Reconstructing the architectural evolution of volcanic islands from combined K/AR, morphologic, tectonic, and magnetic data. The Faial Island exemple (Azores)

The morpho-structural evolution of oceanic islands results from competition between volcano growth and partial destruction by mass-wasting processes. We present here a multi-disciplinary study of the successive stages of development of Faial (Azores) during the last 1 Myr. Using high-resolution digital elevation model (DEM), and new K/Ar, tectonic, and magnetic data, we reconstruct the rapidly evolving topography at successive stages, in response to complex interactions between volcanic construction and mass wasting, including the development of a graben. We show that: (1) sub-aerial evolution of the island first involved the rapid growth of a large elongated volcano at ca. 0.85 Ma, followed by its partial destruction over half a million years; (2) beginning about 360 ka a new small edifice grew on the NE of the island, and was subsequently cut by normal faults responsible for initiation of the graben; (3) after an apparent pause of ca. 250 kyr, the large Central Volcano (CV) developed on the western side of the island at ca 120 ka, accumulating a thick pile of lava flows in less than 20 kyr, which were partly channelized within the graben; (4) the period between 120 ka and 40 ka is marked by widespread deformation at the island scale, including westward propagation of faulting and associated erosion of the graben walls, which produced sedimentary deposits; subsequent growth of the CV at 40 ka was then constrained within the graben, with lava flowing onto the sediments up to the eastern shore; (5) the island evolution during the Holocene involves basaltic volcanic activity along the main southern faults and pyroclastic eruptions associated with the formation of a caldera volcano-tectonic depression. We conclude that the whole evolution of Faial Island has been characterized by successive short volcanic pulses probably controlled by brief episodes of regional deformation. Each pulse has been separated by considerable periods of volcanic inactivity during which the Faial graben gradually developed. We propose that the volume loss associated with sudden magma extraction from a shallow reservoir in different episodes triggered incremental downward graben movement, as observed historically, when immediate vertical collapse of up to 2 m was observed along the western segments of the graben at the end of the Capelinhos eruptive crises (1957-58).

Arithmetic-based binary-to-RNS converter modulo {2(n)+/- k} for jn-Bit dynamic range

In this brief, a read-only-memoryless structure for binary-to-residue number system (RNS) conversion modulo {2(n) +/- k} is proposed. This structure is based only on adders and constant multipliers. This brief is motivated by the existing {2(n) +/- k} binary-to-RNS converters, which are particular inefficient for larger values of n. The experimental results obtained for 4n and 8n bits of dynamic range suggest that the proposed conversion structures are able to significantly improve the forward conversion efficiency, with an AT metric improvement above 100%, regarding the related state of the art. Delay improvements of 2.17 times with only 5% area increase can be achieved if a proper selection of the {2(n) +/- k} moduli is performed.

Complete synchronization and delayed synchronization in couplings

We consider a general coupling of two identical chaotic dynamical systems, and we obtain the conditions for synchronization. We consider two types of synchronization: complete synchronization and delayed synchronization. Then, we consider four different couplings having different behaviors regarding their ability to synchronize either completely or with delay: Symmetric Linear Coupled System, Commanded Linear Coupled System, Commanded Coupled System with delay and symmetric coupled system with delay. The values of the coupling strength for which a coupling synchronizes define its Window of synchronization. We obtain analytically the Windows of complete synchronization, and we apply it for the considered couplings that admit complete synchronization. We also obtain analytically the Window of chaotic delayed synchronization for the only considered coupling that admits a chaotic delayed synchronization, the commanded coupled system with delay. At last, we use four different free chaotic dynamics (based in tent map, logistic map, three-piecewise linear map and cubic-like map) in order to observe numerically the analytically predicted windows.

Spectral and dynamical invariants in a complete clustered network

The main result of this work is a new criterion for the formation of good clusters in a graph. This criterion uses a new dynamical invariant, the performance of a clustering, that characterizes the quality of the formation of clusters. We prove that the growth of the dynamical invariant, the network topological entropy, has the effect of worsening the quality of a clustering, in a process of cluster formation by the successive removal of edges. Several examples of clustering on the same network are presented to compare the behavior of other parameters such as network topological entropy, conductance, coefficient of clustering and performance of a clustering with the number of edges in a process of clustering by successive removal.

Weakly spectrally complete pair of matrices

Let and be matrices over an algebraically closed field. Let be elements of such that and . We give necessary and sufficient condition for the existence of matrices and similar to and, respectively, such that has eigenvalues.