In order to overcome the challenges caused by flash memories and also to protect against errors related to reading information stored in DNA molecules in the shotgun sequencing method, the rank modulation method has been proposed. In the rank modulation framework, codewords are permutations. In this paper, we study the largest size P(n, d) of permutation codes of length n, i.e., subsets of the set Sn of all permutations on {1, ..., n} with the minimum distance at least d ∈ {1, ..., (n/2)} under the Kendall τ-metric. By presenting an algorithm and two theorems, we improve the known lower and upper bounds for P(n, d). In particular, we show that P(n, d) = 4 for all n ≥ 6 and 3/5 (n/2) < d ≤ 2/3 (n/2). Additionally, we prove that for any prime number n and integer r ≤ n/6, P(n, 3) ≤ (n − 1)! − n − 6r/√n2 − 8rn + 20r2 √(n − 1)!/n(n − r)!. This result greatly improves the upper bound of P(n, 3) for all primes n ≥ 37.

Searching similarity in time series (TS) datasets has gained widespread attention lately in databases classification and forecast domain. In this study, a TS similarity detection framework is proposed to explore alike-behavior fresh produce (FP) in the yield forecast domain through several factors. The sequential daily yield datasets of three types of FP, including strawberry, raspberry, and blueberry, as well as environmental information related to the Santa Maria region, California, between the years 2011 to 2019, are used to develop and evaluate the models. The framework's output is decided to be the similarity percentage (SP) by considering some thresholds that have been tuned using several synthetic yield datasets. According to the results, the SP is 82% and 52% for strawberry versus raspberry and strawberry versus blueberry, respectively. This indicates the fact that strawberry and raspberry have a relatively similar yield pattern compared to blueberry, which is a considerable matter in generalizing forecast models.

Adequately priced orders and time for fresh produce (FP) are two factors that bring commercial benefits to vendors and minimizes waste. However, many factors, such as income, labor, and other trade issues, affect the price that include uncertainties due to climate change, making decisions on FP procurement prices and quantities extremely challenging. Two artificial intelligence-based forecasting tools, i.e., a single variate and a multivariate model, are trained, tested, and compared in this study to predict future daily offer prices up to 7 days ahead for strawberries using mutual transactions for the distribution centers of Loblaws Companies Limited (LCL) in Canada. Results reveal that the developed multivariate model, utilizing both prices of the LCL dataset and California's strawberries yield dataset as predictors, outperforms the best single variate model.

In this study, a comparison of time-series modeling with linear and nonlinear ML tools is conducted for fresh produce (FP) yield forecast. The consecutive monthly weather and yield dataset of Oxnard, California, corresponding to the years 2007 to 2014, are applied for models' development and training by examining the diverse combinations of predictors. The forecast performance is then assessed on the next two years ahead. The sensitivity analysis is performed as the preprocessing approach to ascertain the effective lag-time of the predictors. Results reveal the efficiency of time-series analysis and modeling in FP yield forecast as the implementation of autoregressive predictors along with the exogenous variables, significantly improves the forecast accuracy.