A Convolutional Neural Network for Spatial Downscaling of Satellite-Based Solar-Induced Chlorophyll Fluorescence (SIFnet)

Gross primary productivity (GPP) is the sum of leaf photosynthesis and represents a crucial component of the global carbon cycle. Space-borne estimates of GPP typically rely on observable quantities that co-vary with GPP such as vegetation indices using reflectance measurements (e.g., NDVI, NIRv, and kNDVI). Recent work has also utilized measurements of solar-induced chlorophyll fluorescence (SIF) as a proxy for GPP. However, these SIF measurements are typically coarse resolution while many processes influencing GPP occur at fine spatial scales. Here, we develop a Convolutional Neural Network (CNN), named SIFnet, that increases the resolution of SIF from the TROPOspheric Monitoring Instrument (TROPOMI) on board of the satellite Sentinel-5P by a factor of 10 to a spatial resolution of 500 m. SIFnet utilizes coarse SIF observations together with high resolution auxiliary data. The auxiliary data used here may carry information related to GPP and SIF. We use training data from non-US regions between April 2018 until March 2021 and evaluate our CNN over the conterminous United States (CONUS). We show that SIFnet is able to increase the resolution of TROPOMI SIF by a factor of 10 with a r2 and RMSE metrics of 0.92 and 0.17 mW m−2 sr−1 nm−1, respectively. We further compare SIFnet against a recently developed downscaling approach and evaluate both methods against independent SIF measurements from Orbiting Carbon Observatory 2 and 3 (OCO-2/3). SIFnet performs systematically better than the downscaling approach (r = 0.78 for SIFnet, r = 0.72 for downscaling), indicating that it is picking up on key features related to SIF and GPP. Examination of the feature importance in the neural network indicates a few key parameters and the spatial regions these parameters matter. Namely, the CNN finds low resolution SIF data to be the most significant parameter with the NIRv vegetation index as the second most important parameter. NIRv consistently outperforms the recently proposed kNDVI vegetation index. Advantages and limitations of SIFnet are investigated and presented through a series of case studies across the United States. SIFnet represents a robust method to infer continuous, high spatial resolution SIF data.

On Graphs whose Orientations are Determined by their Hermitian Spectra

A mixed graph $D$ is obtained from a simple graph $G$, the underlying graph of $D$, by orienting some edges of $G$. A simple graph $G$ is said to be ODHS (all orientations of $G$ are determined by their $H$-spectra) if every two $H$-cospectral graphs in $\mathcal{D}(G)$ are switching equivalent to each other, where $\mathcal{D}(G)$ is the set of all mixed graphs with $G$ as their underlying graph. In this paper, we characterize all bicyclic ODHS graphs and construct infinitely many ODHS graphs whose cycle spaces are of dimension $k$. For a connected graph $G$ whose cycle space is of dimension $k$, we also obtain an achievable upper bound $2^{2k-1} + 2^{k-1}$ for the number of switching equivalence classes in $\mathcal{D}(G)$, which naturally is an upper bound of the number of cospectral classes in $\mathcal{D}(G)$. To achieve these, we propose a valid method to estimate the number of switching equivalence classes in $\mathcal{D}(G)$ based on the strong cycle basis, a special cycle basis introduced in this paper.

Singularities in the flying electromagnetic doughnuts

Flying doughnuts (FDs) are exact propagating solutions of Maxwell equations in the form of single-cycle, space-time non-separable toroidal pulses. Here we review their properties and reveal the existence of a complex and robust fine topological structure. In particular, the electric and magnetic fields of the FD pulse vanish across a number of planes, spherical shells and rings, and display a number of point singularities including saddle points and vortices. Moreover, the instantaneous Poynting vector of the field exhibits a large number of singularities, which are often accompanied by extended areas energy backflow.

Skew-rank of an oriented graph in terms of the rank and dimension of cycle space of its underlying graph

Let G? be an oriented graph and S(G?) be its skew-adjacency matrix, where G is called the underlying graph of G?. The skew-rank of G?, denoted by sr(G?), is the rank of S(G?). Denote by d(G) = |E(G)|-|V(G)| + ?(G) the dimension of cycle spaces of G, where |E(G)|, |V(G)| and ?(G) are the edge number, vertex number and the number of connected components of G, respectively. Recently, Wong, Ma and Tian [European J. Combin. 54 (2016) 76-86] proved that sr(G?) ? r(G) + 2d(G) for an oriented graph G?, where r(G) is the rank of the adjacency matrix of G, and characterized the graphs whose skew-rank attain the upper bound. However, the problem of the lower bound of sr(G?) of an oriented graph G? in terms of r(G) and d(G) of its underlying graph G is left open till now. In this paper, we prove that sr(G?) ? r(G)-2d(G) for an oriented graph G? and characterize the graphs whose skew-rank attain the lower bound.