Solar activity during the Holocene: the Hallstatt cycle and its consequence for grand minima and maxim

Cosmogenic isotopes provide the only quantitative proxy for analyzing the long-term solar variability over a centennial timescale. While essential progress has been achieved in both measurements and modeling of the cosmogenic proxy, uncertainties still remain in the determination of the geomagnetic dipole moment evolution. Here we improve the reconstruction of solar activity over the past nine millennia using a multi-proxy approach. We used records of the 14C and 10Be cosmogenic isotopes, current numerical models of the isotope production and transport in Earth's atmosphere, and available geomagnetic field reconstructions, including a new reconstruction relying on an updated archeo-/paleointensity database. The obtained series were analyzed using the singular spectrum analysis (SSA) method to study the millennial-scale trends. A new reconstruction of the geomagnetic dipole field moment, GMAG.9k, is built for the last nine millennia. New reconstructions of solar activity covering the last nine millennia, quantified in sunspot numbers, are presented and analyzed. A conservative list of grand minima and maxima is provided. The primary components of the reconstructed solar activity, as determined using the SSA method, are different for the series based on 14C and 10Be. These primary components can only be ascribed to long-term changes in the terrestrial system and not to the Sun. They have been removed from the reconstructed series. In contrast, the secondary SSA components of the reconstructed solar activity are found to be dominated by a common ~2400-yr quasi-periodicity, the so-called Hallstatt cycle, in both the 14C and 10Be based series. This Hallstatt cycle thus appears to be related to solar activity. Finally, we show that the grand minima and maxima occurred intermittently over the studied period, with clustering near highs and lows of the Hallstatt cycle, respectively.Comment: In press in Astronomy & Astrophysics, doi: 10.1051/0004-6361/20152729

Counting Realizations of Laman Graphs on the Sphere

We present an algorithm that computes the number of realizations of a Laman graph on a sphere for a general choice of the angles between the vertices. The algorithm is based on the interpretation of such a realization as a point in the moduli space of stable curves of genus zero with marked points, and on the explicit description, due to Keel, of the Chow ring of this space

Combinatorics of Bricard's octahedra

We re-prove the classification of motions of an octahedron — obtained by Bricard at the beginning of the XX century — by means of combinatorial objects satisfying some elementary rules. The explanations of these rules rely on the use of a well-known creation of modern algebraic geometry, the moduli space of stable rational curves with marked points, for the description of configurations of graphs on the sphere. Once one accepts the objects and the rules, the classification becomes elementary (though not trivial) and can be enjoyed without the need of a very deep background on the topic

Zero-Sum Cycles in Flexible Non-triangular Polyhedra

Finding necessary conditions for the geometry of flexible polyhedra is a classical problem that has received attention also in recent times. For flexible polyhedra with triangular faces, we showed in a previous work the existence of cycles with a sign assignment for their edges, such that the signed sum of the edge lengths along the cycle is zero. In this work, we extend this result to flexible non-triangular polyhedra

Destabilizing Taylor-Couette flow with suction

We consider the effect of radial fluid injection and suction on Taylor-Couette flow. Injection at the outer cylinder and suction at the inner cylinder generally results in a linearly unstable steady spiralling flow, even for cylindrical shears that are linearly stable in the absence of a radial flux. We study nonlinear aspects of the unstable motions with the energy stability method. Our results, though specialized, may have implications for drag reduction by suction, accretion in astrophysical disks, and perhaps even in the flow in the earth's polar vortex.Comment: 34 pages, 9 figure

The SPICE carbon isotope excursion in Siberia: a combined study of the upper Middle Cambrian-lowermost Ordovician Kulyumbe River section, northwestern Siberian Platform

An integrated, high-resolution chemostratigraphic (C, O and Sr isotopes) and magnetostratigraphic study through the upper Middle Cambrian–lowermost Ordovician shallowmarine carbonates of the northwestern margin of the Siberian Platform is reported. The interval was analysed at the Kulyumbe section, which is exposed along the Kulyumbe River, an eastern tributary of the Enisej River. It comprises the upper Ust’-Brus, Labaz, Orakta, Kulyumbe, Ujgur and lower Iltyk formations and includes the Steptoean positive carbon isotopic excursion (SPICE) studied here in detail from upper Cambrian carbonates of the Siberian Platform for the first time. The peak of the excursion, showing δ13C positive values as high as+4.6‰and least-altered 87Sr/86Sr ratios of 0.70909, is reported herein from the Yurakhian Horizon of the Kulyumbe Formation. The stratigraphic position of the SPICE excursion does not support traditional correlation of the boundary between theOrakta and Labaz formations at the Kulyumbe River with its supposedly equivalent level in Australia, Laurentia, South China and Kazakhstan, where the Glyptagnostus stolidotus and G. reticulatus biozones are known to immediately precede the SPICE excursion and span the Middle–Upper Cambrian boundary. The Cambrian–Ordovician boundary is probably situated in the middle Nyajan Horizon of the Iltyk Formation, in which carbon isotope values show a local maximum below a decrease in the upper part of the Nyajan Horizon, attributed herein to the Tremadocian Stage. A refined magnetic polarity sequence confirms that the geomagnetic reversal frequency was very high during Middle Cambrian times at 7–10 reversals per Ma, assuming a total duration of about 10 Ma and up to 100 magnetic intervals in the Middle Cambrian. By contrast, the sequence attributed herein to the Upper Cambrian on chemostratigraphic grounds contains only 10–11 magnetic intervals

Probing active forces via a fluctuation-dissipation relation: Application to living cells

We derive a new fluctuation-dissipation relation for non-equilibrium systems with long-term memory. We show how this relation allows one to access new experimental information regarding active forces in living cells that cannot otherwise be accessed. For a silica bead attached to the wall of a living cell, we identify a crossover time between thermally controlled fluctuations and those produced by the active forces. We show that the probe position is eventually slaved to the underlying random drive produced by the so-called active forces.Comment: 5 page

Mobile Icosapods

Pods are mechanical devices constituted of two rigid bodies, the base and the platform, connected by a number of other rigid bodies, called legs, that are anchored via spherical joints. It is possible to prove that the maximal number of legs of a mobile pod, when finite, is 20. In 1904, Borel designed a technique to construct examples of such 20-pods, but could not constrain the legs to have base and platform points with real coordinates. We show that Borel’s construction yields all mobile 20-pods, and that it is possible to construct examples where all coordinates are real

Charge distribution in two-dimensional electrostatics

We examine the stability of ringlike configurations of N charges on a plane interacting through the potential $V(z_1,...,z_N)=\sum_i |z_i|^2-\sum_{i<j} ln|z_i-z_j|^2$. We interpret the equilibrium distributions in terms of a shell model and compare predictions of the model with the results of numerical simulations for systems with up to 100 particles.Comment: LaTe

Classification in sparse, high dimensional environments applied to distributed systems failure prediction

Network failures are still one of the main causes of distributed systems’ lack of reliability. To overcome this problem we present an improvement over a failure prediction system, based on Elastic Net Logistic Regression and the application of rare events prediction techniques, able to work with sparse, high dimensional datasets. Specifically, we prove its stability, fine tune its hyperparameter and improve its industrial utility by showing that, with a slight change in dataset creation, it can also predict the location of a failure, a key asset when trying to take a proactive approach to failure management