Related papers: Coalescent tree based functional representations f…
We consider a probability distribution on the set of Boolean functions in n variables which is induced by random Boolean expressions. Such an expression is a random rooted plane tree where the internal vertices are labelled with connectives…
The growth-fragmentation equation describes a system of growing and dividing particles, and arises in models of cell division, protein polymerisation and even telecommunications protocols. Several important questions about the equation…
Using the Feynman path integral representation of quantum mechanics it is possible to derive a model of an electron in a random system containing dense and weakly-coupled scatterers, see [Proc. Phys. Soc. 83, 495-496 (1964)]. The main goal…
The tree metric theorem provides a combinatorial four point condition that characterizes dissimilarity maps derived from pairwise compatible split systems. A similar (but weaker) four point condition characterizes dissimilarity maps derived…
We develop fully noncommutative Feynman-Kac formulae by employing quantum stochastic processes. To this end we establish some theory for perturbing quantum stochastic flows on von Neumann algebras by multiplier cocycles. Multiplier cocycles…
We introduce tree linear cascades, a class of linear structural equation models for which the error variables are uncorrelated but need not be Gaussian nor independent. We show that, in spite of this weak assumption, the tree structure of…
We study a class of one-dimensional particle systems with true (Bird type) binary interactions, which includes Kac's model of the Boltzmann equation and nonlinear equations for the evolution of wealth distribution arising in kinetic…
This article introduces a flexible and adaptive nonparametric method for estimating the association between multiple covariates and power spectra of multiple time series. The proposed approach uses a Bayesian sum of trees model to capture…
Weak values and Kirkwood--Dirac (KD) quasiprobability distributions have been independently associated with both foundational issues in quantum theory and advantages in quantum metrology. We propose simple quantum circuits to measure weak…
Although regression trees were originally designed for large datasets, they can profitably be used on small datasets as well, including those from replicated or unreplicated complete factorial experiments. We show that in the latter…
In the paper we begin a description of functional methods of quantum field theory for systems of interacting q-particles. These particles obey exotic statistics and are the q-generalization of the colored particles which appear in many…
We consider the compact space of pairs of nested partitions of $\mathbb N$, where by analogy with models used in molecular evolution, we call "gene partition" the finer partition and "species partition" the coarser one. We introduce the…
Following an argument advanced by Feynman, we consider a method for obtaining the effective action which generates the sum of tree diagrams with external physical particles. This technique is applied, in the unbroken \lambda \phi^4 theory,…
In the present paper we construct the star products concerning scalar fields in the covariant case from a new approach. We construct the star products at three levels, which are levels of functions on Rd, fields and functionals…
We present a comprehensive quantum many body theory for kq deformed particles, offering a novel framework that relates particle statistics directly to effective interaction strength. Deformed by the parameters k and q, these particles…
Interacting particle methods are increasingly used to sample from complex and high-dimensional distributions. These stochastic particle integration techniques can be interpreted as an universal acceptance-rejection sequential particle…
We propose Partition Tree, a novel tree-based framework for conditional density estimation over general outcome spaces that supports both continuous and categorical variables within a unified formulation. Our approach models conditional…
A representation of the perturbation series of a general functional measure is given in terms of generalized Feynman graphs and -rules. The graphical calculus is applied to certain functional measures of L\'evy type. A graphical notion of…
The one-dimensional forest-fire model including lightnings is studied numerically and analytically. For the tree correlation function, a new correlation length with critical exponent \nu ~ 5/6 is found by simulations. A Hamiltonian…
We introduce a new class of numerical schemes which allow for low regularity approximations to the expectation $ \mathbb{E}(|u_{k}(\tau, v^{\eta})|^2)$, where $u_k$ denotes the $k$-th Fourier coefficient of the solution $u$ of the…