To Queue or Not to Queue: When Queueing is Better Than Timesharing in a Distributed System

We examine the question of whether to employ the first-come-first-served (FCFS) discipline or the processor-sharing (PS) discipline at the hosts in a distributed server system. We are interested in the case in which service times are drawn from a heavy-tailed distribution, and so have very high variability. Traditional wisdom when task sizes are highly variable would prefer the PS discipline, because it allows small tasks to avoid being delayed behind large tasks in a queue. However, we show that system performance can actually be significantly better under FCFS queueing, if each task is assigned to a host based on the task's size. By task assignment, we mean an algorithm that inspects incoming tasks and assigns them to hosts for service. The particular task assignment policy we propose is called SITA-E: Size Interval Task Assignment with Equal Load. Surprisingly, under SITA-E, FCFS queueing typically outperforms the PS discipline by a factor of about two, as measured by mean waiting time and mean slowdown (waiting time of task divided by its service time). We compare the FCFS/SITA-E policy to the processor-sharing case analytically; in addition we compare it to a number of other policies in simulation. We show that the benefits of SITA-E are present even in small-scale distributed systems (four or more hosts). Furthermore, SITA-E is a static policy that does not incorporate feedback knowledge of the state of the hosts, which allows for a simple and scalable implementation.

Genome-wide association with bone mass and geometry in the Framingham Heart Study

BACKGROUND:Osteoporosis is characterized by low bone mass and compromised bone structure, heritable traits that contribute to fracture risk. There have been no genome-wide association and linkage studies for these traits using high-density genotyping platforms.METHODS:We used the Affymetrix 100K SNP GeneChip marker set in the Framingham Heart Study (FHS) to examine genetic associations with ten primary quantitative traits: bone mineral density (BMD), calcaneal ultrasound, and geometric indices of the hip. To test associations with multivariable-adjusted residual trait values, we used additive generalized estimating equation (GEE) and family-based association tests (FBAT) models within each sex as well as sexes combined. We evaluated 70,987 autosomal SNPs with genotypic call rates [greater than or equal to]80%, HWE p [greater than or equal to] 0.001, and MAF [greater than or equal to]10% in up to 1141 phenotyped individuals (495 men and 646 women, mean age 62.5 yrs). Variance component linkage analysis was performed using 11,200 markers.RESULTS:Heritability estimates for all bone phenotypes were 30-66%. LOD scores [greater than or equal to]3.0 were found on chromosomes 15 (1.5 LOD confidence interval: 51,336,679-58,934,236 bp) and 22 (35,890,398-48,603,847 bp) for femoral shaft section modulus. The ten primary phenotypes had 12 associations with 100K SNPs in GEE models at p < 0.000001 and 2 associations in FBAT models at p < 0.000001. The 25 most significant p-values for GEE and FBAT were all less than 3.5 x 10-6 and 2.5 x 10-5, respectively. Of the 40 top SNPs with the greatest numbers of significantly associated BMD traits (including femoral neck, trochanter, and lumbar spine), one half to two-thirds were in or near genes that have not previously been studied for osteoporosis. Notably, pleiotropic associations between BMD and bone geometric traits were uncommon. Evidence for association (FBAT or GEE p < 0.05) was observed for several SNPs in candidate genes for osteoporosis, such as rs1801133 in MTHFR; rs1884052 and rs3778099 in ESR1; rs4988300 in LRP5; rs2189480 in VDR; rs2075555 in COLIA1; rs10519297 and rs2008691 in CYP19, as well as SNPs in PPARG (rs10510418 and rs2938392) and ANKH (rs2454873 and rs379016). All GEE, FBAT and linkage results are provided as an open-access results resource at http://www.ncbi.nlm.nih.gov/projects/gap/cgi-bin/study.cgi?id=phs000007.CONCLUSION:The FHS 100K SNP project offers an unbiased genome-wide strategy to identify new candidate loci and to replicate previously suggested candidate genes for osteoporosis.

On Learning Counting Functions With Queries

We investigate the problem of learning disjunctions of counting functions, which are general cases of parity and modulo functions, with equivalence and membership queries. We prove that, for any prime number p, the class of disjunctions of integer-weighted counting functions with modulus p over the domain Znq (or Zn) for any given integer q ≥ 2 is polynomial time learnable using at most n + 1 equivalence queries, where the hypotheses issued by the learner are disjunctions of at most n counting functions with weights from Zp. The result is obtained through learning linear systems over an arbitrary field. In general a counting function may have a composite modulus. We prove that, for any given integer q ≥ 2, over the domain Zn2, the class of read-once disjunctions of Boolean-weighted counting functions with modulus q is polynomial time learnable with only one equivalence query, and the class of disjunctions of log log n Boolean-weighted counting functions with modulus q is polynomial time learnable. Finally, we present an algorithm for learning graph-based counting functions.

Spatial Pattern Learning, Catastophic Forgetting and Optimal Rules of Synaptic Transmission

It is a neural network truth universally acknowledged, that the signal transmitted to a target node must be equal to the product of the path signal times a weight. Analysis of catastrophic forgetting by distributed codes leads to the unexpected conclusion that this universal synaptic transmission rule may not be optimal in certain neural networks. The distributed outstar, a network designed to support stable codes with fast or slow learning, generalizes the outstar network for spatial pattern learning. In the outstar, signals from a source node cause weights to learn and recall arbitrary patterns across a target field of nodes. The distributed outstar replaces the outstar source node with a source field, of arbitrarily many nodes, where the activity pattern may be arbitrarily distributed or compressed. Learning proceeds according to a principle of atrophy due to disuse whereby a path weight decreases in joint proportion to the transmittcd path signal and the degree of disuse of the target node. During learning, the total signal to a target node converges toward that node's activity level. Weight changes at a node are apportioned according to the distributed pattern of converging signals three types of synaptic transmission, a product rule, a capacity rule, and a threshold rule, are examined for this system. The three rules are computationally equivalent when source field activity is maximally compressed, or winner-take-all when source field activity is distributed, catastrophic forgetting may occur. Only the threshold rule solves this problem. Analysis of spatial pattern learning by distributed codes thereby leads to the conjecture that the optimal unit of long-term memory in such a system is a subtractive threshold, rather than a multiplicative weight.

Fuzzy ART

Adaptive Resonance Theory (ART) models are real-time neural networks for category learning, pattern recognition, and prediction. Unsupervised fuzzy ART and supervised fuzzy ARTMAP synthesize fuzzy logic and ART networks by exploiting the formal similarity between the computations of fuzzy subsethood and the dynamics of ART category choice, search, and learning. Fuzzy ART self-organizes stable recognition categories in response to arbitrary sequences of analog or binary input patterns. It generalizes the binary ART 1 model, replacing the set-theoretic: intersection (∩) with the fuzzy intersection (∧), or component-wise minimum. A normalization procedure called complement coding leads to a symmetric: theory in which the fuzzy inter:>ec:tion and the fuzzy union (∨), or component-wise maximum, play complementary roles. Complement coding preserves individual feature amplitudes while normalizing the input vector, and prevents a potential category proliferation problem. Adaptive weights :otart equal to one and can only decrease in time. A geometric interpretation of fuzzy AHT represents each category as a box that increases in size as weights decrease. A matching criterion controls search, determining how close an input and a learned representation must be for a category to accept the input as a new exemplar. A vigilance parameter (p) sets the matching criterion and determines how finely or coarsely an ART system will partition inputs. High vigilance creates fine categories, represented by small boxes. Learning stops when boxes cover the input space. With fast learning, fixed vigilance, and an arbitrary input set, learning stabilizes after just one presentation of each input. A fast-commit slow-recode option allows rapid learning of rare events yet buffers memories against recoding by noisy inputs. Fuzzy ARTMAP unites two fuzzy ART networks to solve supervised learning and prediction problems. A Minimax Learning Rule controls ARTMAP category structure, conjointly minimizing predictive error and maximizing code compression. Low vigilance maximizes compression but may therefore cause very different inputs to make the same prediction. When this coarse grouping strategy causes a predictive error, an internal match tracking control process increases vigilance just enough to correct the error. ARTMAP automatically constructs a minimal number of recognition categories, or "hidden units," to meet accuracy criteria. An ARTMAP voting strategy improves prediction by training the system several times using different orderings of the input set. Voting assigns confidence estimates to competing predictions given small, noisy, or incomplete training sets. ARPA benchmark simulations illustrate fuzzy ARTMAP dynamics. The chapter also compares fuzzy ARTMAP to Salzberg's Nested Generalized Exemplar (NGE) and to Simpson's Fuzzy Min-Max Classifier (FMMC); and concludes with a summary of ART and ARTMAP applications.