Search for: All records

We consider the problem of recovering a complex vector (up to a global unimodular constant) given noisy and incomplete outer product measurements. Such problems arise when implementing distributed clock synchronization schemes, radar autofocus methods, and phaseless signal recovery. This problem is known as vector synchronization and is a variant of the more common angular synchronization problem. In applications with windowed measurements and/or convolutional models - for example, phase retrieval from STFT magnitude data, the outer product measurement matrix is highly incomplete and has a block diagonal structure. We describe a vector synchronization technique which applies an eigenvector computation to blocks of this matrix followed by a block compatibility operation to piece together the final solution. We provide theoretical guarantees (in the noiseless case) and empirical simulations demonstrating the accuracy and efficiency of the method. 

Abstract Chemically reduced nitrogen forms are increasing in aquatic systems and beginning to reach concentrations not previously measured. Despite this, little research has examined the potential of reduced nitrogen forms to encourage excess nitrogen storage and promote algal bloom longevity compared to oxidised forms.A 2‐week field, pulse‐application experiment was carried out using 1,100‐L plastic limnocorrals to examine cyanobacterial community response to three nitrogen forms, including nitrate, ammonium, and urea (added as 600 µg N/L). Cell pigments and counts were used to calculate cell‐specific pigment concentrations, and cell‐associated microcystin concentrations were also measured to examine toxin response to a shift in nitrogen source.Results showed that, upon nitrogen introduction, extracellular nitrogen quickly decreased in accordance with an increase in cellular phycocyanin 72 hr after fertilisation. Ammonium and urea treatments had more phycocyanin/cell than nitrate or control treatments at 72 hr. After 72 hr, phycocyanin content quickly decreased, consistent with the use of nitrogen from phycobiliproteins. Despite the decrease in light‐harvesting pigments, the total number of cyanobacterial cells increased in the ammonium and urea treatments after 2 weeks. Cyanobacterial particulate toxin (microcystin) quotas were not affected by nitrogen additions.Results show that reduced nitrogen forms encourage greater nitrogen storage as pigments and increase bloom longevity compared to oxidised forms.Findings support previous studies that suggest reduced nitrogen forms encourage greater cell density and algal bloom persistence. Results further point to excess nitrogen storage as another mechanism that allows cyanobacteria to dominate freshwater systems despite variable environmental conditions.