20360088
Commentary on an open question
Abstract In this commentary, we give the triangular recurrence relations for the elements of the matrix T  = ( T i , j ) =  L 1 D −1 S 1 and its inverse T - 1 = ( T ¯ i , j ) = S 2 DL 1 - 1 , respectively, which have also answered the open question put forward by El-Mikkawy. Moreover, with the recurrences, a computational MAPLE program is written to generate the elements of T and T −1 .
22669776
Identities via Bell matrix and Fibonacci matrix
In this paper, we study the relations between the Bell matrix and the Fibonacci matrix, which provide a unified approach to some lower triangular matrices, such as the Stirling matrices of both kinds, the Lah matrix, and the generalized Pascal matrix. To make the results more general, the discussion is also extended to the generalized Fibonacci numbers and the corresponding matrix. Moreover, based on the matrix representations, various identities are derived.
17247210
Identities on Bell polynomials and Sheffer sequences
In this paper, we study exponential partial Bell polynomials and Sheffer sequences. Two new characterizations of Sheffer sequences are presented, which indicate the relations between Sheffer sequences and Riordan arrays. Several general identities involving Bell polynomials and Sheffer sequences are established, which reduce to some elegant identities for associated sequences and cross sequences.
6659460
Generalized Riordan arrays
In this paper, we generalize the concept of Riordan array. A generalized Riordan array with respect to c"n is an infinite, lower triangular array determined by the pair (g(t),f(t)) and has the generic element d"n","k=[t^n/c"n]g(t)(f(t))^k/c"k, where c"n is a fixed sequence of non-zero constants with c"0=1. We demonstrate that the generalized Riordan arrays have similar properties to those of the classical Riordan arrays. Based on the definition, the iteration matrices related to the Bell polynomials are special cases of the generalized Riordan arrays and the set of iteration matrices is a subgroup of the Riordan group. We also study the relationships between the generalized Riordan arrays and the Sheffer sequences and show that the Riordan group and the group of Sheffer sequences are isomorphic. From the Sheffer sequences, many special Riordan arrays are obtained. Additionally, we investigate the recurrence relations satisfied by the elements of the Riordan arrays. Based on one of the recurrences, some matrix factorizations satisfied by the Riordan arrays are presented. Finally, we give two applications of the Riordan arrays, including the inverse relations problem and the connection constants problem.
12965386
A Note on the Relationships Between the Generalized Bernoulli and Euler Polynomials
1. IntroductionIn many contexts, matrix representation of a particular counting se-quence is considered, and such a representation provides a powerful com-putational tool for deriving identities and explicit formulas related to thesequence, see, for example [3, 7].Recently, Cheon [2] rederived several known properties and relationshipsinvolving the classical Bernoulli polynomials
6454595
Generating Incremental ETL Processes Automatically
Incremental ETL processes are used for the incremental maintenance of data warehouses, which is generally designed by users with ETL tools. Using existing methods of incremental maintenance of materialized views for reference, we put forward an approach to generate an incremental ETL process automatically from the full ETL process in this paper. Existing researches are focused on the incremental maintenance of materialized views in such circumstances which involve the operators of selection, projection, join and aggregation but difference operators excluded. Since difference operators are used frequently in an ETL process, we first discuss incremental maintenance of materialized views defined with difference operators in detail
1912292
Opportunistic Energy-Efficient Contact Probing in Delay-Tolerant Applications
In many delay-tolerant applications, information is opportunistically exchanged between mobile devices that encounter each other. In order to affect such information exchange, mobile devices must have knowledge of other devices in their vicinity. We consider scenarios in which there is no infrastructure and devices must probe their environment to discover other devices. This can be an extremely energy-consuming process and highlights the need for energy-conscious contact-probing mechanisms. If devices probe very infrequently, they might miss many of their contacts. On the other hand, frequent contact probing might be energy inefficient. In this paper, we investigate the tradeoff between the probability of missing a contact and the contact-probing frequency. First, via theoretical analysis, we characterize the tradeoff between the probability of a missed contact and the contact-probing interval for stationary processes. Next, for time-varying contact arrival rates, we provide an optimization framework to compute the optimal contact-probing interval as a function of the arrival rate. We characterize real-world contact patterns via Bluetooth phone contact-logging experiments and show that the contact arrival process is self-similar. We design STAR, a contact-probing algorithm that adapts to the contact arrival process. Instead of using constant probing intervals, STAR dynamically chooses the probing interval using both the short-term contact history and the long-term history based on time of day information. Via trace-driven simulations on our experimental data, we demonstrate that STAR requires three to five times less energy for device discovery than a constant contact-probing interval scheme.
14325893
Maintaining K-Anonymity against Incremental Updates
K-anonymity is a simple yet practical mechanismto protect privacy against attacks of re-identifying individuals by joining multiple public data sources. All existing methods achieving k-anonymity assume implicitly that the data objects to be anonymized are given once and fixed. However, in many applications, the real world data sources are dynamic. In this paper, we investigate the problem of maintaining k-anonymity against incremental updates, and propose a simple yet effective solution. We analyze how inferences from multiple releases may temper the k-anonymity of data, and propose the monotonic incremental anonymization property. The general idea is to progressively and consistently reduce the generalization granularity as incremental updates arrive. Our new approach guarantees the k-anonymity on each release, and also on the inferred table using multiple releases. At the same time, our new approach utilizes the more and more accumulated data to reduce the information loss.
19790030
Extracting frequent connected subgraphs from large graph sets
Mining frequent patterns from datasets is one of the key success of data mining research. Currently, most of the studies focus on the data sets in which the elements are independent, such as the items in the marketing basket. However, the objects in the real world often have close relationship with each other. How to extract frequent patterns from these relations is the objective of this paper. The authors use graphs to model the relations, and select a simple type for analysis. Combining the graph theory and algorithms to generate frequent patterns, a new algorithm called Topology, which can mine these graphs efficiently, has been proposed. The performance of the algorithm is evaluated by doing experiments with synthetic datasets and real data. The experimental results show that Topology can do the job well. At the end of this paper, the potential improvement is mentioned.
18247103
InfoMiner+: mining partial periodic patterns with gap penalties
In this paper we focus on mining periodic patterns allowing some degree of imperfection in the form of random replacement from a perfect periodic pattern. Information gain was proposed to identify patterns with events of vastly different occurrence frequencies and adjust for deviation from a pattern. However, it does not involve a penalty if there exists some gap between pattern occurrences. In many applications, e.g., bioinformatics, it is important to identify subsequences that a pattern repeats perfectly (or near perfectly). As a solution, we extend the information gain measure to include a penalty for gaps between pattern occurrences. We call this measure generalized information gain. Furthermore, we need to find a subsequence S' such that for a pattern P, the generalized information gain of P in S' is high. This is particularly useful in locating repeats in DNA sequences. In this paper, we developed an effective mining algorithm, InfoMiner+, to simultaneously mine significant patterns and associated subsequences.