Static assignment of complex stochastic tasks using stochastic majorization

We consider the problem of statically assigning many tasks to a (smaller) system of homogeneous processors, where a task's structure is modeled as a branching process, and all tasks are assumed to have identical behavior. We show how the theory of majorization can be used to obtain a partial order among possible task assignments. Our results show that if the vector of numbers of tasks assigned to each processor under one mapping is majorized by that of another mapping, then the former mapping is better than the latter with respect to a large number of objective functions. In particular, we show how measurements of finishing time, resource utilization, and reliability are all captured by the theory. We also show how the theory may be applied to the problem of partitioning a pool of processors for distribution among parallelizable tasks

Peer-Reviewed Exploration in Teaching: A Program for Stimulating and Recognizing Innovations in Teaching

In an academic world driven by student ratings and publication counts, faculty members are discouraged from exploring new pedagogical ideas because exploration takes time and often goes unrecognized. The contrast with research is striking: everyone is expected to explore and innovate in research, whereas very few make exploration in teaching their norm. This paper presents a case study illustrating a program, the Peer-Reviewed Exploration in Teaching (PRET) program, designed to encourage and recognize faculty when they implement teaching innovations. The program provides feedback during all stages of a teaching innovation, including outside-classroom activities, and incorporates a rigorous peer review process so that successive such PRETs can accumulate into a record for tenure and promotion. The paper describes the program’s rationale, initial implementation, and lessons learned. Perhaps one of the most interesting lessons is that faculty explorations often go beyond a standard inventory of active learning techniques when they are encouraged and supported to explore

Optimal processor assignment for pipeline computations

The availability of large scale multitasked parallel architectures introduces the following processor assignment problem for pipelined computations. Given a set of tasks and their precedence constraints, along with their experimentally determined individual responses times for different processor sizes, find an assignment of processor to tasks. Two objectives are of interest: minimal response given a throughput requirement, and maximal throughput given a response time requirement. These assignment problems differ considerably from the classical mapping problem in which several tasks share a processor; instead, it is assumed that a large number of processors are to be assigned to a relatively small number of tasks. Efficient assignment algorithms were developed for different classes of task structures. For a p processor system and a series parallel precedence graph with n constituent tasks, an O(np2) algorithm is provided that finds the optimal assignment for the response time optimization problem; it was found that the assignment optimizing the constrained throughput in O(np2log p) time. Special cases of linear, independent, and tree graphs are also considered

Pathway Switching Explains the Sharp Response Characteristic of Hypoxia Response Network

Hypoxia induces the expression of genes that alter metabolism through the hypoxia-inducible factor (HIF). A theoretical model based on differential equations of the hypoxia response network has been previously proposed in which a sharp response to changes in oxygen concentration was observed but not quantitatively explained. That model consisted of reactions involving 23 molecular species among which the concentrations of HIF and oxygen were linked through a complex set of reactions. In this paper, we analyze this previous model using a combination of mathematical tools to draw out the key components of the network and explain quantitatively how they contribute to the sharp oxygen response. We find that the switch-like behavior is due to pathway-switching wherein HIF degrades rapidly under normoxia in one pathway, while the other pathway accumulates HIF to trigger downstream genes under hypoxia. The analytic technique is potentially useful in studying larger biomedical networks

Optimization of resource control in communication systems

We consider a class of resource control problems in communication systems, such as packet-switched networks and telephone networks, which consist of spatially distributed resources and multiple controllers. In the problems we examine, small units of work (messages, telephone calls) arrive randomly in large numbers to the system, utilize some resources and then leave. In controlling system parameters on-line for the optimal usage of these resources, it is often prohibitively expensive to pass around instantaneous state information to the controllers in order to facilitate dynamic scheduling and thus, what is desirable is optimization with respect to some long term statistics of the random system behavior. We study the case in which little is assumed about the effects of the control parameters on the networks\u27 performance. In this case on-line measurements (prone to random errors or noise) can still be taken and used to help improve performance. A general technique for using such error-prone measurements to iteratively improve system performance, called stochastic approximation, has been advanced since the 50\u27s and studied extensively. We study the use of resource allocation algorithms based on stochastic approximation, present a new stochastic approximation technique and demonstrate its use in a class of chosen problems. The new technique is shown to have several advantages, including the ability to handle estimator bias, which is prevalent in several known estimators. Both theoretical and experimental results have been obtained, including the case of multiple, asynchronously operating controllers and where control parameter constraints are unknown and must themselves be estimated

Peer-Reviewed Exploration in Teaching: A Program for Stimulating and Recognizing Innovations in Teaching

In an academic world driven by student ratings and publication counts, faculty members are discouraged from exploring new pedagogical ideas because exploration takes time and often goes unrecognized. The contrast with research is striking: everyone is expected to explore and innovate in research, whereas very few make exploration in teaching their norm. This paper presents a case study illustrating a program, the Peer-Reviewed Exploration in Teaching (PRET) program, designed to encourage and recognize faculty when they implement teaching innovations. The program provides feedback during all stages of a teaching innovation, including outside-classroom activities, and incorporates a rigorous peer review process so that successive such PRETs can accumulate into a record for tenure and promotion. The paper describes the program’s rationale, initial implementation, and lessons learned. Perhaps one of the most interesting lessons is that faculty explorations often go beyond a standard inventory of active learning techniques when they are encouraged and supported to explore