On-line Digit Set Conversion for Rational Digit Number

A number system that is well-designed can affect the computational time and the hardware implementation. An interesting number system called Round-to-Nearest coding (RN-coding) was proposed to reduce a time consuming in a rounding process. Rounding to the nearest in RN-coding can be done using only truncation at any positions in a sequence of digits (representation). This concept can save a lot of time in a parallel or pipeline computation manner. However, an RN-coding does not support an on-line arithmetic computation. In this paper, we propose a rational digit number system which is composed of rational signed-digits in the digit set. This new system preserves a round-to-nearest property and is suitable for an on-line arithmetic computation. Performing on-line elementary arithmetic operations in our system can be done by an on-line digit set conversion algorithm. We show that our new algorithm, which is an improvement of an on-line addition algorithm in our previous work, can be demonstrated by an on-line finite automaton with a finite on-line delay k.A number system that is well-designed can affect the computational time and the hardware implementation. An interesting number system called Round-to-Nearest coding (RN-coding) was proposed to reduce a time consuming in a rounding process. Rounding to the nearest in RN-coding can be done using only truncation at any positions in a sequence of digits (representation). This concept can save a lot of time in a parallel or pipeline computation manner. However, an RN-coding does not support an on-line arithmetic computation. In this paper, we propose a rational digit number system which is composed of rational signed-digits in the digit set. This new system preserves a round-to-nearest property and is suitable for an on-line arithmetic computation. Performing on-line elementary arithmetic operations in our system can be done by an on-line digit set conversion algorithm. We show that our new algorithm, which is an improvement of an on-line addition algorithm in our previous work, can be demonstrated by an on-line finite automaton with a finite on-line delay k

Faster cellular automata cryptosystems with neighbor sequences

The encryption processes and cryptosystems are very important. We use them to protect our private information over the Internet. Cellular automata are ones of the computational models that can also be used in cryptosystems. The advantage of the cellular automata is their abilities to work in parallel, and thus can reduce the encryption time. Some applications require the encryption time to be small, so this paper aims to reduce the encryption time of the cellular automata cryptosystems. We propose a new technique to permit the cryptosystems to get the avalanche effect faster. This avalanche effect is one of the desired properties for cryptosystems. In the proposed technique, the new type of neighbor is defined, a sequence of neighbor tuples. We apply our technique to Seredynski and Bouvry’s work, and the results show that the number of iterations can be reduced up to three times. This makes our cellular automata cryptosystems run faster. The relationship between the size of the neighbor and the size of the cellular automata, and the effect of neighbor sequences to the hardware implementations are left for further studies

Mining High Utility Itemsets with Regular Occurrence

High utility itemset mining (HUIM) plays an important role in the data mining community and in a wide range of applications. For example, in retail business it is used for finding sets of sold products that give high profit, low cost, etc. These itemsets can help improve marketing strategies, make promotions/ advertisements, etc. However, since HUIM only considers utility values of items/itemsets, it may not be sufficient to observe product-buying behavior of customers such as information related to "regular purchases of sets of products having a high profit margin". To address this issue, the occurrence behavior of itemsets (in the term of regularity) simultaneously with their utility values was investigated. Then, the problem of mining high utility itemsets with regular occurrence (MHUIR) to find sets of co-occurrence items with high utility values and regular occurrence in a database was considered. An efficient single-pass algorithm, called MHUIRA, was introduced. A new modified utility-list structure, called NUL, was designed to efficiently maintain utility values and occurrence information and to increase the efficiency of computing the utility of itemsets. Experimental studies on real and synthetic datasets and complexity analyses are provided to show the efficiency of MHUIRA combined with NUL in terms of time and space usage for mining interesting itemsets based on regularity and utility constraints

On-line multiplication in real and complex base

Multiplication of two numbers represented in base is shown to be computable by an on-line algorithm when is a negative integer, a positive non-integer real number, or a complex number of the form�, where is a positive integer.

Arithmétique en ligne en base réelle et complexe

PARIS-BIUSJ-Thèses (751052125) / SudocCentre Technique Livre Ens. Sup. (774682301) / SudocPARIS-BIUSJ-Mathématiques rech (751052111) / SudocSudocFranceF

Mining top-k periodic-frequent pattern from transactional databases without support threshold

International audienceTemporal periodicity of patterns can be regarded as an important criterion for measuring the interestingness of frequent patterns in several applications. A frequent pattern can be said periodic-frequent if it appears at a regular interval. In this paper, we introduce the problem of mining the top-k periodic frequent patterns i.e. the periodic patterns with the k highest support. An efficient single-pass algorithm using a best-first search strategy without support threshold, called MTKPP (Mining Top-K Periodic-frequent Patterns), is proposed. Our experiments show that our proposal is efficient

Efficient mining top-k regular-frequent itemset using compressed tidsets

International audienceAssociation rule discovery based on support-confidence framework is an important task in data mining. However, the occurrence frequency (support) of a pattern (itemset) may not be a sufficient criterion for discovering interesting patterns. Temporal regularity, which can be a trace of behavior, with frequency behavior can be revealed as an important key in several applications. A pattern can be regarded as a regular pattern if it occurs regularly in a user-given period. In this paper, we consider the problem of mining top-k regular-frequent itemsets from transactional databases without support threshold. A new concise representation, called compressed transaction-ids set (compressed tidset), and a single pass algorithm, called TR-CT (Top-k Regular frequent itemset mining based on Compressed Tidsets), are proposed to maintain occurrence information of patterns and discover k regular itemsets with highest supports, respectively. Experimental results show that the use of the compressed tidset representation achieves highly efficiency in terms of execution time and memory consumption, especially on dense datasets

Efficient mining Top-k regular-frequent itemset using compressed tidsets

International audienceAssociation rule discovery based on support-confidence frame-work is an important task in data mining. However, the occurrence frequency (support) of a pattern (itemset) may not be a sufficient criterion for discovering interesting patterns. Temporal regularity, which can be a trace of behavior, with frequency behavior can be revealed as an important key in several applications. A pattern can be regarded as a regular pattern if it occurs regularly in a user-given period. In this paper, we consider the problem of mining top-k regular-frequent itemsets from transactional databases without support threshold. A new concise representation, called compressed transaction-ids set (compressed tidset), and a single pass algorithm, called TR-CT (Top-k Regular frequent itemset mining based on Compressed Tidsets), are proposed to maintain occurrence information of patterns and discover k regular itemsets with highest supports, respectively. Experimental results show that the use of the compressed tidset representation achieves highly efficiency in terms of execution time and memory consumption, especially on dense datasets