Related papers: Multispecies Virial Expansions
Let K be a field of positive characteristic. When V is a linear variety in K^n and G is a finitely generated subgroup of K^*, we show how to compute the intersection of V and G^n effectively using heights. We calculate all the estimates…
In recent years, conditional copulas, that allow dependence between variables to vary according to the values of one or more covariates, have attracted increasing attention. In high dimension, vine copulas offer greater flexibility compared…
We study high-dimensional Bayesian linear regression with product priors. Using the nascent theory of non-linear large deviations (Chatterjee and Dembo,2016), we derive sufficient conditions for the leading-order correctness of the naive…
We develop a variational technique for some wide classes of nonlinear evolutions. The novelty here is that we derive the main information directly from the corresponding Euler-Lagrange equations. In particular, we prove that not only the…
We analyze in full mathematical rigor the most general quartically perturbed invariant probability measure for a random tensor. Using a version of the Loop Vertex Expansion (which we call the mixed expansion) we show that the cumulants…
Motivated by the Poisson Dixmier-Moeglin equivalence problem, a systematic study of commutative unitary rings equipped with a {\em biderivation}, namely a binary operation that is a derivation in each argument, is here begun, with an eye…
The classical matrix-tree theorem relates the determinant of the combinatorial Laplacian on a graph to the number of spanning trees. We generalize this result to Laplacians on one- and two-dimensional vector bundles, giving a combinatorial…
We employ the $\Phi-$ derivable approach to many particle systems with strong correlations that can lead to the formation of bound states (clusters) of different size. We define a generic form of $\Phi-$ functionals that is fully equivalent…
We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles' positions in the combined limit…
Using the Lagrange inversion formula, $t$-ary trees are enumerated with respect to edge type (left, middle, right for ternary trees).
Variational inference in probabilistic graphical models aims to approximate fundamental quantities such as marginal distributions and the partition function. Popular approaches are the Bethe approximation, tree-reweighted, and other types…
A simple variational Lagrangian is proposed for the time development of an arbitrary density matrix, employing the "factorization" of the density. Only the "kinetic energy" appears in the Lagrangian. The formalism applies to pure and mixed…
A Bialgebra is a module over a ring that is both an associative algebra and a co-associative coalgebra with the product and coproduct additionally satisfying an appropriate commutative relationship. One application of Bialgebras is in the…
Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and nonconvex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction…
Distributional approximations of (bi--) linear functions of sample variance-covariance matrices play a critical role to analyze vector time series, as they are needed for various purposes, especially to draw inference on the dependence…
Global variational approximation methods in graphical models allow efficient approximate inference of complex posterior distributions by using a simpler model. The choice of the approximating model determines a tradeoff between the…
Mixed-effects models are among the most commonly used statistical methods for the exploration of multispecies data. In recent years, also Joint Species Distribution Models and Generalized Linear Latent Variale Models have gained in…
We propose a method to approximate the distribution of robot configurations satisfying multiple objectives. Our approach uses variational inference, a popular method in Bayesian computation, which has several advantages over sampling-based…
The Poisson-Boltzmann approach gives asymptotically exact counter-ion density profiles around charged objects in the weak-coupling limit of low valency and high temperature. In this paper we derive, using field-theoretic methods, a theory…
We show how to obtain a ``heavy'' meson effective lagrangian for the case where the number of heavy particles is not conserved. We apply the method in a simple example at tree level and perform then the reduction for the case of vector…