Parametric circles and spheres

Formulations for parametric circles and spheres in terms of rational Gaussian (RaG) curves and surfaces are introduced. With the proposed formulations, a full circle is generated by interpolating a closed RaG curve to the vertices of an equilateral triangle, and a full sphere is generated by interpolating a closed RaG surface to the vertices of an octahedron with equilateral triangular faces. Generation of circles and spheres in this manner is very intuitive and easy to remember as the weights are all 1 and the nodes are all unique and uniformly spaced.     

Stability analysis of network-based cooperative resource allocation strategies

Resource allocation involves deciding how to divide a resource of limited availability among multiple demands in a way that optimizes current objectives. In this brief paper we focus on one type of distributed resource allocation problem where via an imperfect communication network multiple processors can share the load presented by multiple task types. We introduce asynchronous “cooperative” resource allocation strategies, and show that they lead to a bounded cumulative demand.     

Nonpathological Lyapunov functions and discontinuous Carathéodory systems

Differential equations with discontinuous right-hand side and solutions intended in Carathéodory sense are considered. For these equations, sufficient conditions which guarantee both Lyapunov stability and asymptotic stability in terms of nonsmooth Lyapunov functions are given. An invariance principle is also proven.     

Finding feasible mold parting directions using graphics hardware

We present new programmable graphics hardware accelerated algorithms to test the 2-moldability of geometric parts and assist with part redesign. These algorithms efficiently identify and graphically display undercuts as well as minimum and insufficient draft angles. Their running times grow only linearly with respect to the number of facets in the solid model, making them efficient subroutines for our algorithms that test whether a tessellated CAD model can be manufactured in a two-part mold. We have developed and implemented two such algorithms to choose candidate directions to test for 2-moldability using accessibility analysis and Gauss maps. The efficiency of these algorithms lies in the fact that they identify groups of candidate directions such that if any one direction in the group is undercut-free, all are, or if any one is not undercut-free, none are. We examine trade-offs between the algorithms' speed, accuracy, and whether they guarantee that an undercut-free direction will be found for a part if one exists.     

Bullwhip reduction for ARMA demand: The proportional order-up-to policy versus the full-state-feedback policy

A ‘proportional’ order-up-to policy reacting to ARMA demand is analyzed using stochastic optimal control theory. This policy is compared with a full-state-feedback order-up-to policy. Necessary conditions for an optimum of a weighted sum of the inventory and the ordering variances for both policies are formulated. Based on this a relatively simple expression for the ‘full-state’ policy is derived. The comparison between the two policies demonstrates that the ‘intuitively’ designed proportional policy does not fulfill the objective of controlling both the inventory and ordering variance for all parameter values of the demand model as well as the full-state-feedback policy. The full-state-feedback policy outperforms the proportional policy in several aspects.     

Data decomposition using independent component analysis with prior constraints

In many data analysis problems, it is useful to consider the data as generated from a set of unknown (latent) generators or sources. The observations we make of a system are then taken to be related to these sources through some unknown function. Furthermore, the (unknown) number of underlying latent sources may be less than the number of observations. Recent developments in independent component analysis (ICA) have shown that, in the case where the unknown function linking sources to observations is linear, such data decomposition may be achieved in a mathematically elegant manner. In this paper, we extend the general ICA paradigm to include a very flexible source model, prior constraints and conditioning on sets of intermediate variables so that ICA forms one part of a hierarchical system. We show that such an approach allows for efficient discovery of hidden representation in data and for unsupervised data partitioning.     

Reference free part encapsulation: Materials,machines and methods

Reference Free Part Encapsulation (RFPE) is an automatic, universal workholding process developed by researchers at the Massachusetts Institute of Technology and the University of California-Berkeley. The process encapsulates the stock by freezing it in a low melting point material during machining and transfers datums from one setup to another by refilling and restoring the encapsulation to a known shape after each setup. This paper describes the encapsulator materials and machines developed to test and demonstrate RFPE. The encapsulation material must satisfy stringent thermal properties, and a process is described that concludes that the tin–bismuth eutectic is ideal. The similarities of the encapsulation process to manufacturing processes such as die casting and injection molding are considered; however, it is shown that many intrinsic differences exist between the encapsulation process and injection molding or die casting. Two encapsulation machines are presented. The first is a larger encapsulation machine capable of forming encapsulations with a 6 in. by 6 in. footprint. The second, a much smaller portable machine capable of forming encapsulations with a 2 in. by 2 in. footprint, is also presented. Special features of each encapsulation machine are highlighted and various design decisions are discussed.