Related papers: Exponential Varieties
We introduce a family of extremal polynomials associated with the prolongation of a stratified nilpotent Lie algebra. These polynomials are related to a new algebraic characterization of abnormal subriemannian geodesics in stratified…
A real univariate polynomial of degree $n$ is called hyperbolic if all of its $n$ roots are on the real line. Such polynomials appear quite naturally in different applications, for example, in combinatorics and optimization. The focus of…
New relations between algebraic geometry, information theory and Topological Field Theory are developed. One considers models of databases subject to noise i.e. probability distributions on finite sets, related to exponential families. We…
Iterated monodromy groups of postcritically-finite rational maps form a rich class of self-similar groups with interesting properties. There are examples of such groups that have intermediate growth, as well as examples that have…
In this article two methods to distinguish between polynomial and exponential tails are introduced. The methods are mainly based on the properties of the residual coefficient of variation for the exponential and non-exponential…
The complete first order theories of the exponential differential equations of semiabelian varieties are given. It is shown that these theories also arises from an amalgamation-with-predimension construction in the style of Hrushovski. The…
We give a complete classification of 1-dimensional exponential families $\mathcal{E}$ defined over a finite space $\Omega=\{x_{0}, ...,x_{n}\}$ whose Hessian scalar curvature is constant. We observe an interesting phenomenon: if…
We introduce exponential complexes of sheaves on manifolds. They are resolutions of the (Tate twisted) constant sheaves of the rational numbers, generalising the short exact exponential sequence. There are canonical maps from the…
Hyperbolic polynomials are real polynomials whose real hypersurfaces are nested ovaloids, the inner most of which is convex. These polynomials appear in many areas of mathematics, including optimization, combinatorics and differential…
We study the behavior of exponential random graphs in both the sparse and the dense regime. We show that exponential random graphs are approximate mixtures of graphs with independent edges whose probability matrices are critical points of…
The evolution equations of Einstein's theory and of Maxwell's theory---the latter used as a simple model to illustrate the former--- are written in gauge covariant first order symmetric hyperbolic form with only physically natural…
We investigate extreme values of Mahonian and Eulerian distributions arising from counting inversions and descents of random elements of finite Coxeter groups. To this end, we construct a triangular array of either distribution from a…
Gaussian graphical models have become a well-recognized tool for the analysis of conditional independencies within a set of continuous random variables. From an inferential point of view, it is important to realize that they are composite…
We define varieties of algebras for an arbitrary endofunctor on a cocomplete category using pairs of natural transformations. This approach is proved to be equivalent to the one of equational classes defined by equation arrows. Free…
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…
We derive upper and lower bounds on the determinant of an exponential matrix. They can be transformed into corresponding bounds for the determinant of a univariate Gaussian matrix.
The Weil Conjectures are applied to the Hessenberg Varieties to obtain interesting information about the combinatorics of descents in the symmetric group. Combining this with elementary linear algebra leads to elegant proofs of some…
We extend the concept of exponential B-spline to complex orders. This extension contains as special cases the class of exponential splines and also the class of polynomial B-splines of complex order. We derive a time domain representation…
Associated to any hypergraph is a toric ideal encoding the algebraic relations among its edges. We study these ideals and the combinatorics of their minimal generators, and derive general degree bounds for both uniform and non-uniform…
In this paper, we focus on statistical region-based active contour models where image features (e.g. intensity) are random variables whose distribution belongs to some parametric family (e.g. exponential) rather than confining ourselves to…