the pointwise decay of the Fourier transforms. Viewing these results as uncertainty…
Many complex systems have been shown to share universal properties of organization, such as scale independence, modularity and self-similarity. We borrow tools from statistical physics in order to study structural preferential attachment…
The paper is a brief informal introduction to C*-algebraic foundations of causal contextual subquantum theories. In particular, it is explained how the contextuality property (which is a necessary consistency condition of all causal…
Armstrong's axioms of functional dependency form a well-known logical system that captures properties of functional dependencies between sets of database attributes. This article assumes that there are costs associated with attributes and…
For a stationary sequence that is regularly varying and associated we give conditions which guarantee that partial sums of this sequence, under normalization related to the exponent of regular variation, converge in distribution to a…
In stochastic decision problems, one often wants to estimate the underlying probability measure statistically, and then to use this estimate as a basis for decisions. We shall consider how the uncertainty in this estimation can be…
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…
In this paper, we study the continuity of expected utility functions, and derive a necessary and sufficient condition for a weak order on the space of simple probabilities to have a continuous expected utility function. We also verify that…
Although regular conditional distributions (r.c.d.) are well-defined and widely used measure-theoretic objects, they can violate our intuition from the classical definition of a conditional probability given an event. For that purpose, the…
Recently, symbolic structures were proposed as finite representations of potentially infinite first-order structures, where Linear Integer Arithmetic terms and formulas define the domain and interpretations of a structure. We generalize…
We consider time-delay systems with a finite number of delays in the state space $L^\infty\times\mathbb{R}^n$. In this framework, we show that forward completeness implies the bounded reachability sets property, while this implication was…
We develop a general assumption-lean framework for constructing uniformly valid confidence sets for functionals defined by moment equalities, referred to as $Z$-functionals. Our approach combines self-normalized statistics with a test…
The notion of a symmetric extension extends the usual notion of forcing by identifying a particular class of names which forms an intermediate model of ZF between the ground model and the generic extension, and often the axiom of choice…
A system of quantum reasoning for a closed system is developed by treating non-relativistic quantum mechanics as a stochastic theory. The sample space corresponds to a decomposition, as a sum of orthogonal projectors, of the identity…
Choice functions accept a set of alternatives as input and produce a preferred subset of these alternatives as output. We study the problem of learning such functions under conditions of context-dependence of preferences, which means that…
We study the satisfiability of ordering constraint satisfaction problems (CSPs) above average. We prove the conjecture of Gutin, van Iersel, Mnich, and Yeo that the satisfiability above average of ordering CSPs of arity $k$ is…