Thirty-two Goldbach Variations

We give thirty-two diverse proofs of a small mathematical gem--the fundamental Euler sum identity zeta(2,1)=zeta(3) =8zeta(\bar 2,1). We also discuss various generalizations for multiple harmonic (Euler) sums and some of their many connections, thereby illustrating both the wide variety of techniques fruitfully used to study such sums and the attraction of their study.Comment: v1: 34 pages AMSLaTeX. v2: 41 pages AMSLaTeX. New introductory material added and material on inequalities, Hilbert matrix and Witten zeta functions. Errors in the second section on Complex Line Integrals are corrected. To appear in International Journal of Number Theory. Title change

Tumor and Microenvironment Evolution during Immunotherapy with Nivolumab.

The mechanisms by which immune checkpoint blockade modulates tumor evolution during therapy are unclear. We assessed genomic changes in tumors from 68 patients with advanced melanoma, who progressed on ipilimumab or were ipilimumab-naive, before and after nivolumab initiation (CA209-038 study). Tumors were analyzed by whole-exome, transcriptome, and/or T cell receptor (TCR) sequencing. In responding patients, mutation and neoantigen load were reduced from baseline, and analysis of intratumoral heterogeneity during therapy demonstrated differential clonal evolution within tumors and putative selection against neoantigenic mutations on-therapy. Transcriptome analyses before and during nivolumab therapy revealed increases in distinct immune cell subsets, activation of specific transcriptional networks, and upregulation of immune checkpoint genes that were more pronounced in patients with response. Temporal changes in intratumoral TCR repertoire revealed expansion of T cell clones in the setting of neoantigen loss. Comprehensive genomic profiling data in this study provide insight into nivolumab\u27s mechanism of action

Caspian: Os Results from a Randomised Phase 3 Study of First-Line Durvalumab ± Tremelimumab + Chemotherapy in ES-SCLC

Immune checkpoint blockade targeting the PD-1/PD-L1 pathway in combination with platinum-based chemotherapy (CT) has demonstrated improved clinical outcomes in patients (pts) with extensive-stage small-cell lung cancer (ES-SCLC). Durvalumab ± Tremelimumab in combination with etoposide and platinum-based CT (EP) as first-line treatment for pts with ES-SCLC. Results will be presented at WCLC 2019 including OS, key secondary endpoints, safety and tolerability

Patient-reported outcomes with first-line durvalumab plus platinum-etoposide versus platinum-etoposide in extensive-stage small-cell lung cancer (CASPIAN): a randomized, controlled, open-label, phase III study

Objectives In the phase III CASPIAN study, first-line durvalumab plus etoposide in combination with either cisplatin or carboplatin (EP) significantly improved overall survival (primary endpoint) versus EP alone in patients with extensive-stage small-cell lung cancer (ES-SCLC) at the interim analysis. Here we report patient-reported outcomes (PROs). Materials and methods Treatment-naïve patients with ES-SCLC received 4 cycles of durvalumab plus EP every 3 weeks followed by maintenance durvalumab every 4 weeks until progression, or up to 6 cycles of EP every 3 weeks. PROs, assessed with the European Organisation for Research and Treatment of Cancer (EORTC) Quality of Life Questionnaire-Core 30 (QLQ-C30) version 3 and its lung cancer module, the Quality of Life Questionnaire-Lung Cancer 13 (QLQ-LC13), were prespecified secondary endpoints. Changes from baseline to disease progression or 12 months in prespecified key disease-related symptoms (cough, dyspnea, chest pain, fatigue, appetite loss) were analyzed with a mixed model for repeated measures. Time to deterioration (TTD) of symptoms, functioning, and global health status/quality of life (QoL) from randomization was analyzed. Results In the durvalumab plus EP and EP arms, 261 and 260 patients were PRO-evaluable. Patients in both arms experienced numerically reduced symptom burden over 12 months or until progression for key symptoms. For the improvements from baseline in appetite loss, the between-arm difference was statistically significant, favoring durvalumab plus EP (difference, −4.5; 99% CI: −9.04, −0.04; nominal p = 0.009). Patients experienced longer TTD with durvalumab plus EP versus EP for all symptoms (hazard ratio [95% CI] for key symptoms: cough 0.78 [0.600‒1.026]; dyspnea 0.79 [0.625‒1.006]; chest pain 0.76 [0.575‒0.996]; fatigue 0.82 [0.653‒1.027]; appetite loss 0.70 [0.542‒0.899]), functioning, and global health status/QoL. Conclusion Addition of durvalumab to first-line EP maintained QoL and delayed worsening of patient-reported symptoms, functioning, and global health status/QoL compared with EP

31st Annual Meeting and Associated Programs of the Society for Immunotherapy of Cancer (SITC 2016) : part two

Background The immunological escape of tumors represents one of the main ob- stacles to the treatment of malignancies. The blockade of PD-1 or CTLA-4 receptors represented a milestone in the history of immunotherapy. However, immune checkpoint inhibitors seem to be effective in specific cohorts of patients. It has been proposed that their efficacy relies on the presence of an immunological response. Thus, we hypothesized that disruption of the PD-L1/PD-1 axis would synergize with our oncolytic vaccine platform PeptiCRAd. Methods We used murine B16OVA in vivo tumor models and flow cytometry analysis to investigate the immunological background. Results First, we found that high-burden B16OVA tumors were refractory to combination immunotherapy. However, with a more aggressive schedule, tumors with a lower burden were more susceptible to the combination of PeptiCRAd and PD-L1 blockade. The therapy signifi- cantly increased the median survival of mice (Fig. 7). Interestingly, the reduced growth of contralaterally injected B16F10 cells sug- gested the presence of a long lasting immunological memory also against non-targeted antigens. Concerning the functional state of tumor infiltrating lymphocytes (TILs), we found that all the immune therapies would enhance the percentage of activated (PD-1pos TIM- 3neg) T lymphocytes and reduce the amount of exhausted (PD-1pos TIM-3pos) cells compared to placebo. As expected, we found that PeptiCRAd monotherapy could increase the number of antigen spe- cific CD8+ T cells compared to other treatments. However, only the combination with PD-L1 blockade could significantly increase the ra- tio between activated and exhausted pentamer positive cells (p= 0.0058), suggesting that by disrupting the PD-1/PD-L1 axis we could decrease the amount of dysfunctional antigen specific T cells. We ob- served that the anatomical location deeply influenced the state of CD4+ and CD8+ T lymphocytes. In fact, TIM-3 expression was in- creased by 2 fold on TILs compared to splenic and lymphoid T cells. In the CD8+ compartment, the expression of PD-1 on the surface seemed to be restricted to the tumor micro-environment, while CD4 + T cells had a high expression of PD-1 also in lymphoid organs. Interestingly, we found that the levels of PD-1 were significantly higher on CD8+ T cells than on CD4+ T cells into the tumor micro- environment (p < 0.0001). Conclusions In conclusion, we demonstrated that the efficacy of immune check- point inhibitors might be strongly enhanced by their combination with cancer vaccines. PeptiCRAd was able to increase the number of antigen-specific T cells and PD-L1 blockade prevented their exhaus- tion, resulting in long-lasting immunological memory and increased median survival

Hypothalamic leptin signaling regulates hepatic insulin sensitivity via a neurocircuit involving the vagus nerve.

Recent evidence suggests that hormones such as insulin and leptin act in the hypothalamus to regulate energy balance and glucose metabolism. Here we show that in leptin receptor-deficient Koletsky (fa(k)/fa(k)) rats, adenovirally induced expression of leptin receptors in the area of the hypothalamic arcuate nucleus improved peripheral insulin sensitivity via enhanced suppression of hepatic glucose production, with no change of insulin-stimulated glucose uptake or disposal. This effect was associated with increased insulin signal transduction via phosphatidylinositol-3-OH kinase (as measured by pY-insulin receptor substrate-1 and pS-PKB/Akt) in liver, but not skeletal muscle, and with reduced hepatic expression of the gluconeogenic genes, glucose-6-phosphatase and phosphoenolpyruvate kinase. Moreover, the beneficial effects of hypothalamic leptin signaling on hepatic insulin sensitivity were blocked by selective hepatic vagotomy. We conclude that hypothalamic leptin action increases peripheral insulin sensitivity primarily via effects on the liver and that the mechanism underlying this effect is dependent on the hepatic branch of the vagus nerve

Hypothalamic Leptin Signaling Regulates Hepatic Insulin Sensitivity via a Neurocircuit Involving the Vagus Nerve

Recent evidence suggests that hormones such as insulin and leptin act in the hypothalamus to regulate energy balance and glucose metabolism. Here we show that in leptin receptor-deficient Koletsky (fak/fak) rats, adenovirally induced expression of leptin receptors in the area of the hypothalamic arcuate nucleus improved peripheral insulin sensitivity via enhanced suppression of hepatic glucose production, with no change of insulin-stimulated glucose uptake or disposal. This effect was associated with increased insulin signal transduction via phosphatidylinositol-3-OH kinase (as measured by pY-insulin receptor substrate-1 and pS-PKB/Akt) in liver, but not skeletal muscle, and with reduced hepatic expression of the gluconeogenic genes, glucose-6-phosphatase and phosphoenolpyruvate kinase. Moreover, the beneficial effects of hypothalamic leptin signaling on hepatic insulin sensitivity were blocked by selective hepatic vagotomy. We conclude that hypothalamic leptin action increases peripheral insulin sensitivity primarily via effects on the liver and that the mechanism underlying this effect is dependent on the hepatic branch of the vagus nerve