A pseudo-differential calculus on non-standard symplectic space; Spectral and regularity results in modulation spaces.

The usual Weyl calculus is intimately associated with the choice of the standard symplectic structure on [Formula: see text]. In this paper we will show that the replacement of this structure by an arbitrary symplectic structure leads to a pseudo-differential calculus of operators acting on functions or distributions defined, not on [Formula: see text] but rather on [Formula: see text]. These operators are intertwined with the standard Weyl pseudo-differential operators using an infinite family of partial isometries of [Formula: see text] indexed by [Formula: see text]. This allows us to obtain spectral and regularity results for our operators using Shubin's symbol classes and Feichtinger's modulation spaces.

Online program 'vipcal' for calculating lytic viral production and lysogenic cells based on a viral reduction approach.

Assessing viral production (VP) requires robust methodological settings combined with precise mathematical calculations. This contribution improves and standardizes mathematical calculations of VP and the assessment of the proportion of lysogenic cells in a sample. We present an online tool 'Viral Production Calculator' (vipcal, http://www.univie.ac.at/nuhag-php/vipcal) that calculates lytic production and the percentage of lysogenic cells based on data obtained from a viral reduction approach (VRA). The main advantage of our method lies in its universal applicability, even to different piecewise-linear curves. We demonstrate the application of our tool for calculating lytic VP and the proportion of lysogenic bacteria in an environmental sample. The program can also be used to calculate different parameters for estimating virus-induced mortality, including the percentage of lytically infected cells, lysis rate of bacteria, percentage of bacterial production lysed, proportion of bacterial loss per day, viral turnover time as well as dissolved organic carbon and nitrogen release. vipcal helps avoid differences in the calculation of VP and diverse viral parameters between studies and laboratories, which facilities interpretation of results. This tool represents a methodological step forward that can help improve our understanding of the role of viral activity in aquatic systems.