Group Divisible Codes and Their Application in the Construction of Optimal Constant-Composition Codes of Weight Three

The concept of group divisible codes, a generalization of group divisible designs with constant block size, is introduced in this paper. This new class of codes is shown to be useful in recursive constructions for constant-weight and constant-composition codes. Large classes of group divisible codes are constructed which enabled the determination of the sizes of optimal constant-composition codes of weight three (and specified distance), leaving only four cases undetermined. Previously, the sizes of constant-composition codes of weight three were known only for those of sufficiently large length.Comment: 13 pages, 1 figure, 4 table

Optimal Memoryless Encoding for Low Power Off-Chip Data Buses

Off-chip buses account for a significant portion of the total system power consumed in embedded systems. Bus encoding schemes have been proposed to minimize power dissipation, but none has been demonstrated to be optimal with respect to any measure. In this paper, we give the first provably optimal and explicit (polynomial-time constructible) families of memoryless codes for minimizing bit transitions in off-chip buses. Our results imply that having access to a clock does not make a memoryless encoding scheme that minimizes bit transitions more powerful.Comment: Proceedings of the 2006 IEEE/ACM international Conference on Computer-Aided Design (San Jose, California, November 05 - 09, 2006). ICCAD '06. ACM, New York, NY, 369-37

Optimal Partitioned Cyclic Difference Packings for Frequency Hopping and Code Synchronization

Optimal partitioned cyclic difference packings (PCDPs) are shown to give rise to optimal frequency-hopping sequences and optimal comma-free codes. New constructions for PCDPs, based on almost difference sets and cyclic difference matrices, are given. These produce new infinite families of optimal PCDPs (and hence optimal frequency-hopping sequences and optimal comma-free codes). The existence problem for optimal PCDPs in ${\mathbb Z}_{3m}$, with $m$ base blocks of size three, is also solved for all $m\not\equiv 8,16\pmod{24}$.Comment: to appear in IEEE Transactions on Information Theor

Linear Size Optimal q-ary Constant-Weight Codes and Constant-Composition Codes

An optimal constant-composition or constant-weight code of weight $w$ has linear size if and only if its distance $d$ is at least $2w-1$. When $d\geq 2w$, the determination of the exact size of such a constant-composition or constant-weight code is trivial, but the case of $d=2w-1$ has been solved previously only for binary and ternary constant-composition and constant-weight codes, and for some sporadic instances. This paper provides a construction for quasicyclic optimal constant-composition and constant-weight codes of weight $w$ and distance $2w-1$ based on a new generalization of difference triangle sets. As a result, the sizes of optimal constant-composition codes and optimal constant-weight codes of weight $w$ and distance $2w-1$ are determined for all such codes of sufficiently large lengths. This solves an open problem of Etzion. The sizes of optimal constant-composition codes of weight $w$ and distance $2w-1$ are also determined for all $w\leq 6$, except in two cases.Comment: 12 page

A BIOMECHANICAL ANALYSIS FOR PROFICIENT AND LESS-PROFICIENT SUBJECTS FOR SOCCER HEADING

Soccer is one of the most popular sports and is played and watched by millions of people around the world. In heading the players intentionally strike the ball using his head; therefore it is essential to instruct them in a proper manner how to do it optimally. Our results showed that lower and upper body had a significant difference between the proficient and less proficient subjects. For upper body kinematics, the proficient subjects exerted lesser elbow angles (47.8" (1.9) than the less-proficient (58.7"(3.5)). In the case of lower bdy kinetics, the proficient subjects exerted greater ankle moment (l.g(O.2) NmlKg) than less proficient subjects (1.5(0.3)Nm/Kg). With the results obtained it became possible to create particular training programs on how to perform a skill better and therefore result in an improvement of their ability

Cost-minimizing preemptive scheduling of mapreduce workloads on hybrid clouds

MapReduce has become the dominant programming model for processing massive amounts of data on cloud platforms. More and more enterprises are now utilizing hybrid clouds, consisting of private infrastructure owned by themselves and public clouds such as Amazon EC2, to process their spiky MapReduce workloads, which fully utilize their own on-premise resources while outsourcing the tasks only when needed. With disparate workloads of different MapReduce tasks, an efficient scheduling mechanism is in need to enable efficient utilization of the on-premise resources and to minimize the task outsourcing cost, while meeting the task completion time requirements as well. In this paper, a fine-grained model is described to characterize the scheduling of heterogeneous MapReduce workloads, and an online algorithm is proposed for joint task admission control into the private cloud, task outsourcing to the public cloud, and VM allocation to execute the admitted tasks on the private cloud, such that the time-averaged task outsourcing cost is minimized over the long run. The online algorithm features preemptive scheduling of the tasks, where a task executed partially on the on-premise infrastructure can be paused and scheduled to run later. It also achieves desirable properties such as meeting a pre-set task admission ratio and bounding the worst-case task completion time, as proven by our rigorous theoretical analysis. © 2013 IEEE.published_or_final_versio

Emerging trends in polymerization-induced self-assembly

In this Perspective, we summarize recent progress in polymerization-induced self-assembly (PISA) for the rational synthesis of block copolymer nanoparticles with various morphologies. Much of the PISA literature has been based on thermally initiated reversible addition–fragmentation chain transfer (RAFT) polymerization. Herein, we pay particular attention to alternative PISA protocols, which allow the preparation of nanoparticles with improved control over copolymer morphology and functionality. For example, initiation based on visible light, redox chemistry, or enzymes enables the incorporation of sensitive monomers and fragile biomolecules into block copolymer nanoparticles. Furthermore, PISA syntheses and postfunctionalization of the resulting nanoparticles (e.g., cross-linking) can be conducted sequentially without intermediate purification by using various external stimuli. Finally, PISA formulations have been optimized via high-throughput polymerization and recently evaluated within flow reactors for facile scale-up syntheses

Atom Interferometry tests of the isotropy of post-Newtonian gravity

We present a test of the local Lorentz invariance of post-Newtonian gravity by monitoring Earth's gravity with a Mach-Zehnder atom interferometer that features a resolution of about 8*10^(-9)g/Hz^(1/2), the highest reported thus far. Expressed within the standard model extension (SME) or Nordtvedt's anisotropic universe model, the analysis limits four coefficients describing anisotropic gravity at the ppb level and three others, for the first time, at the 10ppm level. Using the SME we explicitly demonstrate how the experiment actually compares the isotropy of gravity and electromagnetism.Comment: Added outlook, corrected typos; to appear in PRL. 4 pages, 3 figure

The fine intersection problem for Steiner triple systems

The intersection of two Steiner triple systems (X,A) and (X,B) is the set A intersect B. The fine intersection problem for Steiner triple systems is to determine for each v, the set I(v), consisting of all possible pairs (m,n) such that there exist two Steiner triple systems of order v whose intersection has n blocks over m points. We show that for v = 1 or 3 (mod 6), |I(v)| = Omega(v^3), where previous results only imply that |I(v)| = Omega(v^2).Comment: 9 page

The PBD-Closure of Constant-Composition Codes

We show an interesting PBD-closure result for the set of lengths of constant-composition codes whose distance and size meet certain conditions. A consequence of this PBD-closure result is that the size of optimal constant-composition codes can be determined for infinite families of parameter sets from just a single example of an optimal code. As an application, the size of several infinite families of optimal constant-composition codes are derived. In particular, the problem of determining the size of optimal constant-composition codes having distance four and weight three is solved for all lengths sufficiently large. This problem was previously unresolved for odd lengths, except for lengths seven and eleven.Comment: 8 page