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The resolvent operator plays a central role in matrix models. For instance, with utilizing the loop equation, all of the perturbative amplitudes including correlators, the free-energy and those of instanton corrections can be obtained from the spectral curve of the resolvent operator. However, at the level of non-perturbative completion, the resolvent operator is generally not sufficient to recover all the information from the loop equations. Therefore it is necessary to find a sufficient set of operators which provide the missing non-perturbative information. In this paper, we study generalized Wronskians of the Baker-Akhiezer systems as a manifestation of these new degrees of freedom. In particular, we derive their isomonodromy systems and then extend several spectral dualities to these systems. In addition, we discuss how these Wronskian operators are naturally aligned on the Kac table. Since they are consistent with the Seiberg-Shih relation, we propose that these new degrees of freedom can be identified as FZZT-Cardy branes in Liouville theory. This means that FZZT-Cardy branes are the bound states of elemental FZZT branes (i.e. the twisted fermions) rather than the bound states of principal FZZT-brane (i.e. the resolvent operator).Comment: 131 pages, 4 figure
BackgroundThromboembolic events are increasingly reported in the aging haemophilia population. The purpose of this study was to understand current practices and identify knowledge and research gaps in the management of persons with haemophilia requiring antithrombotic therapy for cardiovascular disorders (CVD) or venous thromboembolism (VTE).MethodsWe searched MEDLINE, EMBASE and Scopus for studies reporting on more than two patients with inherited haemophilia A or B, without inhibitors, requiring antithrombotic therapy for CVD or VTE. Data were extracted by two independent reviewers and analysed using descriptive statistics and narrative synthesis.ResultsWe included 32 studies reporting on 432 persons with haemophilia. Three themes described the observed practice variation: (1) Difficulty weighing competing bleeding and thrombotic risks; (2) Tensions in providing standards of care and minimizing bleeding risk; (3) Advocacy for individualized strategies and multidisciplinary care. Different management strategies were used to treat persons with haemophilia in the setting of thromboembolic events, such as avoiding or choosing lower intensity antithrombotic therapy, or procedural alternatives to antithrombotic therapy. Initiation or alteration in haemostatic therapies along with antithrombotic therapy were common strategies and reported in 30 studies. However, data on target factor levels and bleeding and thrombotic events were largely missing.DiscussionOur scoping review highlights unmet needs in the management of an aging population of persons with haemophilia with increasing prevalence of CVD and VTE. Management is inconsistent and divergent from those of non‐haemophilic patients. Prospective data are needed to inform optimal and evidence‐based management strategies of CVD and VTE in persons with haemophilia.
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