The Fibonacci-Padovan sequence and MacWilliams transform matrices

A relationship between the MacWilliams transform matrices and the classical integer Fibonacci, Lucas, and Padovan sequences is established. Namely, it is proved that the summation over some naturally chosen planes in the pyramid composed of these matrices yields a new integer sequence, which is the convolution of the Fibonacci numbers and the (alternating) Padovan numbers. In turn, this convolution is linearly represented in terms of the Lucas numbers and the Padovan numbers.     

Fibonacci数和Lucas数的联合迭代算法

针对超大Fibonacci数和Lucas数的计算问题,提出一种Fibonacci-Lucas数联合迭代算法,在单次循环中选择二倍步长的方式,采用交替计算Fibonacci数和Lucas数的方法,减低超大数迭代算式的复杂度,提高程序的计算效率。实验结果表明,该算法运行时间比现有的矩阵迭代算法更短。     

Tumble, a fast simple iteration algorithm for Fibonacci

A faster linear iteration process for Fibonacci (and Lucas) numbers is given. Algorithms are derived for individual numbers and for sequence generation. A general algorithm for generalized Fibonacci numbers is derived from these.     

面向噪声图像的自适应高容量隐写算法

面向雷达、遥感图像等含噪图像,提出了一种利用噪声自适应嵌入的位平面加密算法。首先对不同的噪声图像利用遗传算法自适应找到最佳嵌入阈值,在噪声值较高处使用一种无须密钥的加密算法将两位秘密信息分别交叉嵌入到第一、三位平面中。然后利用BBE(binary-block embedding)算法将标记位数据压缩到第二位平面。最后在第二位平面冗余处用同样的加密算法将剩余秘密信息分别嵌入到第二、四位平面中完成信息隐藏。实验分析表明在满足高容量嵌入的条件下,与其他自适应位平面隐写算法相比有良好的隐蔽性以及较强的鲁棒性,同时能抵抗目前较好的隐写分析算法,保证了数据传送的安全性。     

A rough set approach to reasoning under uncertainty

Abstract

Reasoning with uncertain information is a problem of key importance when dealing with information about the real world. Obtaining the precise numbers required by many uncertainty handling formalisms can be a problem. The theory of rough sets makes it possible to handle uncertainty without the need for precise numbers, and so has some advantages in such situations. This paper presents an introduction to various forms of reasoning under uncertainty that are based on rough sets. In particular, a number of sets of numerical and symbolic truth values which may be used to augment propositional logic are developed, and a semantics for these values is provided based upon the notion of possible worlds. Methods of combining the truth values are developed so that they may be propagated when augmented logic formulae are combined, and their use is demonstrated in theorem proving.     

Inversion of the generalized Fibonacci matrix by convolution

A convolution formula containing the generalized Fibonacci numbers and applications of this formula are investigated. Starting from the convolution formula, we derive combinatorial identities involving generalized and usual Fibonacci numbers, as well as the Lucas numbers. The inversion of a lower triangular matrix and the generalized inversion of strictly lower triangular Toeplitz matrix whose non-zero elements are generalized Fibonacci numbers are considered.     

A method for computing Lucas sequences

Most of public-key cryptosystems rely on one-way functions, which can be used to encrypt and sign messages. Their encryption and signature operations are based on the computation of exponentiation. Recently, some public-key cryptosystems are proposed and based on Lucas functions, and the Lucas sequences are performed as S = V(d)modN. In this paper, we will transform the concept of addition chains for computing the exponentiation evaluations to the Lucas chains for computing the Lucas sequences. Theoretically, the shorter Lucas chain for d is generated, the less computation time for evaluating the value V(d) is required. Therefore, we proposed a heuristic algorithm for evaluating a shorter Lucas chain and then use it to compute the Lucas sequence with less modular multiplications.     

Comments on `Dynamic path planning for a mobile automation withlimited information on the environment' [with reply]

Two path-planning algorithms are presented for the case of an uncertain environment, and a bound for the length of path generated by each algorithm is given. Lucas shows that the least upper bound corresponding to the first algorithm is incorrect, and suggests a revised algorithm which has that upper bound for its generated path lengths. However, Lumelsky et al. points out that the modification by Lucas, which requires the automaton to try to stick to the M-line, would defect the main idea behind the algorithm and thus cannot be accepted     

Abstract geometrical computation 3: black holes for classical and analog computing

The so-called Black Hole model of computation involves a non Euclidean space-time where one device is infinitely “accelerated” on one world-line but can send some limited information to an observer working at “normal pace”. The key stone is that after a finite duration, the observer has received the information or knows that no information was ever sent by the device which had an infinite time to complete its computation. This allows to decide semi-decidable problems and clearly falls out of classical computability. A setting in a continuous Euclidean space-time that mimics this is presented. Not only is Zeno effect possible but it is used to unleash the black hole power. Both discrete (classical) computation and analog computation (in the understanding of Blum, Shub and Smale) are considered. Moreover, using nested singularities (which are built), it is shown how to decide higher levels of the corresponding arithmetical hierarchies.     

基于限制非对称相似关系模型的规则获取算法研究

粗糙集理论在不完备信息系统中的应用,是将粗糙集理论进一步推向实用的关键之一,而经典的粗糙集理论对不完备信息系统的处理显得束手无策.在分析研究已有的扩充粗糙集理论模型的基础上,进一步提出基于限制非对称相似关系模型,并将经典的可辨识关系矩阵加以扩充,定义了限制非对称相似关系下的可辨识关系矩阵,采用布尔推理方法,直接从不完备信息系统中提取规则而无需改变初始不完备信息系统的结构.实验结果表明,所获得的决策规则简洁,与缺省值无关.     

Generalized score functions on interval-valued intuitionistic fuzzy sets with preference parameters for different types of decision makers and their application

In this paper, the interval-valued intuitionistic fuzzy sets (IVIFSs) are studied from the viewpoint of the decision makers’ preference. Firstly, two series of principles are proposed to guide the ranking of interval-valued intuitionistic fuzzy numbers (IVIFNs), and two kinds of illustrative generalized score functions on IVIFSs are proposed according to the newly proposed principles. Secondly, two kinds of generalized score functions on IVIFSs are proposed based on decision-makers’ preference. The two generalized score functions are both of two parameters, which represent the decision makers’ attitudinal characters on the classical score values and the classical accuracy values on IVIFNs, respectively. Thirdly, two kinds of generalized score functions on IVIFSs, which are suitable for ranking IVIFNs when there is no information about the importance weights of the classical score values and accuracy values on IVIFNs, are proposed based on integral. Fourthly, three kinds of multi-criteria decision-making (MCDM) methods in interval-valued intuitionistic fuzzy setting are proposed. Finally, an example shows that when a novel generalized score function on IVIFSs is proposed, its suitable application environments should also be pointed out.     

Linking Classical and Quantum Key Agreement: Is There a Classical Analog to Bound Entanglement?

Abstract. After carrying out a protocol for quantum key agreement over a noisy quantum channel, the parties Alice and Bob must process the raw key in order to end up with identical keys about which the adversary has virtually no information. In principle, both classical and quantum protocols can be used for this processing. It is a natural question which type of protocol is more powerful. We show that the limits of tolerable noise are identical for classical and quantum protocols in many cases. More specifically, we prove that a quantum state between two parties is entangled if and only if the classical random variables resulting from optimal measurements provide some mutual classical information between the parties. In addition, we present evidence which strongly suggests that the potentials of classical and of quantum protocols are equal in every situation. An important consequence, in the purely classical regime, of such a correspondence would be the existence of a classical counterpart of so-called bound entanglement, namely ``bound information' that cannot be used for generating a secret key by any protocol. This stands in contrast to what was previously believed.     

A first-order logic for reasoning under uncertainty using rough sets

Reasoning with uncertain information is a problem of key importance when dealing with knowledge from real situations. Obtaining the precise numbers required by many uncertainty-handling formalisms can be a problem when building real systems. The theory of rough sets allows us to handle uncertainty without the need for precise numbers, and so has some advantages in such situations. The authors develop a set of symbolic truth values based upon rough sets which may be used to augment predicate logic, and provide methods for combining these truth values so that they may be propagated when augmented logic formulae are used in automated reasoning.     

Constructing Carmichael Numbers which are Strong Pseudoprimes to Several Bases

We describe here a method of constructing Carmichael numbers which are strong pseudoprimes to some sets of prime bases. We apply it to find composite numbers which are found to be prime by the Rabin-Miller test of packages as Axiom or Maple. We also use a variation of this method to construct strong Lucas pseudoprimes with respect to several pairs of parameters.     

How to fully represent expert information about imprecise properties in a computer system: random sets,fuzzy sets,and beyond: an overview

To help computers make better decisions, it is desirable to describe all our knowledge in computer-understandable terms. This is easy for knowledge described in terms on numerical values: we simply store the corresponding numbers in the computer. This is also easy for knowledge about precise (well-defined) properties which are either true or false for each object: we simply store the corresponding “true” and “false” values in the computer. The challenge is how to store information about imprecise properties. In this paper, we overview different ways to fully store the expert information about imprecise properties. We show that in the simplest case, when the only source of imprecision is disagreement between different experts, a natural way to store all the expert information is to use random sets; we also show how fuzzy sets naturally appear in such random set representation. We then show how the random set representation can be extended to the general (“fuzzy”) case when, in addition to disagreements, experts are also unsure whether some objects satisfy certain properties or not.     

MACBETH — An Interactive Path Towards the Construction of Cardinal Value Functions

The application of classical models and techniques for cardinal measurement of values usually requires a person (D) to answer very difficult questions. The MACBETH approach, presented in this paper, proposes a simple questioning procedure to 'drive' the interactive quantification of values through pairwise verbal judgements of difference of attractiveness between valuable elements of a set A. Technically, MACBETH uses a chain of four linear programs for assigning numbers to the elements of set A based upon the qualitative judgements expressed by D and to reveal possible sources of incoherence. In practice, this information is to be used as a basis for discussion and learning. MACBETH stands for Measuring Attractiveness by a Categorical Based Evaluation TecHnique.     

Implementing

This paper presents a term graph rewriting system as an implementation for the -calculus, a substitution-free language that can be used to describe the behaviour of functional programming languages at a very low level of granularity, and has first been defined in [Stéphane Lengrand. Call-by-value, call-by-name, and strong normalization for the classical sequent calculus. In Bernhard Gramlich and Salvador Lucas, editors, Electronic Notes in Theoretical Computer Science, volume 86. Elsevier, 2003; S. van Bakel, S. Lengrand, and P. Lescanne. The language : circuits, computations and classical logic. Submitted, 2004]. Since the calculus has a notion of binding, in the context of sharing a notion of rebinding is introduced that helps avoid double binding of names.     

From flow focusing to vortex formation in crossing microchannels

The paper is concerned with the experimental and numerical investigations of the vortex formation and flow focusing inside a cross-shaped microchannel domain. The local hydrodynamics in the junction area, upstream of the focusing region, is analyzed with the aim to characterize the onset and the evolution of the vortical structures, in correlation with the operating parameters. The numerical simulations based on a finite-volume approach are validated by direct flow visualizations using epifluorescence and confocal microscopy. The main result of the study is a flow pattern map, providing comprehensive information on the flow dynamics inside the microchannel junction as a function of the input flow rates and the corresponding Reynolds numbers. The flow pattern map identifies the limits of the flow focusing regime and the critical values of the parameters at which the vortical structures are formed. Beyond the breakdown of the classical flow focusing scenario with one focused output stream, flow patterns with two and four output streams are identified.     

A high-capacity performance-preserving blind technique for reversible information hiding via MIDI files using delta times

A new high-capacity information hiding method for embedding secret messages into MIDI files is proposed. The method can preserve the original musical performance of the cover MIDI file. The property of the variable-length quantity, which expresses the magnitude of the delta time before every event in a MIDI file, is utilized for secret bit embedding. The embedding is accomplished by padding the delta times with different numbers of leading constant bytes of 80₁₆ to represent the secret bits. The method is both reversible and blind because the original cover MIDI file can be restored completely from the stego-MIDI file by extracting the embedded data out from the resulting stego-MIDI file without referencing the original cover MIDI file. A capability of hiding a large amount of secret information is achieved since the delta time is a basic parameter that appears before every event in the MIDI file. Good experimental results yielded by the proposed method as well as a comparison of the method with five existing performance-preserving methods from the viewpoints of stego-file quality, payload capacity, and data security show the superiority and feasibility of the proposed method.

     

基于图像伪装与双向差值扩展的密文域可逆信息隐藏算法

数字图像在云环境下的安全性问题已成为信息安全领域的研究热点之一。为解决传统密文域可逆信息隐藏算法缺乏伪装性,容易受到恶意攻击与信息隐藏空间容量小的问题,提出了基于图像伪装加密与双向差值扩展的大容量密文域可逆信息隐藏算法。该算法首先利用矢量量化与离散小波变换两种技术对原始图像进行伪装加密,从而保证隐蔽性,使得图像在云环境中安全传递;其次采用基于双向差值扩展的信息隐藏技术对伪装加密图像进行秘密信息的嵌入,以实现高容量的信息隐藏。实验结果表明,所提算法不仅实现了图像伪装,而且最终得到的含密伪装图像与原始图像在视觉上无明显差别,峰值信噪比达到40 dB以上,对原始图像起到了很好的伪装效果;同时实现了高容量的秘密信息嵌入,图像平均嵌入率接近0.6 bpp,表现出了良好的实验性能。