We consider spectral quantities in lattice QCD and determine the asymptotic behavior of their discretization errors. Wilson fermion with O$(a)$-improvement, (M\"obius) Domain wall (DWF), overlap Dirac operators are considered combination commonly used gauge actions. fermions DWF domain height $M_5=1+{\rm O}(g_0^2)$ have same, approximate, form cutoff effects: $ K\,a^2\left[\bar g^2(a^{-1})\righ...

We study the spectral flow of the Wilson-Dirac operator H(m) with and without an additional Sheikholeslami-Wohlert (SW) term on a variety of SU(3) lattice gauge field ensembles in the range 0 ≤ m ≤ 2. We have used ensembles generated from the Wilson gauge action, an improved gauge action, and several two-flavor dynamical quark ensembles. Two regions in m provide a generic characterization of th...

Recent work by the ALPHA collaboration has focused on non-perturbative renormalization and on-shell O(a) improvement of lattice QCD with Wilson quarks [1–7]. Various improvement coefficients could be determined as functions of the bare coupling g0, including the coefficient of the Sheikholeslami-Wohlert term in the lattice action [8]. While a non-perturbative determination of the improvement co...

The open neighborhood NG(e) of an edge e in a graph G is the set consisting of all edges having a common end-vertex with e and its closed neighborhood is NG[e] = NG(e) ∪ {e}. Let f be a function on E(G), the edge set of G, into the set {−1, 1}. If ∑x∈NG[e] f(x) ≥ 1 for at least a half of the edges e ∈ E(G), then f is called a signed edge majority dominating function of G. The minimum of the val...

A set S of vertices of a graph G = (V ,E) without isolated vertex is a total dominating set if every vertex of V (G) is adjacent to some vertex in S. The total domination number γt (G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number sdγt (G) is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) i...

We present O(g) calculations of both planar and non-planar Wilson loops for various actions in the presence of sea quarks. In particular, the plaquette, the static potential and the static self energy are calculated to this order for massive Wilson, Sheikholeslami-Wohlert and Kogut-Susskind fermions, including the mass and nf dependence. The results can be used to obtain αMS and mb(mb) from lat...

Using orbifold techniques I construct the Schrödinger functional (SF) for a doublet of Wilson quarks with chirally rotated boundary conditions. This allows to perform checks of universality: for instance, the renormalized SF coupling constant, defined with either boundary conditions, must have a unique continuum limit. Similarly, SF correlation functions in twisted mass QCD and standard QCD can...

Let G be a simple graph without isolated vertices with vertex set V (G) and edge set E(G) and let k be a positive integer. A function f : E(G) −→ {−1, 1} is said to be a signed star k-dominating function on G if ∑ e∈E(v) f(e) ≥ k for every vertex v of G, where E(v) = {uv ∈ E(G) | u ∈ N(v)}. A set {f1, f2, . . . , fd} of signed star k-dominating functions on G with the property that ∑d i=1 fi(e)...

We study the spectral flow of the Wilson-Dirac operator H(m) with and without an additional Sheikholeslami-Wohlert (SW) term on a variety of SU(3) lattice gauge field ensembles in the range 0 ≤ m ≤ 2. We have used ensembles generated from the Wilson gauge action, an improved gauge action, and several two-flavor dynamical quark ensembles. Two regions in m provide a generic characterization of th...

Knowledge discovery in databases, commonly referred to as data mining, has attracted enormous research efforts from different domains such as database, statistics, artificial intelligence, data visualization, etc, in the past decade. Most of the research work in data mining such as clustering, association rules mining and classification focus on discovering the “large patterns” from databases (...