A Coding Theoretic Approach for Evaluating Accumulate Distribution on Minimum Cut Capacity of Weighted Random Graphs

The multicast capacity of a directed network is closely related to the $s$-$t$ maximum flow, which is equal to the $s$-$t$ minimum cut capacity due to the max-flow min-cut theorem. If the topology of a network (or link capacities) is dynamically changing or have stochastic nature, it is not so trivial to predict statistical properties on the maximum flow. In this paper, we present a coding theoretic approach for evaluating the accumulate distribution of the minimum cut capacity of weighted random graphs. The main feature of our approach is to utilize the correspondence between the cut space of a graph and a binary LDGM (low-density generator-matrix) code with column weight 2. The graph ensemble treated in the paper is a weighted version of Erd\H{o}s-R\'{e}nyi random graph ensemble. The main contribution of our work is a combinatorial lower bound for the accumulate distribution of the minimum cut capacity. From some computer experiments, it is observed that the lower bound derived here reflects the actual statistical behavior of the minimum cut capacity.Comment: 5 pages, 2 figures, submitted to IEEE ISIT 201

Effect of Controlled-release Fertilizer and Root-proof Capillary Wick Addition to Root-zone on Tomato Growth and Yield

This study was conducted to investigate the effects of controlled-release fertilizers and wick addition to the root-zone on plant growth and yield of medium-fruit sized tomato up to the 18(th) truss in long-term forcing culture. The set-up consisted of a box partitioned by a board into two halves, named box 1 and box 2. Box 1 contained 2.8 ℓ of growth medium (soil : bark : perlite : peat=2 : 2 : 1 : 1). Plant was grown in box 1 with a capillary wick, and at flowering of the 8(th) truss, the partition was removed and box 2 filled with 2.8 ℓ of the medium. There were two treatments, with or without capillary wick in box 2, namely, single wick (S) and double wicks (D). Plant height was greater in D than S in January, and the difference increased gradually thereafter. Flowering time of 18(th) truss in D was 10 days earlier and decapitated shoot weight was twice that of S. Fruit yield per plant was 8 kg in S and 9 kg in D with similar value of Brix and titratable acidity. There was no difference between S and D in dry root weight (7g/plant) or in xylem exudates (8ml/h), while in S in April plant growth was inferior, leaf color yellow greenish and fruit colour uneven towards the end of growth of plants. Xylem sap analysis showed that NO(3)-N was 10 me/ℓ in S and 6 me/ℓ in D. This concentration is weaker than that of Enshi standard nutrient solution generally used in hydroponics. These results suggest that application of controlled-release fertilizers and wick addition to box 2 with root-zone extended was effective for plant growth performance and fruit yield.中玉トマト18段摘心の長期促成栽培における肥効調節型肥料の適用と生育途中の根域拡張に伴う「紐」適用が生育と果実収量に及ぼす効果を調べた．栽培容器は可動仕切り板で2つに仕切り区画当たり容量は2.8ℓとし，第8段花房開花時に仕切り板をはずして5.6ℓ（1st Box＋2nd Box）とした．試験区は2区で2nd Boxに紐を配置しない1本区と2nd Boxにもう１本を配した2本区である．2本区の草丈は1月以降，1本区に比べ高く推移し第18段花房の開花日が約10日早まり，成長の指標とした摘心時の茎頂部新鮮重も1本区の2倍となった．1株の果実収量は1本区で8kg，2本区で9kgとなり果実の糖度，酸度には両区間に差はなかった．栽培終了時の根の乾物重と茎切断面から採取した木部いっ泌液は両区間に差はなかったが，両区とも栽培終期の4月には生育が衰え葉色は黄緑色で果実の着色も不均一であった．木部いっ泌の成分分析ではNO(3)-N濃度が1本区で10me/ℓ，2本区で6me/ℓであり，これらの濃度は一般に養液栽培に使用される園試標準濃度よりも低かった．以上の結果から，第8段花房開花時に仕切りを開放し新区画への土壌と肥料ならびに紐の新たな適用は，生育安定と収量確保に効果的に作用することが明らかとなった．しかし，紐の有無にかかわらず生育後期の生育が不良となったことから，今後は施肥設計の面から，とくにNO(3)-NとSO(4)-Sの両面から検討する必要があると考察した

THE ANALYSIS OF RACE PACING IN ELITE COMPETITIVE LONG-DISTANCE SPEED SKATING

The purpose of this study was to investigate the characteristics of racing pattern adopted by elite male speed skaters in official 5000m race. Twenty-four male skaters, who participated at the World Single Distances Speed Skating Championships 2008, were recorded using video camera (60Hz). The top group (top12 ranked skaters) was significantly faster than the 2nd group (13th to 24th ranked skaters) from 350m line to the finishing line (

Weakly invertible cells in a weak ω\omega-category

We study weakly invertible cells in weak $\omega$-categories in the sense of Leinster, adopting Cheng's coinductive definition of weak invertibility. We show that weakly invertible cells in a weak $\omega$-category are closed under globular pasting. Using this, we generalise elementary properties of weakly invertible cells known to hold in strict $\omega$-categories to weak $\omega$-categories, and show that every weak $\omega$-category has a largest weak $\omega$-subgroupoid.Comment: 21 pages. Comments welcome