Related papers: Relationship between Granger non-causality and gra…
We explore the graph approach to contextuality to restate the extended definition of noncontextuality as given by J. Kujala et. al. [Phys. Rev. Lett. 115, 150401 (2015)] using graph-theoretical terms. This extended definition avoids the…
Contextuality means non-existence of a joint distribution for random variables recorded under mutually incompatible conditions, subject to certain constraints imposed on how the identity of these variables may change across these…
We review some recent results on the minimization of the energy associated to the nonlinear Schr\"odinger Equation on non-compact graphs. Starting from seminal results given by the author together with C. Cacciapuoti, D. Finco, and D. Noja…
The concept of graph compositions is related to several number theoretic concepts, including partitions of positive integers and the cardinality of the power set of finite sets. This paper examines graph compositions where the total number…
The notion of partial trace of a density operator is essential for the understanding of the entanglement and separability properties of quantum states. In this paper we investigate these notions putting an emphasis on the geometrical…
Non-classical states that are characterized by their non-positive quasi-probabilities in phase space are known to be the basis for various quantum effects. In this work, we investigate the interrelation between the non-classicality and…
It is shown here that symmetric hyperbolicity, which guarantees well-posedness, leads to a set of two inequalities for matrices whose elements are determined by a given theory. As a part of the calculation, carried out in a mostly-covariant…
Statistical relationships in observed data can arise for several different reasons: the observed variables may be causally related, they may share a latent common cause, or there may be selection bias. Each of these scenarios can be…
Wahl et al. (2016, 2017) introduced the idea of Granger causality (GC) maps for Langevin systems: dynamics are localised linearly at each point in phase space as vector Ornstein-Uhlenbeck (VOU) processes, for which GCs may in principle be…
Contextuality describes the nontrivial dependence of measurement outcomes on particular choices of jointly measurable observables. In this work we review and generalize the bundle diagram representation introduced in [S. Abramsky et al.,…
Given an arbitrary statistical theory, different from quantum mechanics, how to decide which are the nonclassical correlations? We present a formal framework which allows for a definition of nonclassical correlations in such theories,…
We have recently shown that the entanglement entropy of any bipartition of a quantum state can be approximated as the sum of certain link strengths connecting internal and external sites. The representation is useful to unveil the geometry…
The construction of Generalized Intelligent States (GIS) for the $x^4$% -anharmonic oscillator is presented. These GIS families are required to minimize the Robertson-Schr\"odinger uncertainty relation. As a particular case, we will get the…
The requirement for identifying accurate system representations has not only been a challenge to fulfill, but it has compromised the scalability of formal methods, as the resulting models are often too complex for effective decision making…
Granger causality is a fundamental technique for causal inference in time series data, commonly used in the social and biological sciences. Typical operationalizations of Granger causality make a strong assumption that every time point of…
Wiener and Granger have introduced an intuitive concept of causality between two variables which is based on the idea that an effect never occurs before its cause. Later, Geweke has generalized this concept to a multivariate Granger…
Real-world problems, for example in climate applications, often require causal reasoning on spatially gridded time series data or data with comparable structure. While the underlying system is often believed to behave similarly at different…
An alternative framework underlying connection between tensor ${\rm sl}_2$-calculus and spin networks is suggested. New sign convention for the inner product in the dual spinor space leads to a simpler and direct set of initial rules for…
A factor-graph representation of quantum-mechanical probabilities (involving any number of measurements) is proposed. Unlike standard statistical models, the proposed representation uses auxiliary variables (state variables) that are not…
Gaussian processes (GPs) are used widely in the analysis of astronomical time series. GPs with rational spectral densities have state-space representations which allow O(n) evaluation of the likelihood. We calculate analytic state space…