A methodology to quantify cholesterol oxidation products (COPS) in dairy products has been established by gas-liquid chromatography (GLC). Lipids were extracted according to the Folch method and saponified at room temperature using sodium hydroxide in methanol/benzene (3:2, v/v). Cholesterol oxides were derivatized to trimethylsilyl ethers and resolved by GLC, confirming the structures of chole...

In the game of cops and robbers on a graph G = (V,E), k cops try to catch a robber. On the cop turn, each cop may move to a neighboring vertex or remain in place. On the robber’s turn, he moves similarly. The cops win if there is some time at which a cop is at the same vertex as the robber. Otherwise, the robber wins. The minimum number of cops required to catch the robber is called the cop num...

The cops and robbers game has been extensively studied under the assumption of optimal play by both the cops and the robbers. In this paper we study the problem in which cops are chasing a drunk robber (that is, a robber who performs a random walk) on a graph. Our main goal is to characterize the “cost of drunkenness.” Specifically, we study the ratio of expected capture times for the optimal v...

Vertex pursuit games, such as the game of Cops and Robbers, are a simplified model for network security. In these games, cops try to capture a robber loose on the vertices of the network. The minimum number of cops required to win on a graph G is the cop number of G. We present asymptotic results for the game of Cops and Robbers played in various stochastic network models, such as in G(n, p) wi...

The two-player, complete information game of Cops and Robber is played on undirected finite graphs. A number of cops and one robber are positioned on vertices and take turns in sliding along edges. The cops win if, after a move, a cop and the robber are on the same vertex. The minimum number of cops needed to catch the robber on a graph is called the cop number of that graph. In this paper, we ...

In this paper, we study the vertex pursuit game of Cops and Robbers, in which cops try to capture a robber on the vertices of a graph. The minimum number of cops required to win on a given graph G is called the cop number of G. We focus on G(n, r, p), a percolated random geometric graph in which n vertices are chosen uniformly at random and independently from [0, 1]. Two vertices are adjacent w...

We consider the new game of Cops and Attacking Robbers, which is identical to the usual Cops and Robbers game except that if the robber moves to a vertex containing a single cop, then that cop is removed from the game. We study the minimum number of cops needed to capture a robber on a graph G, written cc(G). We give bounds on cc(G) in terms of the cop number of G in the classes of bipartite gr...

Computer Operations Performance System (COPS) is a simulation tool for network modeling. COPS consists of five interactive components: the command interpreter, the graphical user interface, the library, the simulation engine, and the output analysis. The organization of COPS is illustrated in Figure 1. The user constructs models by using the graphical user interface (GUI). The command interpret...

In the game of cops and robber, the cops try to capture a robber moving on the vertices of the graph. The minimum number of cops required to win on a given graph G is called the cop number of G. In this paper, we consider the variant of the game in which both players play on edges instead of vertices, yielding the edge cop number. We relate the new graph parameter to the classic one, investigat...

This paper presents new optical measurement method for evaluating the defects on a silicon wafer surface quantitatively by detecting the intensity distribution, “ laser scattered defect pattern ( LSDP )“, corresponding to the superposition of scattered light from a defect and reflected light from a surface. In order to verify a feasibility to detect “crystal originated particles ( COPs )” and t...