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Abstract: The study of paper “Cryptanalysis of RSA with Private Key d less than N 0.292’ [IEEE Trans. Information Theory, 46 (2000) 1339], which Boneh and Durfee published in IEEE Transactions on Information Theory in July 2000, supported that when d < N 0.292, the RSA system can be cracked by using the LLL algorithm. In this paper, we find ways to utilize the LLL algorithm to break the RSA system even when the value of d is large. According to the proposed cryptanalysis, if d satisfies ∣λ − d∣< N 0.25, the RSA system will be possible to be resolved computationally. [Copyright &y& Elsevier]

Abstract: In this paper scheduling communications in data gathering networks is analyzed. We study collecting information by a set of sensors, each of which stores the data in its memory buffer and then passes them to a base station. The network lifetime ends as soon as the first node is out of memory. We use a divisible load model to propose a communication scheduling algorithm that maximizes the system lifetime, and hence, the total amount of gathered information. The influence of the sensor communication rates on the obtained schedules is exposed in a series of computational experiments. [Copyright &y& Elsevier]

Abstract: The polygon mesh is an important primitive used in representing 3D models. Its specification consists of topological and geometrical quantities; where the former describes the connection nodes, edges and faces, and the latter describes attributes such as node positions, face colors, etc. Our interest here lies with the encoding of the topology. Specifically, this paper presents a linear-time information-theoretically optimal compression algorithm for encoding a planar 2-manifold polygon mesh to a bit string X. [Copyright &y& Elsevier]

Abstract: While the agility of networked organizational structures is important for organizational performance, studies on how to evaluate it remain scant, probably because the difficulty in measuring network evolution. In this conceptual paper, we propose two measures – network entropy and mutual information – to characterize the agility of networked organizational structure. Rooted in graph theory and information theory, these two measures capture network evolution in a comprehensive and parsimonious way. They indicate the uncertainty (or disorder) at the network level as well as the degree distribution at the individual level. We also propose an algorithm for applying them in the scenario of adding links to a network while holding the number of nodes fixed. Both simulated and real networks are used for demonstration. Implications and areas for future research are discussed in the end. [Copyright &y& Elsevier]

Abstract: Economic theory, game theory and mathematical statistics have all increasingly become algorithmic sciences. Computable Economics, Algorithmic Game Theory and Algorithmic Statistics are frontier research subjects. All of them, each in its own way, are underpinned by (classical) recursion theory – and its applied branches, say computational complexity theory or algorithmic information theory – and, occasionally, proof theory. These research paradigms have posed new mathematical and metamathematical questions and, inadvertently, undermined the traditional mathematical foundations of economic theory. A concise, but partial, pathway into these new frontiers is the subject matter of this paper. Interpreting the core of mathematical economic theory to be defined by General Equilibrium Theory and Game Theory, a general – but concise – analysis of the computable and decidable content of the implications of these two areas are discussed. Issues at the frontiers of macroeconomics, now dominated by Recursive Macroeconomic Theory (The qualification ‘recursive’ here has nothing to do with ‘recursion theory’. Instead, this is a reference to the mathematical formalizations of the rational economic agent’s intertemporal optimization problems, in terms of Markov Decision Processes, (Kalman) Filtering and Dynamic Programming, where a kind of ‘recursion’ is invoked in the solution methods. The metaphor of the rational economic agent as a ‘signal processor’ underpins the recursive macroeconomic paradigm.), are also tackled, albeit ultra briefly. The point of view adopted is that of classical recursion theory and varieties of constructive mathematics. [Copyright &y& Elsevier]

Abstract: In this paper a particle gradient evolutionary algorithm (PGEA) for solving complex multi-objective optimization problems is presented according to the gradient of particles, the transportation orbit of particles, the minimum principle of free energy decreasing, and the law of entropy increasing of particle systems in the phase space based on a transportation theory. This algorithm includes two sub-algorithms: the first is to define the PGEA energy and entropy, a rank function, and a niche function and then calculate the rank function values of every particle in the phase space; the second is to solve for the optimal Pareto front of a multi-objective optimization problem. The theory of a particle system changing from non-equilibrium to equilibrium is used to design the algorithm in order to drive all the individuals in the population to have a chance to participate in the evolving operation to obtain the Pareto optimal solutions of the multi-objective problems quickly and evenly. Our experiments show that this algorithm cannot only converge to the global Pareto optimal front quickly, uniformly, and precisely, but also can avoid the premature phenomenon of multi-objective problems. [Copyright &y& Elsevier]