A Synthesis Method for Designing Shared-Resource Systems

In system synthesis, one needs to derive from a given set of processes a system design which reflects exactly the functionalities of the processes and is free from erroneous situations such as deadlock and capacity overflow. This is especially important for shared-resource systems, in which errors are easily induced because of the sharing of common resources among different competing processes. In this paper, a synthesis method is proposed for designing shared-resource systems. It begins with specifying the given processes as augmented marked graphs. These augmented marked graphs are then synthesized through the fusion of commonplaces which represents the shared resources. The net so obtained serves to represent the integrated system which reflects exactly the functionalities of the processes in the sense that the event sequences as well as the pre-conditions and post-conditions of each event occurrence are preserved. Based on the known properties of augmented marked graphs, the system properties such as liveness, boundedness and reversibility can be analysed effectively. The method is applied to manufacturing system design. Promising results are obtained

Recognizing and Drawing IC-planar Graphs

IC-planar graphs are those graphs that admit a drawing where no two crossed edges share an end-vertex and each edge is crossed at most once. They are a proper subfamily of the 1-planar graphs. Given an embedded IC-planar graph $G$ with $n$ vertices, we present an $O(n)$-time algorithm that computes a straight-line drawing of $G$ in quadratic area, and an $O(n^3)$-time algorithm that computes a straight-line drawing of $G$ with right-angle crossings in exponential area. Both these area requirements are worst-case optimal. We also show that it is NP-complete to test IC-planarity both in the general case and in the case in which a rotation system is fixed for the input graph. Furthermore, we describe a polynomial-time algorithm to test whether a set of matching edges can be added to a triangulated planar graph such that the resulting graph is IC-planar

Crossed simplicial groups and structured surfaces

We propose a generalization of the concept of a Ribbon graph suitable to provide combinatorial models for marked surfaces equipped with a G-structure. Our main insight is that the necessary combinatorics is neatly captured in the concept of a crossed simplicial group as introduced, independently, by Krasauskas and Fiedorowicz-Loday. In this context, Connes' cyclic category leads to Ribbon graphs while other crossed simplicial groups naturally yield different notions of structured graphs which model unoriented, N-spin, framed, etc, surfaces. Our main result is that structured graphs provide orbicell decompositions of the respective G-structured moduli spaces. As an application, we show how, building on our theory of 2-Segal spaces, the resulting theory can be used to construct categorified state sum invariants of G-structured surfaces.Comment: 86 pages, v2: revised versio

Isomorphism of graph classes related to the circular-ones property

We give a linear-time algorithm that checks for isomorphism between two 0-1 matrices that obey the circular-ones property. This algorithm leads to linear-time isomorphism algorithms for related graph classes, including Helly circular-arc graphs, \Gamma-circular-arc graphs, proper circular-arc graphs and convex-round graphs.Comment: 25 pages, 9 figure

Monetary Policy and Asset Prices in a Small Open Economy: A Factor-Augmented VAR Analysis for Singapore

The ongoing global financial turmoil has revived the question of whether central bankers ought to tighten monetary policy preemptively in order to head off asset price misalignments before a sudden crash triggers financial instability. This study explores the issue of the appropriate monetary policy response to asset price swings in the small open economy of Singapore. Empirical analysis of monetary policy based on standard VAR models, unfortunately, is often hindered by the use of sparse information sets. To better reflect the extensive information monitored by Singapore’s central bank, including global economic indicators, we augment a monetary VAR model with common factors extracted from a large panel dataset spanning 122 economic time series and the period 1980q1 to 2008q2. The resulting FAVAR model is used to assess the impact of monetary policy shocks on residential property and stock prices. Impulse response functions and variance decompositions suggest that monetary policy can potentially be used to lean against asset price booms in Singapore.Monetary Policy; Asset Prices; Dynamic Factors; Vector Autoregression

The polytope of non-crossing graphs on a planar point set

For any finite set \A of $n$ points in $\R^2$, we define a $(3n-3)$-dimensional simple polyhedron whose face poset is isomorphic to the poset of ``non-crossing marked graphs'' with vertex set \A, where a marked graph is defined as a geometric graph together with a subset of its vertices. The poset of non-crossing graphs on \A appears as the complement of the star of a face in that polyhedron. The polyhedron has a unique maximal bounded face, of dimension $2n_i +n -3$ where $n_i$ is the number of points of \A in the interior of \conv(\A). The vertices of this polytope are all the pseudo-triangulations of \A, and the edges are flips of two types: the traditional diagonal flips (in pseudo-triangulations) and the removal or insertion of a single edge. As a by-product of our construction we prove that all pseudo-triangulations are infinitesimally rigid graphs.Comment: 28 pages, 16 figures. Main change from v1 and v2: Introduction has been reshape