Speeding up Stochastic Dynamic Programming with Zero-Delay Convolution

We show how a technique from signal processing known as zero-delay convolution can be used to develop more efficient dynamic programming algorithms for a broad class of stochastic optimization problems. This class includes several variants of discrete stochastic shortest path, scheduling, and knapsack problems, all of which involve making a series of decisions over time that have stochastic consequences in terms of the temporal delay between successive decisions. We also correct a flaw in the original analysis of the zero-delay convolution algorithm

The unsplittable stable marriage problem

The Gale-Shapley "propose/reject" algorithm is a wellknown procedure for solving the classical stable marriage problem. In this paper we study this algorithm in the context of the many-to-many stable marriage problem, also known as the stable allocation or ordinal transportation problem. We present an integral variant of the Gale- Shapley algorithm that provides a direct analog, in the context of "ordinal" assignment problems, of a well-known bicriteria approximation algorithm of Shmoys and Tardos for scheduling on unrelated parallel machines with costs. If we are assigning, say, jobs to machines, our algorithm nds an unsplit (non-preemptive) stable assignment where every job is assigned at least as well as it could be in any fractional stable assignment, and where each machine is congested by at most the processing time of the largest job.4th IFIP International Conference on Theoretical Computer ScienceRed de Universidades con Carreras en Informática (RedUNCI

Approximation algorithms for stochastic scheduling problems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005.Includes bibliographical references (p. [109]-113).In this dissertation we study a broad class of stochastic scheduling problems characterized by the presence of hard deadline constraints. The input to such a problem is a set of jobs, each with an associated value, processing time, and deadline. We would like to schedule these jobs on a set of machines over time. In our stochastic setting, the processing time of each job is random, known in advance only as a probability distribution (and we make no assumptions about the structure of this distribution). Only after a job completes do we know its actual "instantiated" processing time with certainty. Each machine can process only a singe job at a time, and each job must be assigned to only one machine for processing. After a job starts processing we require that it must be allowed to complete - it cannot be canceled or "preempted" (put on hold and resumed later). Our goal is to devise a scheduling policy that maximizes the expected value of jobs that are scheduled by their deadlines. A scheduling policy observes the state of our machines over time, and any time a machine becomes available for use, it selects a new job to execute on that machine. Scheduling policies can be classified as adaptive or non-adaptive based on whether or not they utilize information learned from the instantiation of processing times of previously-completed jobs in their future scheduling decisions. A novel aspect of our work lies in studying the benefit one can obtain through adaptivity, as we show that for all of our stochastic scheduling problems, adaptivity can only allow us to improve the expected value obtained by an optimal policy by at most a small constant factor. All of the problems we consider are at least NP-hard since they contain the deterministic 0/1 knapsack problem as a special case. We therefore seek to develop approximation algorithms: algorithms that run in polynomial time and compute a policy whose expected value is provably close to that of an optimal adaptive(cont.) policy. For all the problems we consider, we can approximate the expected value obtained by an optimal adaptive policy to within a small constant factor (which depends on the problem under consideration, but is always less than 10). A small handful of our results are pseudo-approximation algorithms, delivering an approximately optimal policy that is feasible with respect to a slightly expanded set of deadlines. Our algorithms utilize a wide variety of techniques, ranging from fairly well-established methods like randomized rounding to more novel techniques such as those we use to bound the expected value obtained by an optimal adaptive policy. In the scheduling literature to date and also in practice, the "deadline" of a job refers to the time by which a job must be completed. We introduce a new model, called the start deadline model, in which the deadline of a job instead governs the time by which we must start the job. While there is no difference between this model and the standard "completion deadline" model in a deterministic setting, we show that for our stochastic problems, one can generally obtain much stronger approximation results with much simpler analyses in the start deadline model. The simplest problem variant we consider is the so-called stochastic knapsack problem, where all jobs share a common deadline and we schedule them on a single machine. The most general variant we consider involves scheduling jobs with individual deadlines on a set of "unrelated" parallel machines, where the value of a job and its processing time distribution can vary depending on the machine to which it is assigned.(cont.) We also discuss algorithms based on dynamic programming for stochastic scheduling problems and their relatives in a discrete-time setting (where processing times are small integers), and we show how to use a new technique from signal processing called zero-delay convolution to improve the running time of dynamic programming algorithms for some of these problems.by Brian Christopher Dean.Ph.D

Continuous-time dynamics shortest path algorithms

Thesis (S.B. and M.Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1999.Includes bibliographical references (p. 116-117).by Brian C. Dean.S.B.and M.Eng

Electron Transfer Precedes ATP Hydrolysis during Nitrogenase Catalysis

The biological reduction of N2 to NH3 catalyzed by Mo-dependent nitrogenase requires at least eight rounds of a complex cycle of events associated with ATP-driven electron transfer (ET) from the Fe protein to the catalytic MoFe protein, with each ET coupled to the hydrolysis of two ATP molecules. Although steps within this cycle have been studied for decades, the nature of the coupling between ATP hydrolysis and ET, in particular the order of ET and ATP hydrolysis, has been elusive. Here, we have measured first-order rate constants for each key step in the reaction sequence, including direct measurement of the ATP hydrolysis rate constant: kATP = 70 s−1, 25 °C. Comparison of the rate constants establishes that the reaction sequence involves four sequential steps: (i) conformationally gated ET (kET = 140 s−1, 25 °C), (ii) ATP hydrolysis (kATP = 70 s−1, 25 °C), (iii) Phosphate release (kPi = 16 s−1, 25 °C), and (iv) Fe protein dissociation from the MoFe protein (kdiss = 6 s−1, 25 °C). These findings allow completion of the thermodynamic cycle undergone by the Fe protein, showing that the energy of ATP binding and protein–protein association drive ET, with subsequent ATP hydrolysis and Pi release causing dissociation of the complex between the Feox(ADP)2 protein and the reduced MoFe protein

Evidence That the P\u3csub\u3ei\u3c/sub\u3e Release Event Is the Rate-Limiting Step in the Nitrogenase Catalytic Cycle

Nitrogenase reduction of dinitrogen (N2) to ammonia (NH3) involves a sequence of events that occur upon the transient association of the reduced Fe protein containing two ATP molecules with the MoFe protein that includes electron transfer, ATP hydrolysis, Pi release, and dissociation of the oxidized, ADP-containing Fe protein from the reduced MoFe protein. Numerous kinetic studies using the nonphysiological electron donor dithionite have suggested that the rate-limiting step in this reaction cycle is the dissociation of the Fe protein from the MoFe protein. Here, we have established the rate constants for each of the key steps in the catalytic cycle using the physiological reductant flavodoxin protein in its hydroquinone state. The findings indicate that with this reductant, the rate-limiting step in the reaction cycle is not protein–protein dissociation or reduction of the oxidized Fe protein, but rather events associated with the Pi release step. Further, it is demonstrated that (i) Fe protein transfers only one electron to MoFe protein in each Fe protein cycle coupled with hydrolysis of two ATP molecules, (ii) the oxidized Fe protein is not reduced when bound to MoFe protein, and (iii) the Fe protein interacts with flavodoxin using the same binding interface that is used with the MoFe protein. These findings allow a revision of the rate-limiting step in the nitrogenase Fe protein cycle

Uncontrolled asthma: assessing quality of life and productivity of children and their caregivers using a cross-sectional Internet-based survey

<p>Abstract</p> <p>Background</p> <p>Results of a national survey of asthmatic children that evaluated management goals established in 2004 by the National Asthma Education and Prevention Program (NAEPP) indicated that asthma symptom control fell short on nearly every goal.</p> <p>Methods</p> <p>An Internet-based survey was administered to adult caregivers of children aged 6-12 years with moderate to severe asthma. Asthma was categorized as uncontrolled when the caregiver reported pre-specified criteria for daytime symptoms, nighttime awakening, activity limitation, or rescue medication based on the NAEPP guidelines. Children's health-related quality of life (HRQOL) and caregivers' quality of life (QOL) were assessed using the Child Health Questionnaire Parent Form 28 (CHQ-PF28) and caregiver's work productivity using a modified Work Productivity and Activity Impairment Questionnaire. Children with uncontrolled vs. controlled asthma were compared.</p> <p>Results</p> <p>360 caregivers of children with uncontrolled asthma and 113 of children with controlled asthma completed the survey. Children with uncontrolled asthma had significantly lower CHQ-PF28 physical (mean 38.1 vs 49.8, uncontrolled vs controlled, respectively) and psychosocial (48.2 vs 53.8) summary measure scores. They were more likely to miss school (5.5 vs 2.2 days), arrive late or leave early (26.7 vs 7.1%), miss school-related activities (40.6 vs 6.2%), use a rescue inhaler at school (64.2 vs 31.0%), and visit the health office or school nurse (22.5 vs 8.8%). Caregivers of children with uncontrolled asthma reported significantly greater work and activity impairment and lower QOL for emotional, time-related and family activities.</p> <p>Conclusions</p> <p>Poorly controlled asthma symptoms impair HRQOL of children, QOL of their caregivers, and productivity of both. Proper treatment and management to improve symptom control may reduce humanistic and economic burdens on asthmatic children and their caregivers.</p

Negative Cooperativity in the Nitrogenase Fe Protein Electron Delivery Cycle

Nitrogenase catalyzes the ATP-dependent reduction of dinitrogen (N2) to two ammonia (NH3) molecules through the participation of its two protein components, the MoFe and Fe proteins. Electron transfer (ET) from the Fe protein to the catalytic MoFe protein involves a series of synchronized events requiring the transient association of one Fe protein with each αβ half of the α2β2 MoFe protein. This process is referred to as the Fe protein cycle and includes binding of two ATP to an Fe protein, association of an Fe protein with the MoFe protein, ET from the Fe protein to the MoFe protein, hydrolysis of the two ATP to two ADP and two Pi for each ET, Pi release, and dissociation of oxidized Fe protein-(ADP)2 from the MoFe protein. Because the MoFe protein tetramer has two separate αβ active units, it participates in two distinct Fe protein cycles. Quantitative kinetic measurements of ET, ATP hydrolysis, and Pi release during the presteady-state phase of electron delivery demonstrate that the two halves of the ternary complex between the MoFe protein and two reduced Fe protein-(ATP)2 do not undergo the Fe protein cycle independently. Instead, the data are globally fit with a two-branch negative-cooperativity kinetic model in which ET in one-half of the complex partially suppresses this process in the other. A possible mechanism for communication between the two halves of the nitrogenase complex is suggested by normal-mode calculations showing correlated and anticorrelated motions between the two halves