Related papers: Decomposition tables for experiments I. A chain of…
We consider Gallai's graph Modular Decomposition theory for network analytics. On the one hand, by arguing that this is a choice tool for understanding structural and functional similarities among nodes in a network. On the other, by…
We investigate point arrangements $v_i\in\mathbb R^d,i\in \{1,...,n \}$ with certain prescribed symmetries. The arrangement space of $v$ is the column span of the matrix in which the $v_i$ are the rows. We characterize properties of $v$ in…
Answering complex questions often requires multi-step reasoning in order to obtain the final answer. Most research into decompositions of complex questions involves open-domain systems, which have shown success in using these decompositions…
The complexity of condensed matter arises from emergent behaviors that cannot be understood by analyzing individual constituents in isolation. While traditional condensed-matter approaches-developed primarily for ideal crystalline…
Large scale structures in the Universe, ranging from globular clusters to entire galaxies, are the manifestation of relaxation to out-of-equilibrium states that are not described by standard statistical mechanics at equilibrium. Instead,…
Determining the causal structure of a set of variables is critical for both scientific inquiry and decision-making. However, this is often challenging in practice due to limited interventional data. Given that randomized experiments are…
A vast array of transformative technologies developed over the past decade has enabled measurement and perturbation at ever increasing scale, yet our understanding of many systems remains limited by experimental capacity. Overcoming this…
Quantitative measures of randomness in games are useful for game design and have implications for gambling law. We treat the outcome of a game as a random variable and derive a closed-form expression and estimator for the variance in the…
A growing number of researchers are conducting randomized experiments to analyze causal relationships in network settings where units influence one another. A dominant methodology for analyzing these experiments is design-based, leveraging…
The design of experiments involves a compromise between covariate balance and robustness. This paper provides a formalization of this trade-off and describes an experimental design that allows experimenters to navigate it. The design is…
Although atomistic simulations of proteins and other biological systems are approaching microsecond timescales, the quality of trajectories has remained difficult to assess. Such assessment is critical not only for establishing the…
Several methods of statistical analysis are proposed and analyzed in application for a specific task -- extraction of the structure functions from the cross sections of deep inelastic interactions of any type. We formulate the method based…
The most widely used method for finding relationships between several quantities is multiple regression. This however is restricted to a single dependent variable. We present a more general method which allows models to be constructed with…
A theory of structure is formulated for systems of many structureless classical particles with stable local interactions in Euclidean space. Such systems are shown to have their structure in thermodynamic equilibrium determined exactly by a…
Turbulent flows are chaotic and multi-scale dynamical systems, which have large numbers of degrees of freedom. Turbulent flows, however, can be modelled with a smaller number of degrees of freedom when using the appropriate coordinate…
In many areas of applied mathematics, engineering, and social and natural sciences, decentralization of information is a key aspect determining how to approach a problem. In this review article, we study information structures in a…
Orthogonal Arrays allow us to test various levels of each factor and balance the different factors so that we can estimate interactions as well as first order effects. There is a trade-off between how well we can sample different levels of…
Performing multiple experiments is common when learning internal mechanisms of complex systems. These experiments can include perturbations to parameters or external disturbances. A challenging problem is to efficiently incorporate all…
Quantifying the similarity between two mathematical structures or datasets constitutes a particularly interesting and useful operation in several theoretical and applied problems. Aimed at this specific objective, the Jaccard index has been…
Within the decoherence theory we investigate the physical background of the condition of the separability (diagonalizability in noncorrelated basis) of the interaction Hamiltonian of the composite system, "system plus environment". It…