A Generalization of Connes-Kreimer Hopf Algebra

``Bonsai'' Hopf algebras, introduced here, are generalizations of Connes-Kreimer Hopf algebras, which are motivated by Feynman diagrams and renormalization. We show that we can find operad structure on the set of bonsais. We introduce a new differential on these bonsai Hopf algebras, which is inspired by the tree differential. The cohomologies of these are computed here, and the relationship of this differential with the appending operation $*$ of Connes-Kreimer Hopf algebras is investigated

Character formulas for the operad of two compatible brackets and for the bihamiltonian operad

We compute dimensions of the components for the operad of two compatible brackets and for the bihamiltonian operad. We also obtain character formulas for the representations of the symmetric groups and the $SL_2$ group in these spaces.Comment: 24 pages, accepted by Functional Analysis and its Applications, a few typos correcte

Higher Poincare Lemma and Integrability

We prove the non-abelian Poincare lemma in higher gauge theory in two different ways. The first method uses a result by Jacobowitz which states solvability conditions for differential equations of a certain type. The second method extends a proof by Voronov and yields the explicit gauge parameters connecting a flat local connective structure to the trivial one. Finally, we show how higher flatness appears as a necessary integrability condition of a linear system which featured in recently developed twistor descriptions of higher gauge theories.Comment: 1+21 pages, presentation streamlined, section on integrability for higher linear systems significantly improved, published versio

Interval total colorings of graphs

A total coloring of a graph $G$ is a coloring of its vertices and edges such that no adjacent vertices, edges, and no incident vertices and edges obtain the same color. An \emph{interval total $t$-coloring} of a graph $G$ is a total coloring of $G$ with colors $1,2,\...,t$ such that at least one vertex or edge of $G$ is colored by $i$, $i=1,2,\...,t$, and the edges incident to each vertex $v$ together with $v$ are colored by $d_{G}(v)+1$ consecutive colors, where $d_{G}(v)$ is the degree of the vertex $v$ in $G$. In this paper we investigate some properties of interval total colorings. We also determine exact values of the least and the greatest possible number of colors in such colorings for some classes of graphs.Comment: 23 pages, 1 figur

Homotopy Relations for Topological VOA

We consider a parameter-dependent version of the homotopy associative part of the Lian-Zuckerman homotopy algebra and provide the interpretation of multilinear operations of this algebra in terms of integrals over certain polytopes. We explicitly prove the pentagon relation up to homotopy and propose a construction of higher operations.Comment: 15 pages, 1 figure, typos correcte

Improving Data Quality by Leveraging Statistical Relational Learning

Digitally collected data su ↵ ers from many data quality issues, such as duplicate, incorrect, or incomplete data. A common approach for counteracting these issues is to formulate a set of data cleaning rules to identify and repair incorrect, duplicate and missing data. Data cleaning systems must be able to treat data quality rules holistically, to incorporate heterogeneous constraints within a single routine, and to automate data curation. We propose an approach to data cleaning based on statistical relational learning (SRL). We argue that a formalism - Markov logic - is a natural fit for modeling data quality rules. Our approach allows for the usage of probabilistic joint inference over interleaved data cleaning rules to improve data quality. Furthermore, it obliterates the need to specify the order of rule execution. We describe how data quality rules expressed as formulas in first-order logic directly translate into the predictive model in our SRL framework

SFT-inspired Algebraic Structures in Gauge Theories

We consider gauge theories in a String Field Theory-inspired formalism. The constructed algebraic operations lead in particular to homotopy algebras of the related BV theories. We discuss invariant description of the gauge fixing procedure and special algebraic features of gauge theories coupled to matter fields.Comment: LaTeX2e, 26 pages; minor revisions after referee's remarks, typos corrected, title changed, references added, J. Mathematical Physics, in pres

All Stable Characteristic Classes of Homological Vector Fields

An odd vector field $Q$ on a supermanifold $M$ is called homological, if $Q^2=0$. The operator of Lie derivative $L_Q$ makes the algebra of smooth tensor fields on $M$ into a differential tensor algebra. In this paper, we give a complete classification of certain invariants of homological vector fields called characteristic classes. These take values in the cohomology of the operator $L_Q$ and are represented by $Q$-invariant tensors made up of the homological vector field and a symmetric connection on $M$ by means of tensor operations.Comment: 17 pages, references and comments adde