Cartesian Network Research Articles

Boundary Effects in the Diffusion of New Products on Cartesian Networks

The Role of Boundaries in the Spreading of Solar Peer effects by neighbors play a key role in the spreading of residential solar. Thus, people are more likely to install a solar system on their roof if some of their neighbors have already done so. Because people who live near the municipality boundary have fewer neighbors, does this imply that they are less likely to adopt solar? In “Boundary Effects in the Diffusion of New Products on Cartesian Networks,” Fibich, Levin, and Gillingham analyze this problem analytically using the Bass model on two-dimensional networks and empirically using data on installations of solar systems. They show that boundaries have a significant impact on the adoption of residential units near the municipality boundary. Their effect on the aggregate adoption in the municipality, however, is negligible.

Multi-chromosomal CGP-evolved RNN for signal reconstruction

A multi-chromosomal structure for neuro-evolution of recurrent neural networks (RNNs) with Cartesian genetic programming (CGP) architecture is presented to develop a signal reconstruction model. The group behaviour of multi-chromosomes evolved together is explored in terms of computational and structural complexity, and accurate reconstruction of the corrupted signal. Signal reconstruction modelling is done through prediction of missing samples, and a sliding window mechanism is utilized to recover long segments of missing samples in periodic and aperiodic corrupted signals. The proposed model is compared with the conventional single chromosome-based Cartesian Genetic Programming-evolved Recurrent Neural Network (CGPRNN) architecture as well as state-of-the-art machine learning algorithms, i.e. linear regression, random forest and long short-term memory deep learning neural network. Diverse network architectures of the proposed Multi-Chromosomal Cartesian Genetic Programming-evolved Recurrent Neural Network (MC-CGPRNN) are evolved to explore the robustness of algorithm in terms of optimization of hyper parameters, evolutionary speed and generalization ability. The proposed algorithm is trained and tested on speech signal with both periodic and aperiodic noise. The best trained network is also evaluated on standard music signals achieving remarkable results. Experimental results show that the proposed MC-CGPRNN algorithm achieved SNR of 25.23 dB for speech signal, 29.92 dB for guitar signal and 28.45 dB for flute signal in case of 50% missing samples showing best SNR improvement in comparison with its counterparts for time domain signal reconstruction.

All Digital Phase-Locked Loop Networks for Clock Generation and Distribution: Network Stability, Convergence and Performance

In this paper, we study networks of coupled oscillators applied to the distributed synthesis of clock signals for large systems-on-chip. The oscillators are implemented as interconnected all-digital phase-locked loops (ADPLLs), which are asynchronous control systems. We address the issue of modelling, synchronization and stability of both a single ADPLL and interconnected ADPLLs. We prove that the stability domain is universal for large Cartesian networks, and it related to the domain for a single ADPLL. We show that within the stability domain the network synchronises to the reference signal both in frequency and phase. A hardware verification of Cartesian networks is presented, and it is consistent with our theoretical findings. The proposed design may be useful for multiples engineering and physics applications, including clock generation, distributed computations, beamforming, and other applications, where the control over time synchronicity is crucially important for the system performance.

Overhead of using spare nodes

With the increasing fault rate on high-end supercomputers, the topic of fault tolerance has been gathering attention. To cope with this situation, various fault-tolerance techniques are under investigation; these include user-level, algorithm-based fault-tolerance techniques and parallel execution environments that enable jobs to continue following node failure. Even with these techniques, some programs with static load balancing, such as stencil computation, may underperform after a failure recovery. Even when spare nodes are present, they are not always substituted for failed nodes in an effective way. This article considers the questions of how spare nodes should be allocated, how to substitute them for faulty nodes, and how much the communication performance is affected by such a substitution. The third question stems from the modification of the rank mapping by node substitutions, which can incur additional message collisions. In a stencil computation, rank mapping is done in a straightforward way on a Cartesian network without incurring any message collisions. However, once a substitution has occurred, the optimal node-rank mapping may be destroyed. Therefore, these questions must be answered in a way that minimizes the degradation of communication performance. In this article, several spare node allocation and failed node substitution methods will be proposed, analyzed, and compared in terms of communication performance following the substitution. The proposed substitution methods are named sliding methods. The sliding methods are analyzed by using our developed simulation program and evaluated by using the K computer, Blue Gene/Q (BG/Q), and TSUBAME 2.5. It will be shown that when failures occur, the stencil communication performance on the K and BG/Q can be slowed around 10 times depending on the number of node failures. The barrier performance on the K can be cut in half. On BG/Q, barrier performance can be slowed by a factor of 10. Further, it will also be shown that almost no such communication performance degradation can be seen on TSUBAME 2.5. This is because TSUBAME 2.5 has an Infiniband network connected with a FatTree topology, while the K computer and BG/Q have dedicated Cartesian networks. Thus, the communication performance degradation depends on network characteristics.

Percolation of new products

In most models of diffusion of new products, every individual in the social network is a potential adopter. When, however, a fraction α of the individuals cannot adopt the product at any time, the new product percolates (rather than diffuses) in the network, similarly to movement through porous materials. We obtain explicit expressions for the fraction of adopters as a function of time, for complete networks, circular networks, D-dimensional Cartesian networks, small-worlds networks, and scale-free networks. These expressions show that the complex effect of percolation can be captured by two simple aggregate effects: Decreasing the market potential by 1−α, and reducing the peers effect by (1−α)k, where k depends on the network type. Hence, percolation of new products is qualitatively similar to diffusion of new products. In particular, there is no threshold value at which a phase transition occurs.

Generation of a Clocking Signal in Synchronized All-Digital PLL Networks

In this brief, we propose a discrete-time framework for the modeling and studying of all-digital phase-locked loop (ADPLL) networks with applications in clock-generating systems. The framework is based on a set of nonlinear stochastic iterating maps and allows us to study a distributed ADPLL network of arbitrary topology. We determine the optimal set of control parameters for the reliable synchronous clocking regime, taking into account the intrinsic noise from both local and reference oscillators. The simulation results demonstrate very good agreement with experimental measurements of a 65-nm CMOS ADPLL network. This brief shows that an ADPLL network can be synchronized both in frequency and phase. We show that for a large Cartesian network the average network jitter increases insignificantly with the size of the system.

The First Orchestrated Attack on Spinoza: Johannes Melchioris and the Cartesian Network in Utrecht.

This article examines the immediate Dutch reception of the Tractatus theologico-politicus. Using newfound archival sources it demonstrates that the anti-Spinoza activity of the Cartesians in Utrecht extends far beyond the well-known writings of Lambertus van Velthuysen and Regnerus van Mansveld. Their Cartesian network not only produced the very first public refutation to appear, but also formed a center for coordinating much of the Dutch response to Spinoza. This engagement, it is argued in closing, must be accounted for in Spinoza reception history, and forms the background to the mysterious visit Spinoza paid to Utrecht in the summer of 1673.

Turing instabilities on Cartesian product networks.

The problem of Turing instabilities for a reaction-diffusion system defined on a complex Cartesian product network is considered. To this end we operate in the linear regime and expand the time dependent perturbation on a basis formed by the tensor product of the eigenvectors of the discrete Laplacian operators, associated to each of the individual networks that build the Cartesian product. The dispersion relation which controls the onset of the instability depends on a set of discrete wavelengths, the eigenvalues of the aforementioned Laplacians. Patterns can develop on the Cartesian network, if they are supported on at least one of its constitutive sub-graphs. Multiplex networks are also obtained under specific prescriptions. In this case, the criteria for the instability reduce to compact explicit formulae. Numerical simulations carried out for the Mimura-Murray reaction kinetics confirm the adequacy of the proposed theory.

Fault Injection Based Channel Allocation Of Noc Architecture For Ldpc Decoders

Network-on-chip (NoC) architectures are emerging for the highly scalable, reliable, and modular on-chip communication infrastructure platform. The NoC architecture uses layered protocols and packet- switched networks which consist of on-chip routers, links, and network interfaces on a predefined topology. In this Project ,we design network-on-chip which is based on the Cartesian network environment. This project proposes the new Cartesian topology which is uded to reduce network routing time, and it is an suitable alternate to network design and implementation. The cartesian Network-On-Chip can be modelled using Verilog HDL and simulated using Modelsim software&Quartus II. Keywords: Network-on-Chip (NoC), Routing, Switching, Cut-through,Cartesian

Design Of High Performance Reconfigurable Routers Using Fpga

*Abstrsact — Network-on-chip(NoC) architectures are emerging for the highly scalable, reliable, and modular on-chip communication infrastructure platform. The NoC architecture uses layered protocols and packet-switched networks which consist of on-chip routers, links, and network interfaces on a predefined topology. In this Project, we design network-on-chip which is based on the Cartesian network environment. This project proposes the new Cartesian topology which is used to reduce network routing time, and it is a suitable alternate to network design and implementation. The Cartesian Network-OnChip can be modeled using Verilog HDL and simulated using Modelsim software.

Synchronization Analysis of Networks of Self-Sampled All-Digital Phase-Locked Loops

This paper analyses the stability of the synchronized state in Cartesian networks of identical all-digital phase-locked loops (ADPLLs) for clock distribution applications. Such networks consist in Cartesian grids of digitally-controlled oscillator nodes, where each node communicates only with its nearest neighbors. Under certain conditions, we show that the whole network may synchronize both in phase and frequency. A key aspect of this study lies in the fact that, in the absence of an absolute reference clock, the loop-filter in each ADPLL is operated on the irregular rising edges of the local oscillator and consequently, does not use the same operands depending on whether the local clock is leading or lagging. Under simple assumptions, these networks of so-called "self-sampled" all-digital phase-locked-loops (SS-ADPLLs) can be described as piecewise-linear systems, the stability of which is notoriously difficult to establish. The main contribution of this paper is a simple design rule that must be met by the coefficients of each loop-filter in order to achieve synchronization in a Cartesian network of arbitrary size. Transient simulations indicate that this necessary synchronization condition may also be sufficient for a specific (but important) class of SS-ADPLLs. A synthesis of the different approaches that have been conducted in the study of the synchronization of SS-ADPLLs is also done.

From discrete to continuous Wardrop equilibria

The notion of Wardrop equilibrium in congested networks has been very popular in congested traffic modelling since its introduction in the early 50's, it is also well-known that Wardrop equilibria may be obtained by some convex minimization problem. In this paper, in the framework of $\Gamma$-convergence theory, we analyze what happens when a cartesian network becomes very dense. The continuous model we obtain this way is very similar to the continuous model of optimal transport with congestion of Carlier, Jimenez and Santambrogio [6] except that it keeps track of the anisotropy of the network.

Systems view, emergence and complexity

PurposeTo describe a view of parts of the world as assemblies with emergent properties constructed from related properties or objects, and the modelling of production of emergent properties arising by chance or design.Design/methodology/approachOne and two place sentences of a homogeneous language are combined in a static state to show a variety of possibilities of new structures. Combinations of such sentences in a dynamic state derived from narratives that show how static states are produced.FindingsUsing Cartesian products and network theory the kind and number of new structures can be calculated. Semantic diagrams exhibit the propagation of dynamic states leading to the use of predicate logic statements as carriers of properties of objects with uncertainties.Research limitations/implicationsThe approach is based on linguistic analysis being able to encapsulate linguistic complexities, expressions of feelings, emotions, etc. in homogeneous language. Interpretation of semantics is restricted to human mind. Research may lead to a science and design of complex systems.Practical implicationsThe method embedded in the approach can be developed into a design aid for managers subject to its passing the test of debate and development of software.Originality/valueThe research has led to a more rigorous approach to the analysis and design of scenarios including those with human activities.

Cartesian routing

Cartesian routing is a novel packet routing methodology in which a packet's route is determined by the position of the router relative to that of the destination. Cartesian routing differs from existing provider-based unicast routing in that routing tables are unnecessary since communications are topologically dependent, thereby potentially reducing router and network overheads. For example, routing decisions, which can take O(log( n)) to O( n) time using routing tables is reduced to O(1) in Cartesian routing. This paper describes Cartesian routing for unicast communications within a local or metropolitan environment (e.g., limited areas, including buildings, suburbs, and small towns that exhibit an anthropogenic ordering) using two-dimensional address structures, such as latitude and longitude. A Cartesian network is constructed from two types of router: collector (for horizontal communications) and arterial (for both `horizontal' and `vertical' communications). Cartesian routing requires minimal state: typically, routers need only know their location and the reachability of arterial routers on their collector. The paper also shows how the proposed 128-bit IPv6 address structure is an ideal candidate for Cartesian addresses.

Compact analytic expressions of two‐dimensional finite difference forms

AbstractIn this paper a straightforward derivation of one‐ and two‐dimensional finite difference forms for general cartesian networks is given. General analytic compact expressions up to third order for first derivatives are specifically derived. General cartesian networks with locally telescoping subnetworks are also introduced and the basic problem of approximating derivative boundary conditions is clarified. The applicability of these general finite difference forms is shown by solving numerically the Laplace problem with mixed Dirichlet–Neumann boundary conditions for an elliptic domain.

The Kinetic Energy of Hailfalls. Part III: Sampling Errors Inferred, from Radar Data

The representativeness of hailfall kinetic energies derived from point measurements of networks is studied by means of radar data of hail cells. The 202 cells were observed within a radius of 60 km from the 10 cm radar. Different Cartesian networks with grid sizes of 0.5–4km are constructed and used to determine estimates of global kinetic energies of the hail cells. From the investigation of these estimates it is found that the normalized standard deviation (s/E) decreases with the square root of increasing global kinetic energy E and increases with decreasing density of the network: doubling the grid size causes about a factor of 3 change in (s/E). The results can be approximated by a simple relation: E is in MJ and the grid size in km. For networks with a grid size of 2 km and large kinetic energy hailfalls (E ≈ 10 GJ), one finds a normalized standard deviation of ∼ 10%, whereas a value of ∼100% and more is found for small kinetic energy hailfalls (E ≈ 0.1 GJ). Because most of the hail cells are small (68% of the 202 cells investigated), this is an important result for the evaluation of weather modification experiments of hailstorm studies when using ground network data.