Spectral Relationships Between Kicked Harper and On-Resonance Double Kicked Rotor Operators

Kicked Harper operators and on-resonance double kicked rotor operators model quantum systems whose semiclassical limits exhibit chaotic dynamics. Recent computational studies indicate a striking resemblance between the spectrums of these operators. In this paper we apply C*-algebra methods to explain this resemblance. We show that each pair of corresponding operators belong to a common rotation C*-algebra B_\alpha, prove that their spectrums are equal if \alpha is irrational, and prove that the Hausdorff distance between their spectrums converges to zero as q increases if \alpha = p/q with p and q coprime integers. Moreover, we show that corresponding operators in B_\alpha are homomorphic images of mother operators in the universal rotation C*-algebra A_\alpha that are unitarily equivalent and hence have identical spectrums. These results extend analogous results for almost Mathieu operators. We also utilize the C*-algebraic framework to develop efficient algorithms to compute the spectrums of these mother operators for rational \alpha and present preliminary numerical results that support the conjecture that their spectrums are Cantor sets if \alpha is irrational. This conjecture for almost Mathieu operators, called the Ten Martini Problem, was recently proved after intensive efforts over several decades. This proof for the almost Mathieu operators utilized transfer matrix methods, which do not exist for the kicked operators. We outline a strategy, based on a special property of loop groups of semisimple Lie groups, to prove this conjecture for the kicked operators.Comment: 26 pages, 8 figure

Nationwide Survival Benefit after Implementation of First-Line Immunotherapy for Patients with Advanced NSCLC—Real World Efficacy

SIMPLE SUMMARY: The expected change in overall survival (OS) in patients with advanced non-small cell lung cancer (NSCLC) after the clinical implementation of immune checkpoint inhibitor therapy (ICI) has not been substantially investigated in large real-world cohorts outside randomized controlled trials (RCTs). In this nationwide study, we compared OS before and after the implementation of ICI and found that 3-year OS tripled from 6% to 18%. Patients receiving ICI had a lower OS than demonstrated in RCTs, except for patients with performance status (PS) 0. More than a fifth of the patients progressed early within the first six ICI cycles. Adverse prognostic factors were PS ≥ 1 and metastases to the bone and liver. ABSTRACT: Background The selection of patients with non-small cell lung cancer (NSCLC) for immune checkpoint inhibitor (ICI) treatment remains challenging. This real-world study aimed to compare the overall survival (OS) before and after the implementation of ICIs, to identify OS prognostic factors, and to assess treatment data in first-line (1L) ICI-treated patients without epidermal growth factor receptor mutation or anaplastic lymphoma kinase translocation. Methods Data from the Danish NSCLC population initiated with 1L palliative antineoplastic treatment from 1 January 2013 to 1 October 2018, were extracted from the Danish Lung Cancer Registry (DLCR). Long-term survival and median OS pre- and post-approval of 1L ICI were compared. From electronic health records, additional clinical and treatment data were obtained for ICI-treated patients from 1 March 2017 to 1 October 2018. Results The OS was significantly improved in the DLCR post-approval cohort (n = 2055) compared to the pre-approval cohort (n = 1658). The 3-year OS rates were 18% (95% CI 15.6–20.0) and 6% (95% CI 5.1–7.4), respectively. On multivariable Cox regression, bone (HR = 1.63) and liver metastases (HR = 1.47), performance status (PS) 1 (HR = 1.86), and PS ≥ 2 (HR = 2.19) were significantly associated with poor OS in ICI-treated patients. Conclusion OS significantly improved in patients with advanced NSCLC after ICI implementation in Denmark. In ICI-treated patients, PS ≥ 1, and bone and liver metastases were associated with a worse prognosis

High-Throughput High-Resolution Class I HLA Genotyping in East Africa

HLA, the most genetically diverse loci in the human genome, play a crucial role in host-pathogen interaction by mediating innate and adaptive cellular immune responses. A vast number of infectious diseases affect East Africa, including HIV/AIDS, malaria, and tuberculosis, but the HLA genetic diversity in this region remains incompletely described. This is a major obstacle for the design and evaluation of preventive vaccines. Available HLA typing techniques, that provide the 4-digit level resolution needed to interpret immune responses, lack sufficient throughput for large immunoepidemiological studies. Here we present a novel HLA typing assay bridging the gap between high resolution and high throughput. The assay is based on real-time PCR using sequence-specific primers (SSP) and can genotype carriers of the 49 most common East African class I HLA-A, -B, and -C alleles, at the 4-digit level. Using a validation panel of 175 samples from Kampala, Uganda, previously defined by sequence-based typing, the new assay performed with 100% sensitivity and specificity. The assay was also implemented to define the HLA genetic complexity of a previously uncharacterized Tanzanian population, demonstrating its inclusion in the major East African genetic cluster. The availability of genotyping tools with this capacity will be extremely useful in the identification of correlates of immune protection and the evaluation of candidate vaccine efficacy

Leadership and systems of governance: The constraints on the scope for leadership of place-based development in sub-national territories

BENTLEY G., PUGALIS L. and SHUTT J. A triadic conceptualization of leadership, governance systems and central-local relations is constructed in order to aid understandings about the influence of systems of governance on the scope for place-based leadership. Deploying the dual concepts of ‘permissibility’ and ‘acceptability’ provides an innovative analytical device for deciphering the actually existing nature of place-based leadership. Recently initiated public-private-partnerships in one of the OECD’s most centralized countries are analysed to articulate characteristics of controlling mechanisms of the national system of governance which shape the degree of autonomy of leadership of city and regional development in sub-national terrains