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

Non-Koszulness of operads and positivity of Poincaré series

We prove that the operad of mock partially associative $n$-ary algebras is not Koszul, as conjectured by the second and the third author in 2009, and utilise Zeilberger’s algorithm for hypergeometric summation to demonstrate that non-Koszulness of that operad for n = 8 cannot be established by hunting for negative coefficients in the inverse of its Poincaré series

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

Reminiscences on Influential Papers

Reminiscences on Parallel evaluation of multi-join queries. (Proc. SIGMOD Conf. 1995), Annita Wilschut, Jan Flokstra, Peter M.G. Apers

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

Improving Data Quality by Leveraging Statistical Relational\ud Learning

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

Open-closed homotopy algebra in mathematical physics

In this paper we discuss various aspects of open-closed homotopy algebras (OCHAs) presented in our previous paper, inspired by Zwiebach's open-closed string field theory, but that first paper concentrated on the mathematical aspects. Here we show how an OCHA is obtained by extracting the tree part of Zwiebach's quantum open-closed string field theory. We clarify the explicit relation of an OCHA with Kontsevich's deformation quantization and with the B-models of homological mirror symmetry. An explicit form of the minimal model for an OCHA is given as well as its relation to the perturbative expansion of open-closed string field theory. We show that our open-closed homotopy algebra gives us a general scheme for deformation of open string structures ($A_\infty$-algebras) by closed strings ($L_\infty$-algebras).Comment: 38 pages, 4 figures; v2: published versio