Related papers: Lagrange inversion and combinatorial species with …
We show that the Lagrangian for interacting nonrelativistic particles can be coupled to an external gauge field and metric tensor in a way that exhibits a nonrelativistic version of general coordinate invariance. We explore the consequences…
The invariant Hilbert schemes considered in \cite{BC1} were proved to be affine spaces. The proof relied on the classification of strict wonderful varieties. We obtain in the present article a classification-free proof of the affinity of…
This work considers the problem of learning the structure of multivariate linear tree models, which include a variety of directed tree graphical models with continuous, discrete, and mixed latent variables such as linear-Gaussian models,…
A tanglegram is a pair of binary trees with the same set of leaves. Unlabeled tanglegrams were counted recently by Billey, Konvalinka, and Matsen, who also proposed the problem of counting several variations of unlabeled tanglegrams…
The purpose of this article is to show how the isotropy subgroup of leaf permutations on binary trees can be used to systematically identify tree-informative invariants relevant to models of phylogenetic evolution. In the quartet case, we…
Both a general and a diagonal u-invariant for forms of higher degree are defined, generalizing the u-invariant of quadratic forms. Both old and new results on these invariants are collected.
We study the inverse problem for the fractional Laplace equation with multiple nonlinear lower order terms. We show that the direct problem is well-posed and the inverse problem is uniquely solvable. More specifically, the unknown…
We show that if a Lagrangian is invariant under a transformation (with the invariance defined in the standard manner), then the equations of motion obtained from it maintain their form under the transformation. We also show that the…
We study the class of graphs known as k-trees through the lens of Joyal's theory of combinatorial species (and an equivariant extension known as '$\Gamma$-species' which incorporates data about 'structural' group actions). This culminates…
We investigate functionals defined on manifolds through parameterizations. If they are to be meaningful, from a geometrical viewpoint, they ought to be invariant under reparameterizations. Standard, local, integral functionals with this…
A new tree model is introduced based on ordered trees, by distinguishing exactly one child of each node that \emph{has} children. The basic enumeration leads to a cubic equation of the generating function. The extraction of its coefficients…
A notion of the generalized invariant manifold for a nonlinear integrable lattice is considered. Earlier it has been observed that this kind objects provide an effective tool for evaluating the recursion operators and Lax pairs. In this…
It is known that discrete scale invariance leads to log-periodic corrections to scaling. We investigate the correlations of a system with discrete scale symmetry, discuss in detail possible extension of this symmetry such as translation and…
The authors study the classical Lagrange inversion theorem--an antecedent of the modern implicit function theorem--in the smooth case. Examples are given to show that the result is sharp.
The Luttinger-Ward functional was proposed more than five decades ago to provide a link between static and dynamic quantities in a quantum many-body system. Despite its widespread usage, the derivation of the Luttinger-Ward functional…
We consider a stationary variational inequality with gradient constraint and obstacle. We prove that this problem can be described by an equation using a Lagrange multiplier and a characteristic function. The Lagrange multiplier contains…
Under general conditions, the equation $g(x^1, ..., x^q, y) = 0$ implicitly defines $y$ locally as a function of $x^1, ..., x^q$. In this article, we express divided differences of $y$ in terms of divided differences of $g$, generalizing a…
Light-front quantization to many-particle systems of finite temperature and density provides a novel approach towards a relativistic description of quark matter and allows us to calculate the perturbative as well as the non-perturbative…
We deal with regular Lagrangian constrained systems which are invariant under the action of a symmetry group. Fixing a connection on the higher-order principal bundle where the Lagrangian and the (independent) constraints are defined, the…
We prove some formulas relating the inverse of a Cartan matrix with algebraic and geometric invariants of finite group representations.