A portion of this research was undertaken as part of the Ptolemy project, which is supported by the Advanced Research Projects Agency and the U. S. Air Force (under the RASSP program, contract F33615-93-C-1317), Semiconductor Research Corporation (project 94-DC-008), National Science Foundation (MIP-9201605), Office of Naval Technology (via Naval Research Laboratories), the State of California ...

We give a complete classification of torsion pairs in the cluster category of Dynkin type An. Along the way we give a new combinatorial description of Ptolemy diagrams, an infinite version of which was introduced by Ng (1005.4364v1 [math.RT], 2010). This allows us to count the number of torsion pairs in the cluster category of type An. We also count torsion pairs up to Auslander–Reiten translat...

1. INTRODUCTION. In his Almagest, Ptolemy inscribes triangles in a unit circle, a circle with diameter d = 1 (see [5], pp. 90–92). This way the length of each side (now chord) represents the value of the trigonometric function sine of the opposite angle. A similar geometric interpretation of the cosine function is possible. In Figure 1 we present Ptolemy's famous sketch, juxtaposed with a " dua...

autoCode4 synthesizes structured reactive controllers from realizable specifications in the GXW subset of linear temporal logic (LTL). Generated reactive controllers are expressed in terms of an intermediate synchronous dataflow (SDF) format, which is further translated, using an open interface, into SCADE/Lustre and Ptolemy II. Moreover, autoCode4 generates and maintains a traceability relatio...

The mapping class group invariant ideal cell decomposition of the Teichmüller space of a punctured surface times an open simplex has been used in a number of computations. This paper answers a question about the asymptotics of this decomposition, namely, in a given cell of the decomposition, which curves can be short? Screens are a new combinatorial structure which provide an answer to this que...

We detail a method to facilitate development of realtime applications on heterogeneous multiprocessors. We introduce a new model of computation that allows for nondeterminate communication between independent dataflow graphs. The graphs may communicate in a manner that does not introduce data dependencies between them. We examine the implications of this model, introduce the necessary communica...

Code generation from models is the ultimate goal of model-based design. For real-time systems the generated code must be analyzable for the worstcase execution time (WCET). In this paper we evaluate Java code generation from Ptolemy II for embedded real-time Java. The target system is the time-predictable Java processor JOP. The quality of the generated code is verified by WCET analysis for the...

We give a complete classification of torsion pairs in the cluster category of Dynkin type Dn, via a bijection to new combinatorial objects called Ptolemy diagrams of type D. For the latter we give along the way different combinatorial descriptions. One of these allows us to count the number of torsion pairs in the cluster category of type Dn by providing their generating function explicitly.