Generation of new symmetries from explicit symmetry breaking

We study how the explicit symmetry breaking, through a continuous parameter in the Lagrangian, can actually lead to the creation of different types of symmetries. As examples we consider the motion of a relativistic particle in a curved background, where a nonzero mass breaks the symmetry of the conformal algebra of the metric, and the motion in a Bogoslovsky-Finsler space-time, where a Lorentz violation takes place. In the first case, new nonlocal conserved charges emerge in the place of those which were previously generated by the conformal Killing vectors, while in the second, rational in the momenta integrals of motion appear to substitute the linear expressions corresponding to those boosts which fail to be symmetries.

Angularity in DIS at next-to-next-to-leading log accuracy

Angularity is a class of event-shape observables that can be measured in deep-inelastic scattering. With its continuous parameter a one can interpolate angularity between thrust and broadening and further access beyond the region. Providing such systematic way to access various observables makes angularity attractive in analysis with event shapes. We give the definition of angularity for DIS and factorize the cross section by using soft-collinear effective theory. The factorization is valid in a wide range of a below and above thrust region but invalid in broadening limit. It contains an angularity beam function, which is new result and we give the expression at $$ \mathcal{O} $$ O (αs). We also perform large log resummation of angularity and make predictions at various values of a at next-to-next-to-leading log accuracy.

Factorization identities and algebraic Bethe ansatz for $$ {D}_2^{(2)} $$ models

We express $$ {D}_2^{(2)} $$ D 2 2 transfer matrices as products of $$ {A}_1^{(1)} $$ A 1 1 transfer matrices, for both closed and open spin chains. We use these relations, which we call factorization identities, to solve the models by algebraic Bethe ansatz. We also formulate and solve a new integrable XXZ-like open spin chain with an even number of sites that depends on a continuous parameter, which we interpret as the rapidity of the boundary.

Dual description of η-deformed OSP sigma models

We study the dual description of the η-deformed OSP(N|2m) sigma model in the asymptotically free regime (N > 2m + 2). Compared to the case of classical Lie groups, for supergroups there are inequivalent η-deformations corresponding to different choices of simple roots. For a class of such deformations we propose the system of screening charges depending on a continuous parameter b, which defines the η-deformed OSP(N|2m) sigma model in the limit b → ∞ and a certain Toda QFT as b → 0. In the sigma model regime we show that the leading UV asymptotic of the η-deformed model coincides with a perturbed Gaussian theory. In the perturbative regime b → 0 we show that the tree-level two-particle scattering matrix matches the expansion of the trigonometric OSP(N|2m) S-matrix.

Abstract 12759: Diagnostic and Prognostic Utility of T1 Mapping and Extracellular Volume by Magnetic Resonance Imaging for Cardiac Amyloidosis: A Meta-analysis

Background: Cardiac magnetic resonance imaging (CMR) is central to the evaluation of cardiac amyloidosis (CA). Native T1 mapping and extracellular volume (ECV) are novel CMR techniques with evolving utility in cardiovascular diseases including CA. This study aims to meta-analyze the diagnostic and prognostic data of native T1 mapping and extracellular volume (ECV) techniques for assessing CA. Methods: Pubmed, Cochrane and Embase were searched until 31 March 2020 for studies reporting the accuracy of native T1 mapping and ECV for diagnosing CA or predicting all-cause mortality. Area under the receiver-operative characteristics curves (AUC) and hazards ratios (HR) with 95% confidence intervals (95% CI) respectively were pooled using random-effects models and Open-Meta(Analyst) software. Results: Amongst 459 records obtained from the literature search, 41 full-text articles were assessed and 10 studies were eligible totalling 2364 subjects and 1528 patients with confirmed CA. Pooled AUCs (95% CI) for diagnosing CA were 0.924 (0.889-0.959) for native T1 mapping and 0.963 (0.925-1.000) for ECV (Figure panel A/B). Both techniques had similarly high detection rates for AL- and ATTR CA (pooled AUCs of 0.935 and 0.916 for native T1 mapping and 0.980 and 0.952 for ECV). Pooled HRs (95% CI) for predicting all-cause mortality were 1.15 (1.08-1.22) for native T1 mapping as a continuous parameter, 1.19 (1.01-1.40) for ECV as a continuous parameter (Figure panel C/D), and 4.93 (2.64-9.20) for ECV as a binary threshold. Conclusion: Both native T1 mapping and ECV had high diagnostic performance for CA and predicted all-cause mortality after CA. These CMR techniques can play important roles in the multi-modality imaging assessment of CA, including when contrast administration is contraindicated.

THE QUANTITATIVE RELATIONSHIP BETWEEN AUTONOMOUS CORTISOL SECRETION, DYSGLYCEMIA AND THE METABOLIC SYNDROME

Objective: Autonomous cortisol secretion (ACS) is the most common endocrine abnormality in the evaluation of adrenal incidentalomas. The categorization of ACS is derived from a 1 mg dexamethasone suppression test (DST). Impaired DST is associated with several metabolic derangements. In this study we analyzed the association between post-DST cortisol level, analyzed as a continuous parameter, and indices of glycemic metabolism. Methods: We prospectively collected data of 1,976 patients evaluated for adrenal incidentalomas in a large tertiary medical center between December 1, 2017, and August 31, 2019. Seventy-three patients completed the evaluation process. Post-DST cortisol levels were analyzed for correlation with various metabolic parameters, including fasting plasma glucose (FPG) and hemoglobin A1c (HbA1c) among the general cohort and for subgroups stratified by the number of metabolic syndrome (MS) criteria. Results: Post-DST cortisol demonstrated a linear association with FPG and HbA1c across its entire cortisol range ( R = 0.51 and 0.41, respectively; P≤.01). The association between post-DST cortisol and FPG was strengthened with an increased number of metabolic syndrome criteria. Patients with 4 MS criteria show a stronger association ( R = 0.92) compared to patients with only a single criterion ( R = 0.509). Furthermore, mean post-DST cortisol levels increased as the number of MS criteria accumulated. Conclusion: Post-DST cortisol should be viewed as a continuous parameter in risk stratification algorithms for the development of MS and particularly dysglycemia. Abbreviations: ACS = autonomous cortisol secretion; AI = adrenal incidentaloma; BMI = body mass index; BP = blood pressure; DM = diabetes mellitus; DST = dexamethasone suppression test; FPG = fasting plasma glucose; HbA1c = hemoglobin A1c; HDL = high-density lipoprotein; MS = metabolic syndrome; TG = triglycerides; WHR = waist-to-hip ratio

Sequential Regular Variation: Extensions of Kendall’s Theorem

Regular variation is a continuous-parameter theory; we work in a general setting, containing the existing Karamata, Bojanic–Karamata/de Haan and Beurling theories as special cases. We give sequential versions of the main theorems, that is, with sequential rather than continuous limits. This extends the main result, a theorem of Kendall’s (which builds on earlier work of Kingman and Croft), to the general setting.