Delaunay Hodge Star

We define signed dual volumes at all dimensions for circumcentric dual meshes. We show that for pairwise Delaunay triangulations with mild boundary assumptions these signed dual volumes are positive. This allows the use of such Delaunay meshes for Discrete Exterior Calculus (DEC) because the discrete Hodge star operator can now be correctly defined for such meshes. This operator is crucial for DEC and is a diagonal matrix with the ratio of primal and dual volumes along the diagonal. A correct definition requires that all entries be positive. DEC is a framework for numerically solving differential equations on meshes and for geometry processing tasks and has had considerable impact in computer graphics and scientific computing. Our result allows the use of DEC with a much larger class of meshes than was previously considered possible.Comment: Corrected error in Figure 1 (columns 3 and 4) and Figure 6 and a formula error in Section 2. All mathematical statements (theorems and lemmas) are unchanged. The previous arXiv version v3 (minus the Appendix) appeared in the journal Computer-Aided Desig

Unusual landings of Aluterus monoceros (Linnaeus, 1758) along Vizhinjam coast

On the13th of July 2009, unusual heavy landings of Aluterus monoceros (unicorn leather jacket) of the family Monacanthidae were observed along the coast, from Vizhinjam to Marianadu about 40 km north of Vizhinjam (Fig. 1). These fishes, locally known as “komban clathy” or “mara clathy” are rarely observed in large numbers in the landings at Vizhinjam which has become a subject of surprise to the fishermen. This has been the first incident of such a heavy landing of bigger sized unicorn leather jacket in this area

First report of Spotted reef crab off Vizhinjam coast

Carpilius maculatus (Linnaeus, 1758), commonly known as ‘Seven-eleven crab’, ‘Spotted reef crab’, ‘Dark finger coral crab’, or ‘Large spotted crab’ is a member of the family Carpiliidae. One male specimen of the spotted reef crab C. maculatus measuring 130 mm in carapace width was caught by a bottom set gill net along with Portunus sanguinolentus from the rocky area in Vizhinjam coastal waters

Granger causality and transfer entropy are equivalent for Gaussian variables

Granger causality is a statistical notion of causal influence based on prediction via vector autoregression. Developed originally in the field of econometrics, it has since found application in a broader arena, particularly in neuroscience. More recently transfer entropy, an information-theoretic measure of time-directed information transfer between jointly dependent processes, has gained traction in a similarly wide field. While it has been recognized that the two concepts must be related, the exact relationship has until now not been formally described. Here we show that for Gaussian variables, Granger causality and transfer entropy are entirely equivalent, thus bridging autoregressive and information-theoretic approaches to data-driven causal inference.Comment: In review, Phys. Rev. Lett., Nov. 200

Post-flight Analysis and Design Improvement in Command Guidance System for a Short-range Surface-to-air Missile System

A short-range missile with command-to line-of-sight and three-beam guidance has been considered in this paper. The earlier command guidance system (CGS) design shows unacceptablyhigh-low-frequency weave-mode oscillations, leading to high latax and body rate oscillations, even for benign, low-speed non-manoeuvring target engagements. For successful targetengagements with the three-beam guidance, missile is to be handed over from wide-to-medium receiver beam, and finally, from medium-to-the most accurate narrow receiver beam, depending on the angular error wrt line-of-sight as early as possible. Due to large amplitude oscillation in the earlier CGS design, the handing over of the missile to narrow receiver beam, and in many cases, to the medium receiver beam, itself could not take place, leading to failure of guidance. In this paper, the cause for this undesirable high magnitude weave-mode oscillation has been analysed in detail. After establishing this, saturation aspects of the earlier CGS design; a simple implementable CGS re-design was carried out to reduce this saturation aspect drastically for preserving almost full-phase advance effects of the linear new analogue compensators designed to give the required stability margins of guidance loop

Information flow in a kinetic ising model peaks in the disordered phase

There is growing evidence that for a range of dynamical systems featuring complex interactions between large ensembles of interacting elements, mutual information peaks at order-disorder phase transitions. We conjecture that, by contrast, information flow in such systems will generally peak strictly on the disordered side of a phase transition. This conjecture is verified for a ferromagnetic 2D lattice Ising model with Glauber dynamics and a transfer entropy-based measure of systemwide information flow. Implications of the conjecture are considered, in particular, that for a complex dynamical system in the process of transitioning from disordered to ordered dynamics (a mechanism implicated, for example, in financial market crashes and the onset of some types of epileptic seizures); information dynamics may be able to predict an imminent transition

Multivariate Granger Causality and Generalized Variance

Granger causality analysis is a popular method for inference on directed interactions in complex systems of many variables. A shortcoming of the standard framework for Granger causality is that it only allows for examination of interactions between single (univariate) variables within a system, perhaps conditioned on other variables. However, interactions do not necessarily take place between single variables, but may occur among groups, or "ensembles", of variables. In this study we establish a principled framework for Granger causality in the context of causal interactions among two or more multivariate sets of variables. Building on Geweke's seminal 1982 work, we offer new justifications for one particular form of multivariate Granger causality based on the generalized variances of residual errors. Taken together, our results support a comprehensive and theoretically consistent extension of Granger causality to the multivariate case. Treated individually, they highlight several specific advantages of the generalized variance measure, which we illustrate using applications in neuroscience as an example. We further show how the measure can be used to define "partial" Granger causality in the multivariate context and we also motivate reformulations of "causal density" and "Granger autonomy". Our results are directly applicable to experimental data and promise to reveal new types of functional relations in complex systems, neural and otherwise.Comment: added 1 reference, minor change to discussion, typos corrected; 28 pages, 3 figures, 1 table, LaTe

The Polonnaruwa meteorite: oxygen isotope, crystalline and biological composition

Results of X-Ray Diffraction (XRD) analysis, Triple Oxygen Isotope analysis and Scanning Electron Microscopic (SEM) studies are presented for stone fragments recovered from the North Central Province of Sri Lanka following a witnessed fireball event on 29 December 2012. The existence of numerous nitrogen depleted highly carbonaceous fossilized biological structures fused into the rock matrix is inconsistent with recent terrestrial contamination. Oxygen isotope results compare well with those of CI and CI-like chondrites but are inconsistent with the fulgurite hypothesis.Comment: 7 pages, 7 figures, 4 table