Related papers: Exponential Varieties
We study scalar multivariate non-stationary subdivision schemes with a general dilation matrix. We characterize the capability of such schemes to reproduce exponential polynomials in terms of simple algebraic conditions on their symbols.…
Our previous theorems on exponential sums often did not apply or did not give sharp results when certain powers of a variable appearing in the polynomial were divisible by p. We remedy that defect in this paper by systematically applying…
Let $k$ be an algebraically closed field of positive characteristic $p$ and let $\mathbb{G}_a$ denote the additive group of $k$. Let $n \geq 1$ and let ${\rm Mat}(n, k[T])^E$ denote the set of all exponential matrices of ${\rm Mat}(n,…
The exponential family of random graphs has been a topic of continued research interest. Despite the relative simplicity, these models capture a variety of interesting features displayed by large-scale networks and allow us to better…
Classical varieties were characterized by Lawvere as the categories with effective congruences and a varietal generator: an abstractly finite regular generator which is regularly projective (its hom-functor preserves regular epimorphisms).…
We classify translatively exponential and GL(2,Z) covariant valuations on lattice polygons valued at measurable real functions. A typical example of such valuations is induced by the Laplace transform, but as it turns out there are many…
We study holonomic gradient decent for maximum likelihood estimation of exponential-polynomial distribution, whose density is the exponential function of a polynomial in the random variable. We first consider the case that the support of…
We consider derived invariants of varieties in positive characteristic arising from topological Hochschild homology. Using theory developed by Ekedahl and Illusie-Raynaud in their study of the slope spectral sequence, we examine the…
The low-energy expansion of closed-string scattering amplitudes at genus one introduces infinite families of non-holomorphic modular forms called modular graph forms. Their differential and number-theoretic properties motivated Brown's…
We construct a class of positive linear maps on matrix algebras. We find conditions when these maps are atomic, decomposable and completely positive. We obtain a large class of atomic positive linear maps. As applications in quantum…
We study character varieties arising as moduli of representations of an orientable surface group into a reductive group $G$. We first show that if $G/Z$ acts freely on the representation variety, then both the representation variety and the…
We describe arbitrary multiplicative differential forms on Lie groupoids infinitesimally, i.e., in terms of Lie algebroid data. This description is based on the study of linear differential forms on Lie algebroids and encompasses many known…
We consider several generalizations of the classical $\gamma$-positivity of Eulerian polynomials (and their derangement analogues) using generating functions and combinatorial theory of continued fractions. For the symmetric group, we prove…
A variety is a category of ordered (finitary) algebras presented by inequations between terms. We characterize categories enriched over the category of posets which are equivalent to a variety. This is quite analogous to Lawvere's classical…
A class of parametric functions formed by alternating compositions of multivariate polynomials and rectification style monomial maps is studied (the layer-wise exponents are treated as fixed hyperparameters and are not optimized). For this…
Shift and stretch invariance lead to the exponential-Boltzmann probability distribution. Rotational invariance generates the Gaussian distribution. Particular scaling relations transform the canonical exponential and Gaussian patterns into…
We define support varieties in an axiomatic setting using the prime spectrum of a lattice of ideals. A key observation is the functoriality of the spectrum and that this functor admits an adjoint. We assign to each ideal its support and can…
In this paper we present results for bivariate exponential distributions which are represented by phase type distributions. The paper extends results from previous publications [5, 14] on this topic by introducing new representations that…
Maximum likelihood learning with exponential families leads to moment-matching of the sufficient statistics, a classic result. This can be generalized to conditional exponential families and/or when there are hidden data. This document…
In this paper, we derive eight basic identities of symmetry in three variables related to Euler polynomials and alternating power sums. These and most of their corollaries are new, since there have been results only about identities of…