We study the fluctuations, in the large deviations regime, of the longest increasing subsequence of a random i.i.d. sample on the unit square. In particular, our results yield the precise upper and lower exponential tails for the length of the longest increasing subsequence of a random permutation. §.

The interplay between two-dimensional percolation growth models and one-dimensional particle processes has always been a fruitful source of interesting mathematical phenomena. In this paper we develop a connection between the construction of Busemann functions in the Hammersley last-passage percolation model with i.i.d. random weights, and the existence, ergodicity and uniqueness of equilibrium...

OBJECTIVE The effect of flavonoids from alfalfa on the microbial flora was determined using molecular techniques of 16S ribosome deoxyribonucleic acid (rDNA) analysis. METHODS Four primiparous Holstein heifers fitted with ruminal cannulas were used in a 4×4 Latin square design and fed a total mixed ration to which alfalfa flavonoids extract (AFE) was added at the rates of 0 (A, control), 20 (...

We consider the concentration of measure for n iid, two-dimensional random variables, under the conditioning that they form a record. Under mild conditions, we show that all random variables tend to concentrate, as n ! 1, around limiting curves, which are the solutions of an appropriate variational problem. We also show that the same phenomenum occurs, without the records conditioning, for the ...

A longest increasing subsequence problem (LIS) is a well-known combinatorial problem with applications mainly in bioinformatics, where it is used in various projects on DNA sequences. Recently, a number of generalisations of this problem were proposed. One of them is to find an LIS among all fixed-size windows of the input sequence (LISW). We propose an algorithm for the LISW problem based on c...

ABSTRACT. We study the shape of the Young diagram λ associated via the Robinson–Schensted– Knuth algorithm to a random permutation in Sn such that the length of the longest decreasing subsequence is not bigger than a fixed number d; in other words we study the restriction of the Plancherel measure to Young diagrams with at most d rows. We prove that in the limit n → ∞ the rows of λ behave like ...

Given a sequence π1π2 . . . πn, a longest increasing subsequence (LIS) in a window π〈l, r〉= πlπl+1 . . . πr is a longest subsequence σ = πi1πi2 . . . πiT such that l ≤ i1 < i2 < · · · < iT ≤ r and πi1 < πi2 < · · · < πiT . We consider the Lisw problem, which is to find the longest increasing subsequences in a sliding window of fixed-size w over a sequence. Formally, it is to find a LIS for ever...

An experiment was conducted to study the effects of carbon tetrachloride (CCl4) on post-peak performance and serum enzymes of Hy-Line W-36 laying hens from 32-36 weeks of age. The experiment was carried out with a total of 192 laying hens in a completely randomized block design. During the experiment laying hens were allocated to 4 groups consisted of T1) no CCl4 as control diet, T2, T3 and T4)...

The use of a solvent-extraction process that removes corn oil from distillers grains produces a reduced-fat co-product (RFDG). To determine the optimal concentration of RFDG in mid-lactation diets, 22 multiparous and 19 primiparous Holstein cows were used in a completely randomized design for 8 wk, including a 2-wk covariate period. The RFDG was included at 0, 10, 20, and 30% of the diet on a d...

Growth, nutrient balance, plasma ammonia levels and urinary p-cresol excretion were evaluated in growing pigs fed diets containing various levels of zeolite A or clinoptilolite. In one growth trial, crossbred pigs averaging 25 kg initial body weight were assigned to diets containing no zeolite, .3% zeolite A or .5% clinoptilolite for a 6-wk growing phase trial. Average daily gain (ADG), average...