Glicci simplicial complexes

One of the main open questions in liaison theory is whether every homogeneous Cohen-Macaulay ideal in a polynomial ring is glicci, i.e. if it is in the G-liaison class of a complete intersection. We give an affirmative answer to this question for Stanley-Reisner ideals defined by simplicial complexes that are weakly vertex-decomposable. This class of complexes includes matroid, shifted and Gorenstein complexes respectively. Moreover, we construct a simplicial complex which shows that the property of being glicci depends on the characteristic of the base field. As an application of our methods we establish new evidence for two conjectures of Stanley on partitionable complexes and on Stanley decompositions

Criteria for componentwise linearity

We establish characteristic-free criteria for the componentwise linearity of graded ideals. As applications, we classify the componentwise linear ideals among the Gorenstein ideals, the standard determinantal ideals, and the ideals generated by the submaximal minors of a symmetric matrix.Comment: 17 pages; corrected versio

INVESTIGATION OF THE MULTI-SCALE INTERACTIONS BETWEEN AN OFFSHORE WIND TURBINE WAKE AND THE OCEAN-SEDIMENT DYNAMICS IN A INDEALIZED FRAMEWORK

International audienceA coupled two dimensional idealized numerical model of the ocean and sediment layers, forced by an offshore wind turbine wake is used to investigate the complex interactions between the wake, the ocean and the sediment layers, together with the retro-action on the wind energy. Results show that the turbine wake has an impact on both, the ocean and the sediment layers. The turbine wake impacts the ocean surface and generates instabilities or vortex streets for some parameter values. Shallow ocean layers (typically below 15m) are laminar. When water depth is higher, large scale instabilities are generated, leading to a turbulent dynamic in the ocean layer. The size of the generated vortices in the ocean increases with water depth and decreases with the quadratic-law bottom friction coefficient. Considering the morphodynamics three cases are observed, depending on whether the ocean dynamics is laminar (i), has a localized (ii) or domain wide (iii) turbulent behavior. In the first case, changes in seabed elevation are around a few millimeters per month. Results are similar for the localized turbulence case with small spatial variations. For the domain wide turbulence case (iii), instantaneous seabed changes are of the order of a few millimeters per month, whereas the transport averaged over several days decreases to a few tenths of millimeter per month. This behavior is easily explained by the oscillating local velocity which transports sediments back and forth. The above emphasizes that the water depth is a key parameter for the coupled atmosphere-ocean-sediment system around wind turbines. Furthermore, considering the ocean velocity in the atmospheric forcing at the ocean surface leads to a decrease of 4 % of the power lost by friction at the atmosphere-ocean interface. Ocean dynamics could thus have a non-negligible feedback on the wind power available for the turbines and its variability

Computing the probability for data loss in two-dimensional parity RAIDs

Parity RAIDs are used to protect storage systems against disk failures. The idea is to add redundancy to the system by storing the parity of subsets of disks on extra parity disks. A simple two-dimensional scheme is the one in which the data disks are arranged in a rectangular grid, and every row and column is extended by one disk which stores the parity of it. In this paper we describe several two-dimensional parity RAIDs and analyse, for each of them, the probability for data loss given that f random disks fail. This probability can be used to determine the overall probability using the model of Hafner and Rao. We reduce subsets of the forest counting problem to the different cases and show that the generalised problem is #Phard. Further we adapt an exact algorithm by Stones for some of the problems whose worst-case runtime is exponential, but which is very efficient for small fixed f and thus sufficient for all real-world applications