Shimura varieties in the Torelli locus via Galois coverings of elliptic curves

We study Shimura subvarieties of $\mathsf{A}_g$ obtained from families of Galois coverings $f: C \rightarrow C'$ where $C'$ is a smooth complex projective curve of genus $g' \geq 1$ and $g= g(C)$. We give the complete list of all such families that satisfy a simple sufficient condition that ensures that the closure of the image of the family via the Torelli map yields a Shimura subvariety of $\mathsf{A}_g$ for $g' =1,2$ and for all $g \geq 2,4$ and for $g' > 2$ and $g \leq 9$. In a previous work of the first and second author together with A. Ghigi [FGP] similar computations were done in the case $g'=0$. Here we find 6 families of Galois coverings, all with $g' = 1$ and $g=2,3,4$ and we show that these are the only families with $g'=1$ satisfying this sufficient condition. We show that among these examples two families yield new Shimura subvarieties of $\mathsf{A}_g$, while the other examples arise from certain Shimura subvarieties of $\mathsf{A}_g$ already obtained as families of Galois coverings of $\mathbb{P}^1$ in [FGP]. Finally we prove that if a family satisfies this sufficient condition with $g'\geq 1$, then $g \leq 6g'+1$.Comment: 18 pages, to appear in Geometriae Dedicat

Impact of vegetation die-off on spatial flow patterns over a tidal marsh

Large-scale die-off of tidal marsh vegetation, caused by global change, is expected to change flow patterns over tidal wetlands, and hence to affect valuable wetland functions such as reduction of shoreline erosion, attenuation of storm surges, and sedimentation in response to sea level rise. This study quantified for the first time the effects of large-scale (4 ha) artificial vegetation removal, as proxy of die-off, on the spatial flow patterns through a tidal marsh channel and over the surrounding marsh platform. After vegetation removal, the flow velocities measured on the platform increased by a factor of 2 to 4, while the channel flow velocities decreased by almost a factor of 3. This was associated with a change in flow directions on the platform, from perpendicular to the channel edges when vegetation was present, to a tendency of more parallel flow to the channel edges when vegetation was absent. Comparison with hydrodynamic model simulations explains that the vegetation-induced friction causes both flow reduction on the vegetated platform and flow acceleration towards the non-vegetated channels. Our findings imply that large-scale vegetation die-off would not only result in decreased platform sedimentation rates, but also in sediment infilling of the channels, which together would lead to further worsening of plant growth conditions and a potentially runaway feedback to permanent vegetation loss. Citation: Temmerman, S., P. Moonen, J. Schoelynck, G. Govers, and T. J. Bouma (2012), Impact of vegetation die-off on spatial flow patterns over a tidal marsh, Geophys. Res. Lett., 39, L03406, doi: 10.1029/2011GL050502

Relations between some invariants of algebraic varieties in positive characteristic

We discuss relations between certain invariants of varieties in positive characteristic, like the a-number and the height of the Artin-Mazur formal group. We calculate the a-number for Fermat surfacesComment: 13 page

Refactoring test code

Two key aspects of extreme programming (XP) are unit testing and merciless refactoring. Given the fact that the ideal test code / production code ratio approaches 1:1, it is not surprising that unit tests are being refactored. We found that refactoring test code is different from refactoring production code in two ways: (1) there is a distinct set of bad smells involved, and (2) improving test code involves additional test-specific refactorings. To share our experiences with other XP practitioners, we describe a set of bad smells that indicate trouble in test code, and a collection of test refactorings to remove these smells

Intersymbol and Intercarrier Interference in OFDM Systems: Unified Formulation and Analysis

A unified matrix formulation is presented for the analysis of intersymbol and intercarrier interference in orthogonal frequency-division multiplexing (OFDM) systems. The proposed formulation relies on six parameters and allows studying various schemes, including those with windowing in the transmitter and/or in the receiver (called windowed OFDM systems), which may add cyclic suffix and/or cyclic prefix (CP), besides the conventional CP-OFDM. The proposed framework encompasses seven different OFDM systems. It considers the overlap-and-add procedure performed in the transmitter of windowed OFDM systems, being jointly formulated with the channel convolution. The intersymbol and intercarrier interference, caused when the order of the channel impulse response is higher than the number of CP samples, is characterized. A new equivalent channel matrix that is useful for calculating both the received signal and the interference power is defined and characterized. Unlike previous works, this new channel matrix has no restrictions on the length of the channel impulse response, which means that the study is not constrained to the particular case of two or three data blocks interfering in the received signal. Theoretical expressions for the powers of three different kinds of interference are derived. These expressions allow calculating the signal-to-interference-plus-noise ratio, useful for computing the data rate of each OFDM system. The proposed formulation is applied to realistic examples, showing its effectiveness through comparisons based on numerical performance assessments of the considered OFDM systems