Integral Representations for the Class of Generalized Metaplectic Operators

This article gives explicit integral formulas for the so-called generalized metaplectic operators, i.e. Fourier integral operators (FIOs) of Schr\"odinger type, having a symplectic matrix as canonical transformation. These integrals are over specific linear subspaces of R^d, related to the d x d upper left-hand side submatrix of the underlying 2d x 2d symplectic matrix. The arguments use the integral representations for the classical metaplectic operators obtained by Morsche and Oonincx in a previous paper, algebraic properties of symplectic matrices and time-frequency tools. As an application, we give a specific integral representation for solutions to the Cauchy problem of Schr\"odinger equations with bounded perturbations for every instant time t in R, even in the so-called caustic points.Comment: 19 pages in Journal of Fourier Analysis and Applications, 201

An Introduction to the Gabor Wave Front Set

In this expository note we present an introduction to the Gabor wave front set. As is often the case, this tool in microlocal analysis has been introduced and reinvented in different forms which turn out to be equivalent or intimately related. We provide a short review of the history of this notion and then focus on some recent variations inspired by function spaces in time-frequency analysis. Old and new results are presented, together with a number of concrete examples and applications to the problem of propagation of singularities

On the Fredholm property of bisingular pseudodifferential operators

For operators belonging either to a class of global bisingular pseudodifferential operators on $R^m \times R^n$ or to a class of bisingular pseudodifferential operators on a product $M \times N$ of two closed smooth manifolds, we show the equivalence of their ellipticity (defined by the invertibility of certain associated homogeneous principal symbols) and their Fredholm mapping property in associated scales of Sobolev spaces. We also prove the spectral invariance of these operator classes and then extend these results to the even larger classes of Toeplitz type operators.Comment: 21 pages. Expanded sections 3 and 4. Corrected typos. Added reference

The Gabor wave front set of compactly supported distributions

We show that the Gabor wave front set of a compactly supported distribution equals zero times the projection on the second variable of the classical wave front set

A translational approach for limb vascular delivery of the micro-dystrophin gene without high volume or high pressure for treatment of Duchenne muscular dystrophy

Background: Duchenne muscular dystrophy (DMD) is an X-linked recessive disorder with monogenic mutations setting the stage for successful gene therapy treatment. We have completed a study that directly deals with the following key issues that can be directly adapted to a gene therapy clinical trial using rAAV considering the following criteria: 1) A regional vascular delivery approach that will protect the patient from widespread dissemination of virus; 2) an approach to potentially facilitate safe passage of the virus for efficient skeletal muscle transduction; 3) the use of viral doses to accommodate current limitations imposed by vector production methods; 4) and at the same time, achieve a clinically meaningful outcome by transducing multiple muscles in the lower limb to prolong ambulation. Methods: The capacity of AAV1, AAV6 or AAV8 to cross the vascular endothelial barrier carrying a micro-dystrophin cDNA was compared under identical conditions with delivery through a catheter placed in the femoral artery of the mdx mouse. Transduction efficiency was assessed by immuno-staining using an antibody (Manex1a) that recognizes the Nterminus of micro-dystrophin. The degree of physiologic correction was assessed by measuring tetanic force and protection from eccentric contraction in the extensor digitorum longus muscle (EDL). The vascular delivery paradigm found successful in the mouse was carried to the non-human primate to test its potential translation to boys with DMD. Results: Regional vascular delivery resulted in transduction by rAAV8.micro-dystrophin reaching 94.5 ± 0.9 (1 month), 91.3 ± 3.1 (2 months), and 89.6 ± 1.6% (3 months). rAAV6.micro-dystrophin treated animals demonstrated 87.7 ± 6.8 (1 month), 78.9 ± 7.4 (2 months), and 81.2 ± 6.2% (3 months) transduction. In striking contrast, rAAV1 demonstrated very low transduction efficiency [0.9 ± 0.3 (1 month), 2.1 ± 0.8 (2 months), and 2.1 ± 0.7% (3 months)] by vascular delivery. Micro-dystrophin delivered by rAAV8 and rAAV6 through the femoral artery significantly improved tetanic force and protected against eccentric contraction. Mouse studies translated to the hindlimb of cynamologous macaques using a similar vascular delivery paradigm. rAAV8 carrying eGFP in doses proportional to the mouse (5 × 1012 vg/kg in mouse vs 2 × 1012 vg/kg in monkey) demonstrated widespread gene expression [medial gastrocnemius – 63.8 ± 4.9%, lateral gastrocnemius – 66.0 ± 4.5%, EDL – 80.2 ± 3.1%, soleus – 86.4 ± 1.9%, TA – 72.2 ± 4.0%. Conclusion: These studies demonstrate regional vascular gene delivery with AAV serotype(s) in mouse and non-human primate at doses, pressures and volumes applicable for clinical trials in children with DMD

Expectations and experiences of gamete donors and donor-conceived adults searching for genetics relatives using DNA linking through a voluntary register

STUDY QUESTION: What are the experiences of donor-conceived adults and donors who are searching for a genetic link through the use of a DNA-based voluntary register service? SUMMARY ANSWER: Donor-conceived adults and donors held positive beliefs about their search and although some concerns in relation to finding a genetically linked relative were reported, these were not a barrier to searching. WHAT IS KNOWN ALREADY: Research with donor-conceived people has consistently identified their interest in learning about-and in some cases making contact with-their donor and other genetic relatives. However, donor-conceived individuals or donors rarely have the opportunity to act on these desires. STUDY DESIGN, SIZE, AND DURATION: A questionnaire was administered for online completion using Bristol Online Surveys. The survey was live for 3 months and responses were collected anonymously. PARTICIPANTS/MATERIALS, SETTING, AND METHODS: The survey was completed by 65 donor-conceived adults, 21 sperm donors and 5 oocyte donors who had registered with a DNA-based voluntary contact register in the UK. The questionnaire included socio-demographic questions, questions specifically developed for the purposes of this study and the standardized Aspects of Identity Questionnaire (AIQ). MAIN RESULTS AND THE ROLE OF CHANCE: Motivations for searching for genetic relatives were varied, with the most common reasons being curiosity and passing on information. Overall, participants who were already linked and those awaiting a link were positive about being linked and valued access to a DNA-based register. Collective identity (reflecting self-defining feelings of continuity and uniqueness), as assessed by the AIQ, was significantly lower for donor-conceived adults when compared with the donor groups (P 0.05) for donor-conceived adults. LIMITATIONS, REASONS FOR CAUTION: Participants were members of a UK DNA-based registry which is unique. It was therefore not possible to determine how representative participants were of those who did not register for the service, those in other countries or of those who do not seek information exchange or contact. WIDER IMPLICATIONS OF THE FINDINGS: This is the first survey exploring the experiences of donor-conceived adults and donors using a DNA-based voluntary register to seek information about and contact with genetic relatives and the first to measure aspects of identity using standardized measures. Findings provide valuable information about patterns of expectations and experiences of searching through DNA linking, identity and of having contact in the context of donor conception that will inform future research, practice and policy development

Nuclearity of rapidly decreasing ultradifferentiable functions and time-frequency analysis

[EN] We use techniques from time-frequency analysis to show that the space S(omega )of rapidly decreasing omega-ultradifferentiable functions is nuclear for every weight function omega(t) = o(t) as t tends to infinity. Moreover, we prove that, for a sequence (M-p)(p) satisfying the classical condition (M1) of Komatsu, the space of Beurling type S-(M)p when defined with L-2 norms is nuclear exactly when condition (M2)' of Komatsu holds.We thank the reviewer very much for the careful reading of our manuscript and the comments to improve the paper. The first three authors were partially supported by the Project FFABR 2017 (MIUR), and by the Projects FIR 2018 and FAR 2018 (University of Ferrara). The first and third authors are members of the Gruppo Nazionale per l'Analisi Matematica, la Probabilita e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). The research of the second author was partially supported by the project MTM2016-76647-P and the grant BEST/2019/172 from Generalitat Valenciana. The fourth author is supported by FWF-project J 3948-N35.Boiti, C.; Jornet Casanova, D.; Oliaro, A.; Schindl, G. (2021). Nuclearity of rapidly decreasing ultradifferentiable functions and time-frequency analysis. Collectanea mathematica. 72(2):423-442. https://doi.org/10.1007/s13348-020-00296-0S423442722Asensio, V., Jornet, D.: Global pseudodifferential operators of infinite order in classes of ultradifferentiable functions. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 113(4), 3477–3512 (2019)Aubry, J.-M.: Ultrarapidly decreasing ultradifferentiable functions, Wigner distributions and density matrices. J. London Math. Soc. 2(78), 392–406 (2008)Björck, G.: Linear partial differential operators and generalized distributions. Ark. Mat. 6(21), 351–407 (1966)Boiti, C., Jornet, D., Oliaro, A.: Regularity of partial differential operators in ultradifferentiable spaces and Wigner type transforms. J. Math. Anal. Appl. 446, 920–944 (2017)Boiti, C., Jornet, D., Oliaro, A.: The Gabor wave front set in spaces of ultradifferentiable functions. Monatsh. Math. 188(2), 199–246 (2019)Boiti, C., Jornet, D., Oliaro, A.: About the nuclearity of $$\cal{S}_{(M_{p})}$$ and $$\cal{S}_{\omega }$$. In: Boggiatto, P., et al. (eds.) Advances in Microlocal and Time-Frequency Analysis. Applied and Numerical Harmonic Analysis, pp. 121–129. Birkhäuser, Cham (2020)Boiti, C., Jornet, D., Oliaro, A.: Real Paley-Wiener theorems in spaces of ultradifferentiable functions. J. Funct. Anal. 278(4), 108348 (2020)Bonet, J., Meise, R., Melikhov, S.N.: A comparison of two different ways to define classes of ultradifferentiable functions. Bull. Belg. Math. Soc. Simon Stevin 14(3), 425–444 (2007)Braun, R.W., Meise, R., Taylor, B.A.: Ultradifferentiable functions and Fourier analysis. Result. Math. 17, 206–237 (1990)Fernández, C., Galbis, A., Jornet, D.: Pseudodifferential operators on non-quasianalytic classes of Beurling type. Studia Math. 167(2), 99–131 (2005)Fernández, C., Galbis, A., Jornet, D.: Pseudodifferential operators of Beurling type and the wave front set. J. Math. Anal. Appl. 340(2), 1153–1170 (2008)Franken, U.: Weight functions for classes of ultradifferentiable functions. Results Math. 25, 50–53 (1994)Gröchenig, K.: Foundations of Time-Frequency Analysis. Birkhäuser, Boston (2001)Gröchenig, K., Leinert, M.: Wiener’s Lemma for twisted convolution and Gabor frames. J. Am. Math. Soc. 17(1), 1–18 (2004)Gröchenig, K., Zimmermann, G.: Spaces of Test Functions via the STFT. J. Funct. Spaces Appl. 2(1), 25–53 (2004)Heinrich, T., Meise, R.: A support theorem for quasianalytic functionals. Math. Nachr. 280(4), 364–387 (2007)Hörmander, L.: Notions of Convexity. Progress in Mathematics, vol. 127. Birkhäuser, Boston (1994)Janssen, A.J.E.M.: Duality and Biorthogonality for Weyl-Heisenberg Frames. J. Fourier Anal. Appl. 1(4), 403–436 (1995)Komatsu, H.: Ultradistributions I. Structure theorems and a characterization. J. Fac. Sci. Univ. Tokyo Sect IA Math. 20, 25–105 (1973)Langenbruch, M.: Hermite functions and weighted spaces of generalized functions. Manuscripta Math. 119(3), 269–285 (2006)Meise, R., Vogt, D.: Introduction to Functional Analysis. Clarendon Press, Oxford (1997)Petzsche, H.J.: Die nuklearität der ultradistributionsräume und der satz vom kern I. Manuscripta Math. 24, 133–171 (1978)Pietsch, A.: Nuclear Locally Convex Spaces. Springer, Berlin (1972)Pilipović, S., Prangoski, B., Vindas, J.: On quasianalytic classes of Gelfand-Shilov type. Parametrix and convolution. J. Math. Pures Appl. 116, 174–210 (2018)Rodino, L.: Linear Partial Differential Operators in Gevrey Spaces. World Scientific Publishing Co. Inc, River Edge, NJ (1993)Rodino, L., Wahlberg, P.: The Gabor wave front set. Monatsh. Math. 173, 625–655 (2014)Schmets, J., Valdivia, M.: Analytic extension of ultradifferentiable Whitney jets. Collect. Math. 50(1), 73–94 (1999

Orientia tsutsugamushi ankyrin repeat-containing protein family members are Type 1 secretion system substrates that traffic to the host cell endoplasmic reticulum

Scrub typhus is an understudied, potentially fatal infection that threatens one billion persons in the Asia-Pacific region. How the causative obligate intracellular bacterium, Orientia tsutsugamushi, facilitates its intracellular survival and pathogenesis is poorly understood. Many intracellular bacterial pathogens utilize the Type 1 (T1SS) or Type 4 secretion system (T4SS) to translocate ankyrin repeat-containing proteins (Anks) that traffic to distinct subcellular locations and modulate host cell processes. The O. tsutsugamushi genome encodes one of the largest known bacterial Ank repertoires plus T1SS and T4SS components. Whether these potential virulence factors are expressed during infection, how the Anks are potentially secreted, and to where they localize in the host cell are not known. We determined that O. tsutsugamushi transcriptionally expresses 20 unique ank genes as well as genes for both T1SS and T4SS during infection of mammalian host cells. Examination of the Anks’ C-termini revealed that the majority of them resemble T1SS substrates. Escherichia coli expressing a functional T1SS was able to secrete chimeric hemolysin proteins bearing the C-termini of 19 of 20 O. tsutsugamushi Anks in an HlyBD-dependent manner. Thus, O. tsutsugamushi Anks C-termini are T1SS-compatible. Conversely, Coxiella burnetii could not secrete heterologously expressed Anks in a T4SS-dependent manner. Analysis of the subcellular distribution patterns of 20 ectopically expressed Anks revealed that, while 6 remained cytosolic or trafficked to the nucleus, 14 localized to, and in some cases, altered the morphology of the endoplasmic reticulum. This study identifies O. tsutsugamushi Anks as T1SS substrates and indicates that many display a tropism for the host cell secretory pathway