Related papers: Automorphism Groups of Graphical Models and Lifted…
In this paper we describe how one can obtain Lie group structures on the group of (vertical) bundle automorphisms for a locally convex principal bundle P over the compact manifold M. This is done by first considering Lie group structures on…
We study domains in complex $n$-space with automorphism group that does not depend on the full $n$ dimensions of the ambient space. A sufficient geometric condition is obtained to guarantee that a domain has such a "thin" automorphism…
Any finite group can be encoded as the automorphism group of an unlabeled simple graph. Recently Hartke, Kolb, Nishikawa, and Stolee (2010) demonstrated a construction that allows any ordered pair of finite groups to be represented as the…
We first present an overview of our previous work on the dynamics of subgroups of automorphism groups of compact complex surfaces, together with a selection of open problems and new classification results. Then, we study two families of…
Graphical models use graphs to compactly capture stochastic dependencies amongst a collection of random variables. Inference over graphical models corresponds to finding marginal probability distributions given joint probability…
For a real semisimple Lie algebra, we consider its automorphism group quotient by its identity component. This is known as the outer automorphism group. In this article, we compute the outer automorphism groups of all real semisimple Lie…
An adjoint Chevalley group of rank at least 2 over a rational algebra (or a similar ring), its elementary subgroup, and the corresponding Lie ring have the same automorphism group. These automorphisms are explicitly described.
Representation learning seeks meaningful sensory representations without supervision and can model aspects of human development. Although many neural networks empirically learn useful features, a principled account of what makes a…
We present a new local approximation algorithm for computing Maximum a Posteriori (MAP) and log-partition function for arbitrary exponential family distribution represented by a finite-valued pair-wise Markov random field (MRF), say $G$.…
We describe the full automorphism group of the directed reduced power graph and the undirected reduced power graph of a finite group. We compute the full automorphism groups of these graphs of several classes of finite groups. Also, we…
Several different areas of group theory, topology and geometry have led to the study of the action of Aut(Fn) | the automorphism group of the free group on n generators | on Hom(Fn;G) when G is either finite,compact or simple Lie group. In…
Random graphs offer a useful mathematical representation of a variety of real world complex networks. Exponential random graphs, for example, are particularly suited towards generating random graphs constrained to have specified statistical…
It is difficult to use subsampling with variational inference in hierarchical models since the number of local latent variables scales with the dataset. Thus, inference in hierarchical models remains a challenge at large scale. It is…
We give an algorithm which computes a presentation for a subgroup, denoted $\AM_{g,1,p}$, of the automorphism group of a free group. It is known that $\AM_{g,1,p}$ is isomorphic to the mapping-class group of an orientable genus-$g$ surface…
In universal algebraic geometry the category of the finite generated free algebras of some fixed variety of algebras and the quotient group A/Y are very important. Here A is a group of all automorphisms of this category and Y is a group of…
Gauge theories are important descriptions for many physical phenomena and systems in quantum computation. Automorphism of gauge group naturally gives global symmetries of gauge theories. In this work we study such symmetries in gauge…
The group membership prediction (GMP) problem involves predicting whether or not a collection of instances share a certain semantic property. For instance, in kinship verification given a collection of images, the goal is to predict whether…
This paper proposes a novel framework for multi-group shape analysis relying on a hierarchical graphical statistical model on shapes within a population.The framework represents individual shapes as point setsmodulo translation, rotation,…
Given a locally finite graph $\Gamma$, an amenable subgroup $G$ of graph automorphisms acting freely and almost transitively on its vertices, and a $G$-invariant activity function $\lambda$, consider the free energy $f_G(\Gamma,\lambda)$ of…
In this paper we consider some classical varieties of linear algebras over the field which has characteristic 0. For every considered variety we take a category of the finite generated free algebras of this variety. And for every this…