Recurrence Relations for the Linear Transformation Preserving the Strong $q$-Log-Convexity

Liu, Lily Li; Li, Yanan

doi:10.37236/5913

Cited by 7 publications

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“…Remark 1.4. For a 2 ≥ 0, b 2 ≥ 0 and a 1 = b 1 = 0 in Theorem 1.3, recently Liu and Li [25] independently proved the result.…”

Section: Introductionmentioning

confidence: 93%

q-log-convexity from linear transformations and polynomials with only real zeros

Zhu

2018

European Journal of Combinatorics

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In this paper, we mainly study the stability of iterated polynomials and linear transformations preserving the strong q-log-convexity of polynomials Let [T n,k ] n,k≥0 be an array of nonnegative numbers. We give some criteria for the linear transformationpreserving the strong q-log-convexity (resp. log-convexity). As applications, we derive that some linear transformations (for instance, the Stirling transformations of two kinds, the Jacobi-Stirling transformations of two kinds, the Legendre-Stirling transformations of two kinds, the central factorial transformations, and so on) preserve the strong q-log-convexity (resp. log-convexity) in a unified manner. In particular, we confirm a conjecture of Lin and Zeng, and extend some results of Chen et al., and Zhu for strong q-log-convexity of polynomials, and some results of Liu and Wang for transformations preserving the log-convexity.The stability property of iterated polynomials implies the q-log-convexity. By applying the method of interlacing of zeros, we also present two criteria for the stability of the iterated Sturm sequences and q-log-convexity of polynomials. As consequences, we get the stabilities of iterated Eulerian polynomials of type A and B, and their q-analogs. In addition, we also prove that the generating functions of alternating runs of type A and B, the longest alternating subsequence and up-down runs of permutations form a q-log-convex sequence, respectively.MSC: 05A20, 11B68

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“…Remark 1.4. For a 2 ≥ 0, b 2 ≥ 0 and a 1 = b 1 = 0 in Theorem 1.3, recently Liu and Li [25] independently proved the result.…”

Section: Introductionmentioning

confidence: 93%

q-log-convexity from linear transformations and polynomials with only real zeros

Zhu

2018

European Journal of Combinatorics

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“…However, only one quality dimension of web services is considered in the recommendation model, which is often not enough for the practical recommendation requirements. In the future, we will further refine our work by considering multiple quality dimensions as well as their linear correlations [51][52][53] and nonlinear correlations [54][55][56][57][58]. Besides, data type diversity is another challenge in the big data environment.…”

Section: Discussionmentioning

confidence: 96%

Robust and Privacy-Preserving Service Recommendation over Sparse Data in Education

Chen

Yan

2019

Wireless Communications and Mobile Computing

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Service recommendation has become one of the most effective approaches to quickly extract insightful information from big educational data. However, the sparsity of educational service quality data (from multiple platforms or parties) used to make service recommendations often leads to few even null recommended results. Moreover, to protect sensitive business information and obey laws, preserving user privacy during the abovementioned multisource data integration process is a very important but challenging requirement. Considering the above challenges, this paper integrates Locality-Sensitive Hashing (LSH) with hybrid Collaborative Filtering (HCF) techniques for robust and privacy-aware data sharing between different platforms involved in the cross-platform service recommendation process. Furthermore, to minimize the “False negative” recommended results incurred by LSH and enhance the success of recommended results, we propose two optimization strategies to reduce the probability that similar neighbours of a target user or similar services of a target service are overlooked by mistake. Finally, we conduct a set of experiments based on a real distributed service quality dataset, i.e., WS-DREAM, to validate the feasibility and advantages of our proposed recommendation approach. The extensive experimental results show that our proposal performs better than three competitive methods in terms of efficiency, accuracy, and successful rate while guaranteeing privacy-preservation.

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“…For simple experiments, we only test the discrete data in Movielens dataset without testing other data types popular in the big data environment, e.g., continuous data type [25][26][27][28][29], Boolean data type [30], and fuzzy data type [31][32][33]. In addition, we only test a single criterion (user rating) without discussing the popular cases with multiple criteria [34][35][36][37][38][39][40][41][42][43][44] and their inner linear correlations [45][46][47][48], nonlinear correlations [49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66], and weights [67][68][69][70][71][72]…”

Section: Discussionmentioning

confidence: 99%

Improved LSH for privacy-aware and robust recommender system with sparse data in edge environment

Chen

Yang

2019

J Wireless Com Network

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Recommender systems have become a popular and effective way to quickly discover new service items that are probably preferred by prospective users. Through analyzing the historical service usage data produced in the past, a recommender system can infer the potential user preferences and make accurate recommendations accordingly. However, in the edge environment, the service usage data stored in each edge server are often very sparse, which may result in expected cold-start problems. Besides, in the edge environment, the data required to make an optimal service recommendation decision are often stored in different edge clients or servers, which require additional privacy-preservation strategies to secure the sensitive data involved. Considering the above two drawbacks, traditional locality-sensitive hashing (LSH) is improved to be multi-probing LSH and then introduced to aid the recommendation process so as to guarantee the security and robustness of recommender systems. Experiments conducted on well-known dataset prove the effectiveness and efficiency of the work.

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Recurrence Relations for the Linear Transformation Preserving the Strong $q$-Log-Convexity

Cited by 7 publications

References 0 publications

q-log-convexity from linear transformations and polynomials with only real zeros

q-log-convexity from linear transformations and polynomials with only real zeros

Robust and Privacy-Preserving Service Recommendation over Sparse Data in Education

Improved LSH for privacy-aware and robust recommender system with sparse data in edge environment

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