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We study binomiality of the steady state ideals of chemical reaction networks. Considering rate constants as indeterminates, the concept of unconditional binomiality has been introduced and an algorithm based on linear algebra has been…
We present Binomials, a package for the computer algebra system Macaulay2, which specializes well known algorithms to binomial ideals. These come up frequently in algebraic statistics and commutative algebra, and it is shown that…
Anomaly detection based on one-class classification algorithms is broadly used in many applied domains like image processing (e.g. detection of whether a patient is "cancerous" or "healthy" from mammography image), network intrusion…
Binomial ideals are special polynomial ideals with many algorithmically and theoretically nice properties. We discuss the problem of deciding if a given polynomial ideal is binomial. While the methods are general, our main motivation and…
The package Binomials contains implementations of specialized algorithms for binomial ideals, including primary decomposition into binomial ideals. The current implementation works in characteristic zero. Primary decomposition is restricted…
Motivated by problems from Chemical Reaction Network Theory, we investigate whether steady state ideals of reversible reaction networks are generated by binomials. We take an algebraic approach considering, besides concentrations of…
We consider the problem of binomiality of the steady state ideals of biochemical reaction networks. We are interested in finding polynomial conditions on the parameters such that the steady state ideal of a chemical reaction network is…
Ecological networks are often composed of different sub-communities (often referred to as modules). Identifying such modules has the potential to develop a better understanding of the assembly of ecological communities and to investigate…
Process discovery approaches analyze the business data to automatically uncover structured information, known as a process model. The quality of a process model is measured using quality dimensions -- completeness (replay fitness),…
Binomial Cayley graphs are obtained by considering the binomial coefficient of the weight function of a given Cayley graph and a natural number. We introduce these objects and study two families: one associated with symmetric groups and the…
Binary classification problems can be naturally modeled as bipartite graphs, where we attempt to classify right nodes based on their left adjacencies. We consider the case of labeled bipartite graphs in which some labels and edges are not…
Clustering multivariate binary data is of interest in many scientific fields, including ecology, biomedicine, and social policy. Beyond heuristic clustering algorithms, such data can be modelled using multivariate Bernoulli mixture models.…
Data matrix having different sets of entities in its rows and columns are known as two mode data or affiliation data. Many practical problems require to find relationships between the two modes by simultaneously clustering the rows and…
We interpret the complexes defining rack cohomology in terms of a certain differential graded bialgebra. This yields elementary algebraic proofs of old and new structural results for this cohomology theory. For instance, we exhibit two…
We discuss statistical techniques for detecting and quantifying bimodality in astronomical datasets. We concentrate on the KMM algorithm, which estimates the statistical significance of bimodality in such datasets and objectively partitions…
We prove a duality theorem for Cohen--Macaulay simplicial complexes. This is a generalisation of Poincar\'e Duality, framed in the language of combinatorial sheaves. Our treatment is self-contained and accessible for readers with a working…
Cohen-Macaulayness of bipartite graphs is investigated by several mathematicians and has been characterized combinatorially. In this note, we give some different combinatorial conditions for a bipartite graph which are equal to…
The statistical distribution of eigenvalues of pairs of coupled random matrices can be expressed in terms of integral kernels having a generalized Christoffel--Darboux form constructed from sequences of biorthogonal polynomials. For…
We establish a log-supermodularity property for probability distributions on binary patterns observed at the tips of a tree that are generated under any 2--state Markov process. We illustrate the applicability of this result in…
While the study of a single network is well-established, technological advances now allow for the collection of multiple networks with relative ease. Increasingly, anywhere from several to thousands of networks can be created from brain…