Related papers: Random Variables with Measurability Constraints wi…
Many algorithms are specified with respect to a fixed but unspecified parameter. Examples of this are especially common in cryptography, where protocols often feature a security parameter such as the bit length of a secret key. Our aim is…
We prove a Borel version of the local lemma, i.e. we show that, under suitable assumptions, if the set of variables in the local lemma has a structure of a Borel space, then there exists a satisfying assignment which is a Borel function.…
We prove that the relation of bisimilarity between countable labelled transition systems is $\Sigma_1^1$-complete (hence not Borel), by reducing the set of non-wellorders over the natural numbers continuously to it. This has an impact on…
In conformally invariant quantum field theories one encounters besides the standard DHR superselection theory based on spacelike (Einstein-causal) commutation relations and their Haag duality another timelike (''Huygens'') based…
We study measurable dependence of measures on a parameter in the following two classical problems: constructing conditional measures and the Kantorovich optimal transportation. We obtain broad sufficient conditions for the existence of…
In physical systems possessing symmetry, reconstructing the underlying causal structure from observational data constitutes an inverse problem of fundamental importance. In this work, we formulate the inverse problem of causal inference…
We investigate the extrinsic geometry of causal sets in $(1+1)$-dimensional Minkowski spacetime. The properties of boundaries in an embedding space can be used not only to measure observables, but also to supplement the discrete action in…
This paper develops new limit theory for data that are generated by networks or more generally display cross-sectional dependence structures that are governed by observable and unobservable characteristics. Strategic network formation…
Causal inference from observational data following the restricted structural causal model (SCM) framework hinges largely on the asymmetry between cause and effect from the data generating mechanisms, such as non-Gaussianity or nonlinearity.…
The Copenhagen Interpretation describes individual systems, using the same Hilbert space formalism as does the statistical ensemble interpretation (SQM). This leads to the well-known paradoxes surrounding the Measurement Problem. We extend…
When dealing with process calculi and automata which express both nondeterministic and probabilistic behavior, it is customary to introduce the notion of scheduler to solve the nondeterminism. It has been observed that for certain…
In this paper, we are interested in the synthesis of schedulers in double-weighted Markov decision processes, which satisfy both a percentile constraint over a weighted reachability condition, and a quantitative constraint on the expected…
Many scientific problems require identifying a small set of covariates that are associated with a target response and estimating their effects. Often, these effects are nonlinear and include interactions, so linear and additive methods can…
We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of…
We demonstrate a fundamental relation between the structures of physical space and of quantum theory: the set of quantum correlations in a rotational prepare-and-measure scenario can be derived from covariance alone, without assuming…
We present a data-driven algorithm for efficiently computing stochastic control policies for general joint chance constrained optimal control problems. Our approach leverages the theory of kernel distribution embeddings, which allows…
We propose the concept of a system algebra with a parallel composition operation and an interface connection operation, and formalize composition-order invariance, which postulates that the order of composing and connecting systems is…
We derive the sampling properties of random networks based on weights whose pairwise products parameterize independent Bernoulli trials. This enables an understanding of many degree-based network models, in which the structure of realized…
After a review of the arrows of time, we describe the possibilities of a time-asymmetry in quantum theory. Whereas Hilbert space quantum mechanics is time-symmetric, the rigged Hilbert space formulation, which arose from Dirac's bra-ket…
It is well-known that a random variable, i.e., a function defined on a probability space, with values in a Borel space, can be represented on the special probability space consisting of the unit interval with Lebesgue measure. We show an…