Relations between M\"obius and coboundary polynomial

It is known that, in general, the coboundary polynomial and the M\"obius polynomial of a matroid do not determine each other. Less is known about more specific cases. In this paper, we will try to answer if it is possible that the M\"obius polynomial of a matroid, together with the M\"obius polynomial of the dual matroid, define the coboundary polynomial of the matroid. In some cases, the answer is affirmative, and we will give two constructions to determine the coboundary polynomial in these cases.Comment: 12 page

Quantifying groundwater fluxes from an aapa mire to a riverside esker formation

Water flows in peatland margins is an under-researched topic. This study examines recharge from a peatland to an esker aquifer in an aapa mire complex of northern Finland. Our objective was to study how the aapa mire margin is hydrogeologically connected to the riverside aquifer and spatial and temporal variations in the recharge of peatland water to groundwater (GW). Following geophysical studies and monitoring of the saturated zone, a GW model (MODFLOW) was used in combination with stable isotopes to quantify GW flow volumes and directions. Peatland water recharge to the sandy aquifer indicated a strong connection at the peatland–aquifer boundary. Recharge volumes from peatland to esker were high and rather constant (873 m3 d−1) and dominated esker recharge at the study site. The peat water recharging the esker boundary was rich in dissolved organic carbon (DOC). Stable isotope studies on water (δ18O, δ2H, and d-excess) from GW wells verified the recharge of DOC-rich water from peatlands to mineral soil esker. Biogeochemical analysis revealed changes from DOC to dissolved inorganic carbon in the flow pathway from peatland margin to the river Kitinen. This study highlights the importance of careful investigation of aapa mire margin areas and their potential role in regional GW recharge patterns. HIGHLIGHTS Peatland water recharge to aquifer showed connection at the peatland–aquifer boundary.; Analysis revealed changes from dissolved organic carbon to dissolved inorganic carbon in groundwater flow pathway from peatland.; Connection between an aapa mire margin and riverside esker was documented.

Testing peatland water-table depth transfer functions using high-resolution hydrological monitoring data

Transfer functions are now commonly used to reconstruct past environmental variability from palaeoecological data. However, such approaches need to be critically appraised. Testate amoeba-based transfer functions are an established method for the quantitative reconstruction of past water-table variations in peatlands, and have been applied to research questions in palaeoclimatology, peatland ecohydrology and archaeology. We analysed automatically-logged peatland water-table data from dipwells located in England, Wales and Finland and a suite of three year, one year and summer water-table statistics were calculated from each location. Surface moss samples were extracted from beside each dipwell and the testate amoebae community composition was determined. Two published transfer functions were applied to the testate-amoeba data for prediction of water-table depth (England and Europe). Our results show that estimated water-table depths based on the testate amoeba community reflect directional changes, but that they are poor representations of the real mean or median water-table magnitudes for the study sites. We suggest that although testate amoeba-based reconstructions can be used to identify past shifts in peat hydrology, they cannot currently be used to establish precise hydrological baselines such as those needed to inform management and restoration of peatlands. One approach to avoid confusion with contemporary water-table determinations is to use residuals or standardised values for peatland water-table reconstructions. We contend that our test of transfer functions against independent instrumental data sets may be more powerful than relying on statistical testing alone

Two constructions of permutation arrays

10.1109/TIT.2004.826659IEEE Transactions on Information Theory505881-883IETT