We explore some topics in the model theory of sheaves of modules. First we describe the formal language that we use. Then we present some examples of sheaves obtained from quivers. These, and other examples, will serve as illustrations and as counterexamples. Then we investigate the notion of strong minimality from model theory to see what it means in this context. We also look briefly at the r...

This paper initiates the study of testing properties of directed graphs. In particular, the paper considers the most basic property of directed graphs – acyclicity. Because the choice of representation affects the choice of algorithm, the two main representations of graphs are studied. For the adjacency matrix representation, most appropriate for dense graphs, a testing algorithm is developed t...

The notions of hypertree width and generalized hypertree width were introduced by Gottlob, Leone, and Scarcello in order to extend the concept of hypergraph acyclicity. These notions were further generalized by Grohe and Marx, who introduced the fractional hypertree width of a hypergraph. All these width parameters on hypergraphs are useful for extending the tractability of many problems in dat...

We present two link-reversal algorithms and some interesting properties that they satisfy. First, we describe the Partial Reversal (PR) algorithm [13], which ensures that the underlying graph structure is destination-oriented and acyclic. These properties of PR make it useful in routing protocols and algorithms for solving leader election and mutual exclusion. While proofs exist to establish th...

We introduce the notion of a connectivity graph —an abstract representation topology concurrently interacting entities, which allows us to encapsulate generic principles reasoning about deadlock freedom . Connectivity graphs are parametric in their vertices (representing entities like threads and channels) edges references between entities) with labels interaction protocols). prove memory leak ...

Two new properties of a finite strategic game, strong and weak BR-dominance solvability, are introduced. The first property holds, e.g., if the game is strongly dominance solvable or if it is weakly dominance solvable and all best responses are unique. It ensures that every simultaneous best response adjustment path, as well as every non-discriminatory individual best response improvement path,...

In 1993 Stanley showed that if a simplicial complex is acyclic over some field, then its face poset can be decomposed into disjoint rank \(1\) boolean intervals whose minimal faces together form subcomplex. further conjectured complexes with higher notion of acyclicity could in similar way using rank. We provide an explicit counterexample to this conjecture. also prove version the conjecture fo...

Hyperprolactinemia is the most common cause of hypogonadotropic anovulation and is one of the leading causes of infertility in women aged 25-34. Hyperprolactinemia has been proposed to block ovulation through inhibition of GnRH release. Kisspeptin neurons, which express prolactin receptors, were recently identified as major regulators of GnRH neurons. To mimic the human pathology of anovulation...