Error and attack tolerance of complex networks

Many complex systems, such as communication networks, display a surprising degree of robustness: while key components regularly malfunction, local failures rarely lead to the loss of the global information-carrying ability of the network. The stability of these complex systems is often attributed to the redundant wiring of the functional web defined by the systems' components. In this paper we demonstrate that error tolerance is not shared by all redundant systems, but it is displayed only by a class of inhomogeneously wired networks, called scale-free networks. We find that scale-free networks, describing a number of systems, such as the World Wide Web, Internet, social networks or a cell, display an unexpected degree of robustness, the ability of their nodes to communicate being unaffected by even unrealistically high failure rates. However, error tolerance comes at a high price: these networks are extremely vulnerable to attacks, i.e. to the selection and removal of a few nodes that play the most important role in assuring the network's connectivity.Comment: 14 pages, 4 figures, Late

HIGH-SPEED CO-PROCESSORS BASED ON REDUNDANT NUMBER SYSTEMS

There is a growing demand for high-speed arithmetic co-processors for use in applications with computationally intensive tasks. For instance, Fast Fourier Transform (FFT) co-processors are used in real-time multimedia services and financial applications use decimal co-processors to perform large amounts of decimal computations. Using redundant number systems to eliminate word-wide carry propagation within interim operations is a well-known technique to increase the speed of arithmetic hardware units. Redundant number systems are mostly useful in applications where many consecutive arithmetic operations are performed prior to the final result, making it advantageous for arithmetic co-processors. This thesis discusses the implementation of two popular arithmetic co-processors based on redundant number systems: namely, the binary FFT co-processor and the decimal arithmetic co-processor. FFT co-processors consist of several consecutive multipliers and adders over complex numbers. FFT architectures are implemented based on fixed-point and floating-point arithmetic. The main advantage of floating-point over fixed-point arithmetic is the wide dynamic range it introduces. Moreover, it avoids numerical issues such as scaling and overflow/underflow concerns at the expense of higher cost. Furthermore, floating-point implementation allows for an FFT co-processor to collaborate with general purpose processors. This offloads computationally intensive tasks from the primary processor. The first part of this thesis, which is devoted to FFT co-processors, proposes a new FFT architecture that uses a new Binary-Signed Digit (BSD) carry-limited adder, a new floating-point BSD multiplier and a new floating-point BSD three-operand adder. Finally, a new unit labeled as Fused-Dot-Product-Add (FDPA) is designed to compute AB+CD+E over floating-point BSD operands. The second part of the thesis discusses decimal arithmetic operations implemented in hardware using redundant number systems. These operations are popularly used in decimal floating-point co-processors. A new signed-digit decimal adder is proposed along with a sequential decimal multiplier that uses redundant number systems to increase the operational frequency of the multiplier. New redundant decimal division and square-root units are also proposed. The architectures proposed in this thesis were all implemented using Hardware-Description-Language (Verilog) and synthesized using Synopsys Design Compiler. The evaluation results prove the speed improvement of the new arithmetic units over previous pertinent works. Consequently, the FFT and decimal co-processors designed in this thesis work with at least 10% higher speed than that of previous works. These architectures are meant to fulfill the demand for the high-speed co-processors required in various applications such as multimedia services and financial computations

High-Level Modular Autopilot Solution for Fast Prototyping of Unmanned Aerial Systems

Article number 9291382A redundant fast prototyping autopilot solution for unmanned aerial systems has been developed and successfully tested outdoors. While its low-level backbone is executed in a Raspberry Pi R 3 + NAVIO2 R with a backup autopilot, the computational power of an Intel R NUC mini-computer is employed to implement complex functionalities directly in Simulink R , thus including in-flight debugging, tuning and monitoring. Altogether, the presented tool provides a flexible and user-friendly high-level environment with enhanced computational capabilities, which drastically reduces the prototyping timespans of complex algorithms –between 50% and 75%, according to our long and proven experience in aerial robotics–, while preventing incidents thanks to its redundant design with a human-in-the-loop pilot on the reliable PX4. Three typical outdoor cases are carried out for validation in real-life scenarios, all mounted in a DJI c F550 platform. Full integration results and telemetry for more than 50 hours of outdoor flight tests are provided.Ministerio de Economía, Industria y Competitividad DPI2017-89790-RPrograma Horizonte 2020. Unión Europea 779411Programa Horizonte 2020. Unión Europea 87147

The Huges Array Co-Processor and Its Application to Robotics

This report describes the results of twelve months research involving the Hughes array co-processor. This work began with the testing and debugging of the existing system, continued with the development of software to interface the co-processor to a host machine and concluded with the implementation of a trajectory planning algorithm for redundant manipulators. A loader program has been developed which allows simple programs to be executed. A library of C-callable routines has also been created and this enables the fabrication of more complex systems which require a high level of interaction between the host and co-processor. Routines to perform square root, sine and cosine functions have been designed and these have been used successfully in the development of a trajectory planning algorithm. This algorithm uses the co-processor to compute in parallel a large number of forward kinematics solutions and by doing so is able to convert a cartesian space trajectory into a joint space path for a redundant manipulator. The performance of the processor has been analyzed and a number of recommendations have been made concerning future implementations

Efficient Reduced-Bias Genetic Algorithm (ERBGA) for Generic Community Detection Objectives

Community structure identification has been an important research area for biology, physics, information systems, and social sciences for studying properties of networks representing complex relationships. Lately, Genetic Algorithms (GAs) are being utilized for community detection. GAs are machine-learning methods that mimic natural selection. However, previous approaches suffer from some deficiencies: redundant representation and linearity assumption, that we will try to address. in. The algorithm presented here is a novel framework that addresses both of these above issues. This algorithm is also flexible as it is easily adapted to any given mathematical objective. Additionally, our approach doesn’t require prior information about the number of true communities in the network. Overall, our efficient approach holds potential for sifting out communities representing complex relationships in networks of interest across different domains

Linear Radom Vibration of Structural Systems with Singular Mass Matrices

A framework is developed for determining the stochastic response of linear multi-degree-of-freedom (MDOF) structural systems with singular matrices. This system modeling can arise when using more than the minimum number of coordinates, and can be advantageous, for instance, in cases of complex multibody systems whose dynamics satisfy a number of constraints. In such cases the explicit formulation of the equations of motion can be a nontrivial task, whereas the introduction of additional/redundant degrees of freedom can facilitate the formulation of the equations of motion in a less labor-intensive manner. Relying on the generalized matrix inverse theory and on the Moore-Penrose (M-P) matrix inverse, standard concepts, relationships, and equations of the linear random vibration theory are extended and generalized herein to account for systems with singular matrices. Adopting a state-variable formulation, equations governing the system response mean vector and covariance matrix are formed and solved. Further, it is shown that a complex modal analysis treatment, unlike the standard system modeling case, does not lead to decoupling of the equations of motion. However, relying on a singular value decomposition of the system transition matrix significantly facilitates the efficient computation of the system response statistics. A linear structural system with singular matrices is considered as a numerical example for demonstrating the applicability of the methodology and for elucidating certain related numerical aspects

Metabolite essentiality elucidates robustness of Escherichia coli metabolism

Complex biological systems are very robust to genetic and environmental changes at all levels of organization. Many biological functions of Escherichia coli metabolism can be sustained against single-gene or even multiple-gene mutations by using redundant or alternative pathways. Thus, only a limited number of genes have been identified to be lethal to the cell. In this regard, the reaction-centric gene deletion study has a limitation in understanding the metabolic robustness. Here, we report the use of flux-sum, which is the summation of all incoming or outgoing fluxes around a particular metabolite under pseudo-steady state conditions, as a good conserved property for elucidating such robustness of E. coli from the metabolite point of view. The functional behavior, as well as the structural and evolutionary properties of metabolites essential to the cell survival, was investigated by means of a constraints-based flux analysis under perturbed conditions. The essential metabolites are capable of maintaining a steady flux-sum even against severe perturbation by actively redistributing the relevant fluxes. Disrupting the flux-sum maintenance was found to suppress cell growth. This approach of analyzing metabolite essentiality provides insight into cellular robustness and concomitant fragility, which can be used for several applications, including the development of new drugs for treating pathogens.Comment: Supplements available at http://stat.kaist.ac.kr/publication/2007/PJKim_pnas_supplement.pd