Equality of the homogeneous and the Gabor wave front set

We prove that Hörmander's global wave front set and Nakamura's homogeneous wave front set of a tempered distribution coincide. In addition we construct a tempered distribution with a given wave front set, and we develop a pseudodifferential calculus adapted to Nakamura's homogeneous wave front set

Conormal distributions in the Shubin calculus of pseudodifferential operators

We characterize the Schwartz kernels of pseudodifferential operators of Shubin type by means of an FBI transform. Based on this we introduce as a generalization a new class of tempered distributions called Shubin conormal distributions. We study their transformation behavior, normal forms and microlocal properties

Lagrangian distributions and Fourier integral operators with quadratic phase functions and Shubin amplitudes

We study Fourier integral operators with Shubin amplitudes and quadratic phase functions associated to twisted graph Lagrangians with respect to symplectic matrices. We factorize such an operator as the composition of a Weyl pseudodifferential operator and a metaplectic operator and derive a characterization of its Schwartz kernel in terms of phase space estimates. Extending the conormal distributions in the Shubin calculus, we define an adapted notion of Lagrangian tempered distribution. We show that the kernels of Fourier integral operators are identical to Lagrangian distributions with respect to twisted graph Lagrangians

REndo: Internal Instrumental Variables to Address Endogeneity

Endogeneity is a common problem in any causal analysis. It arises when the independence assumption between an explanatory variable and the error in a statistical model is violated. The causes of endogeneity are manifold and include response bias in surveys, omission of important explanatory variables, or simultaneity between explanatory and response variables. Instrumental variable estimation provides a possible solution. However, valid and strong external instruments are difficult to find. Consequently, internal instrumental variable approaches have been proposed to correct for endogeneity without relying on external instruments. The R package REndo implements various internal instrumental variable approaches, i.e., latent instrumental variables estimation (Ebbes, Wedel, Boeckenholt, and Steerneman 2005), higher moments estimation (Lewbel 1997), heteroscedastic error estimation (Lewbel 2012), joint estimation using copula (Park and Gupta 2012) and multilevel generalized method of moments estimation (Kim and Frees 2007). Package usage is illustrated on simulated and real-world data

REndo: Internal Instrumental Variables to Address Endogeneity

Endogeneity is a common problem in any causal analysis. It arises when the independence assumption between an explanatory variable and the error in a statistical model is violated. The causes of endogeneity are manifold and include response bias in surveys, omission of important explanatory variables, or simultaneity between explanatory and response variables. Instrumental variable estimation provides a possible solution. However, valid and strong external instruments are difficult to find. Consequently, internal instrumental variable approaches have been proposed to correct for endogeneity without relying on external instruments. The R package REndo implements various internal instrumental variable approaches, i.e., latent instrumental variables estimation (Ebbes, Wedel, Boeckenholt, and Steerneman 2005), higher moments estimation (Lewbel 1997), heteroscedastic error estimation (Lewbel 2012), joint estimation using copula (Park and Gupta 2012) and multilevel generalized method of moments estimation (Kim and Frees 2007). Package usage is illustrated on simulated and real-world data

Conormal distributions in the Shubin calculus of pseudodifferential operators

We characterize the Schwartz kernels of pseudodifferential operators of Shubin type by means of an FBI transform. Based on this we introduce as a generalization a new class of tempered distributions called Shubin conormal distributions. We study their transformation behavior, normal forms and microlocal properties.Comment: 23 page

SARS-CoV-2 variants of concern and spike protein mutational dynamics in a Swedish cohort during 2021, studied by Nanopore sequencing

From Springer Nature via Jisc Publications RouterHistory: received 2022-04-21, rev-recd 2022-09-08, accepted 2022-10-05, registration 2022-10-10, pub-electronic 2022-10-18, online 2022-10-18, collection 2022-12Acknowledgements: Acknowledgements: We are immensely grateful to all our co-workers at the Section for Clinical Microbiology and Hospital Hygiene at Uppsala University Hospital, who PCR tested all the COVID-19 samples and consequently extracted the viral RNA for us from the positive samples. Secondly, we are deeply thankful to Tor-Elesh Albrigtsen for the remarkable assistance with data science, analysis and programming in Python.Publication status: PublishedFunder: Science for Life Laboratory; doi: http://dx.doi.org/10.13039/501100009252; Grant(s): ZSC – National core facility for pandemic preparednessFunder: Scandinavian Society for Antimicrobial Chemotherapy Foundation; doi: http://dx.doi.org/10.13039/501100011777; Grant(s): SLS-961049Funder: Erik, Karin and Gösta Selander Foundation; Grant(s): 2022Funder: Regionala Forskningsrådet Uppsala/Örebro; doi: http://dx.doi.org/10.13039/100019032; Grant(s): RFR-930984Funder: Uppsala UniversityAbstract: Background: Since the beginning of the COVID-19 pandemic, new variants of significance to public health have emerged. Consequently, early detection of new mutations and variants through whole-genome sequencing remains crucial to assist health officials in employing appropriate public health measures. Methods: We utilized the ARTIC Network SARS-CoV-2 tiled amplicon approach and Nanopore sequencing to sequence 4,674 COVID-19 positive patient samples from Uppsala County, Sweden, between week 15 and 52 in 2021. Using this data, we mapped the circulating variants of concern (VOC) in the county over time and analysed the Spike (S) protein mutational dynamics in the Delta variant throughout 2021. Results: The distribution of the SARS-CoV-2 VOC matched the national VOC distribution in Sweden, in 2021. In the S protein of the Delta variant, we detected mutations attributable to variants under monitoring and variants of interest (e.g., E484Q, Q613H, Q677H, A222V and Y145H) and future VOC (e.g., T95I and Y144 deletion, which are signature mutations in the Omicron variant). We also frequently detected some less well-described S protein mutations in our Delta sequences, that might play a role in shaping future emerging variants. These include A262S, Q675K, I850L, Q1201H, V1228L and M1237I. Lastly, we observed that some of the Delta variant’s signature mutations were underrepresented in our study due to artifacts of the used bioinformatics tools, approach and sequencing method. We therefore discuss some pitfalls and considerations when sequencing SARS-CoV-2 genomes. Conclusion: Our results suggest that genomic surveillance in a small, representative cohort can be used to make predictions about the circulating variants nationally. Moreover, we show that detection of transient mutations in currently circulating variants can give valuable clues to signature mutations of future VOC. Here we suggest six such mutations, that we detected frequently in the Delta variant during 2021. Lastly, we report multiple systematic errors that occurred when following the ARTIC Network SARS-CoV-2 tiled amplicon approach using the V3 primers and Nanopore sequencing, which led to the masking of some of the important signature mutations in the Delta sequences