Related papers: Random Variables with Measurability Constraints wi…

Descriptive set theory is mainly concerned with studying subsets of the space of all countable binary sequences. In this paper we study the generalization where countable is replaced by uncountable. We explore properties of generalized…

Eigenvalues are defined for any element of an algebra of observables and do not require a representation in terms of wave functions or density matrices. A systematic algebraic derivation based on moments is presented here for the harmonic…

Decomposable models and Bayesian networks can be defined as sequences of oligo-dimensional probability measures connected with operators of composition. The preliminary results suggest that the probabilistic models allowing for effective…

A new definition of random sets is proposed. It is based on the distance in measurable space and uses negative definite kernels for continuation from initial space to that of random sets. This approach has no connection to Hausdorff…

Random coding arguments are the backbone of most channel capacity achievability proofs. In this paper, we show that in their standard form, such arguments are insufficient for proving some network capacity theorems: structured coding…

In this paper, we present structured message passing (SMP), a unifying framework for approximate inference algorithms that take advantage of structured representations such as algebraic decision diagrams and sparse hash tables. These…

Distributions of data or sensory stimuli often enjoy underlying invariances. How and to what extent those symmetries are captured by unsupervised learning methods is a relevant question in machine learning and in computational neuroscience.…

We consider stochastic programs conditional on some covariate information, where the only knowledge of the possible relationship between the uncertain parameters and the covariates is reduced to a finite data sample of their joint…

We consider the decidability of state-to-state reachability in linear time-invariant control systems over continuous time. We analyse this problem with respect to the allowable control sets, which are assumed to be the image under a linear…

Many applications require the collection of data on different variables or measurements over many system performance metrics. We term those broadly as measures or variables. Often data collection along each measure incurs a cost, thus it is…

This article is a fundamental study in computable measure theory. We use the framework of TTE, the representation approach, where computability on an abstract set X is defined by representing its elements with concrete "names", possibly…

Quantum randomness evidently transcends the classical framework of random variables defined on a single comprehensive Kolmogorov probability space. One prominent example is the quantum double-slit experiment due to Feynman (1951, 1966). A…

We briefly summarize the kernel regression approach, as used recently in materials modelling, to fitting functions, particularly potential energy surfaces, and highlight how the linear algebra framework can be used to both predict and train…

We develop a synthesis of Turing's paradigm of computation and von Neumann's quantum logic to serve as a model for quantum computation with recursion, such that potentially non-terminating computation can take place, as in a quantum Turing…

It was proved in 1998 by Ben-David and Litman that a concept space has a sample compression scheme of size d if and only if every finite subspace has a sample compression scheme of size d. In the compactness theorem, measurability of the…

The necessity of rejecting the numerical model of geometrical extension is postulated on the basis of the idea of identity of space-time and physical vacuum. An attempt is made to define space-time not via the concept of manifold, but via…

This paper investigates a purely qualitative version of Savage's theory for decision making under uncertainty. Until now, most representation theorems for preference over acts rely on a numerical representation of utility and uncertainty…

In this paper we investigate the extent to which the Lov\'asz Local Lemma (an important tool in probabilistic combinatorics) can be adapted for the measurable setting. In most applications, the Lov\'asz Local Lemma is used to produce a…

We introduce a class of monotone $\sigma$-complete effect algebras, called representable, which are $\sigma$-homomorphic images of a class of monotone $\sigma$-complete effect algebras of functions taking values in the interval $[0,1]$ and…

We prove a general existence result in stochastic optimal control in discrete time where controls take values in conditional metric spaces, and depend on the current state and the information of past decisions through the evolution of a…