Necessary and sufficient conditions are given (in terms of monodromy) for extending a family of smooth curves over an open subset U ⊂ S to a family of stable curves over S. More precisely, we introduce the abelian monodromy extension (AME) property and show that the standard Deligne-Mumford compactification is the unique, maximal AME compactification of the moduli space of curves. We also show ...

For a graph $G$ let $gamma (G)$ be its domination number. We define a graph G to be (i) a hypo-efficient domination graph (or a hypo-$mathcal{ED}$ graph) if $G$ has no efficient dominating set (EDS) but every graph formed by removing a single vertex from $G$ has at least one EDS, and (ii) a hypo-unique domination graph (a hypo-$mathcal{UD}$ graph) if $G$ has at least two minimum dominating sets...

there is undoubtedly general agreement that the efficiency of educational investments should he maximized through the managerial process as far as possible. agricultural extension is one of the crucial tasks in developing agricultural societies calling for considerable consumption of intellectual investment. the management of agricultural extension projects (aeps) however, needs careful pla...

A novel speech bandwidth extension method based on audio watermark is presented in this paper. The time-domain and frequency-domain envelope parameters are extracted from the high-frequency components of speech signal, and then these parameters are embedded in the corresponding narrowband speech bit stream by the modified least significant bit watermark method which uses perception property. At...

A reflexive graph is a simple undirected graph where a loop has been added at each vertex. If G and H are reflexive graphs and U ⊆ V (H), then a vertex map f : U → V (G) is called nonexpansive if for every two vertices x, y ∈ U , the distance between f(x) and f(y) in G is at most that between x and y in H . A reflexive graph G is said to have the extension property (EP) if for every reflexive g...

Household food security remains a challenge in South Africa. The national government instituted the Integrated Food Security Strategy (IFSS) programme which identifies household agricultural production as an important element of improving household-level food security. Agricultural extension is well positioned to help achieve this aim, but its current contribution is unknown. This study identif...

This paper introduces the concept of Vertex Unique Labelled Subgraph Mining (VULSM), a specialised form of subgraph mining. A VULS is a subgraph defined by a set of edge labels that has a unique vertex labelling associated with it. A minimal VULS is then a VULS which is not a supergraph of any other VULS. The application considered in this paper, for evaluation purposes, is error prediction wit...

The Lovász extension of a pseudo-Boolean function f : {0, 1}n → R is defined on each simplex of the standard triangulation of [0, 1]n as the unique affine function f̂ : [0, 1]n → R that interpolates f at the n+1 vertices of the simplex. Its degree is that of the unique multilinear polynomial that expresses f . In this paper we investigate the least squares approximation problem of an arbitrary L...

In these notes we develop a link between the Kadison-Singer problem and questions about certain dynamical systems. We conjecture that whether or not a given state has a unique extension is related to certain dynamical properties of the state. We prove that if any state corresponding to a minimal idempotent point extends uniquely to the von Neumann algebra of the group, then every state extends ...

Meditope, a cyclic 12-residue peptide, binds to a unique binding side between the light and heavy chains of the cetuximab Fab. In an effort to improve the affinity of the interaction, it was sought to extend the side chain of Arg8 in the meditope, a residue that is accessible from the other side of the meditope binding site, in order to increase the number of interactions. These modifications i...