ISO_q(3) and ISO_q(2,1)

We prove the embedding of ISO_q(3) \hook ISU^{ex}_{\sqrt{q}}(2) and ISO_q(2,1) \hook ISL^{ex}_q(2,R) as $^*$-algebras and give a Hilbert space representation of $ISU^{ex}_{\sqrt{q}}(2)$Comment: 10 pages, 12 figures, Late

I’ll Try That, Too

The effect of variety on consumer choice has been studied extensively, with some stream of literature showing the positive effects on choice and others arguing that too many alternatives may result in negative consequences (i.e., choice deferral or no purchase at all), often referred to as choice overload. In a field experiment with a major chocolate brand conducted at a German retail chain, we test for variety during a price and display promotion. Participating stores either include the full variety of products on the display or a reduced selection (low variety). Contrary to the literature on choice overload, we find a significantly positive effect of the display promotion on unit sales, which is stronger for stores with high variety. Further findings show a stronger promotion uplift for less popular products in stores with high variety on the display. This suggests that more variety may increase consumers’ willingness to try new products, when the financial risk is low. We also test for the effect of product distribution on displays by analysing the number of facings. Additionally, we introduce an approach to determine an optimal space allocation of products on the display. Our findings suggest that an even distribution results in the highest profits for the retailer. We contribute to the literature on variety for consumer choices by offering insights from actual purchases with store-level scanner data of display promotions

Automated Test Assembly in R: The eatATA Package

Combining items from an item pool into test forms (test assembly) is a frequent task in psychological and educational testing. Although efficient methods for automated test assembly exist, these are often unknown or unavailable to practitioners. In this paper we present the R package eatATA, which allows using several mixed-integer programming solvers for automated test assembly in R. We describe the general functionality and the common work flow of eatATA using a minimal example. We also provide four more elaborate use cases of automated test assembly: (a) The assembly of multiple test forms for a pilot study; (b) the assembly of blocks of items for a multiple matrix booklet design in the context of a large-scale assessment; (c) the assembly of two linear test forms for individual diagnostic purposes; (d) the assembly of multi-stage testing modules for individual diagnostic purposes. All use cases are accompanied with example item pools and commented R code.Peer Reviewe

Lie Superalgebras and the Multiplet Structure of the Genetic Code II: Branching Schemes

Continuing our attempt to explain the degeneracy of the genetic code using basic classical Lie superalgebras, we present the branching schemes for the typical codon representations (typical 64-dimensional irreducible representations) of basic classical Lie superalgebras and find three schemes that do reproduce the degeneracies of the standard code, based on the orthosymplectic algebra osp(5|2) and differing only in details of the symmetry breaking pattern during the last step.Comment: 34 pages, 9 tables, LaTe

MAPKinase inhibition after failure of immune checkpoint blockade in patients with advanced melanoma – an evaluation of the multicenter prospective skin cancer registry ADOREG

Objectives: Forty to sixty percent of patients with advanced melanoma show primary resistance to PD-1-based immunotherapy, 30-40% of initial responders also progress. Here, we evaluated the outcome of second-line targeted therapy (TT) after progression on PD-1-based immune checkpoint inhibition (ICI) in BRAFV600-mutated melanoma. In addition, we report data on the activity of re-exposure with PD-1-based regimes. Methods: Patients with advanced (non- resectable stage III or IV, AJCC 2017, 8th edition) melanoma progressing on PD-1-based ICI (nivolumab, pembrolizumab or ipilimumab plus nivolumab) and receiving second-line BRAF plus MEK inhibition were identified from the prospective multicenter skin cancer registry ADOREG. Results: We identified 108 patients with unresectable stage III or stage IV melanoma progressing on first-line ICI (nivolumab, pembrolizumab or ipilimumab plus nivolumab) and receiving second-line combined BRAF/MEK inhibition. Seventy- three percent of the cohort presented with primary PD-1 resistant disease. Median progression-free survival ( PFS) on ICI was 2.6 (95% CI 2.2-2.9) months. Median PFS on subsequent TT was 6.6 (95% CI 5.4 -7.8) months. Median OS from start of second-line TT was 16.0 (95% CI 11.2-20.8) months. The 3-year PFS and OS rates on second-line TT were 16% and 30%. The objective response rate (ORR) and disease control rate (DCR) to TT were 42.6% and 55.6%. In patients with brain metastases, the ORR and DCR were 31.4% and 43.1%. Patients without brain metastases showed an ORR and DCR of 52.6% and 66.7%, respectively. Response to first-line ICI was associated with a numerically higher ORR and DCR to second-line TT and improved OS on TT. Twenty-three patients received third-line ICI of whom two patients showed an objective response. Conclusions: BRAF plus MEK inhibition shows meaningful activity and outcome in patients with advanced melanoma resistant to anti-PD-1- based immunotherapy. Rates of long- term benefit and survival in our study were similar to those reported for treatment-naive patients receiving first-line MAPKi

Impact of radiotherapy and sequencing of systemic therapy on survival outcomes in melanoma patients with previously untreated brain metastasis: a multicenter DeCOG study on 450 patients from the prospective skin cancer registry ADOREG

BACKGROUND: Despite of various therapeutic strategies, treatment of patients with melanoma brain metastasis (MBM) still is a major challenge. This study aimed at investigating the impact of type and sequence of immune checkpoint blockade (ICB) and targeted therapy (TT), radiotherapy, and surgery on the survival outcome of patients with MBM. METHOD: We assessed data of 450 patients collected within the prospective multicenter real-world skin cancer registry ADOREG who were diagnosed with MBM before start of the first non-adjuvant systemic therapy. Study endpoints were progression-free survival (PFS) and overall survival (OS). RESULTS: Of 450 MBM patients, 175 (38.9%) received CTLA-4+PD-1 ICB, 161 (35.8%) PD-1 ICB, and 114 (25.3%) BRAF+MEK TT as first-line treatment. Additional to systemic therapy, 67.3% of the patients received radiotherapy (stereotactic radiosurgery (SRS); conventional radiotherapy (CRT)) and 24.4% had surgery of MBM. 199 patients (42.2%) received a second-line systemic therapy. Multivariate Cox regression analysis revealed the application of radiotherapy (HR for SRS: 0.213, 95% CI 0.094 to 0.485, p1 cm: 1.977, 95% CI 1.117 to 3.500, p=0.019), age (HR for age >65 years: 1.802, 95% CI 1.016 to 3.197, p=0.044), and ECOG performance status (HR for ECOG ≥2: HR: 2.615, 95% CI 1.024 to 6.676, p=0.044) as independent prognostic factors of OS on first-line therapy. The type of first-line therapy (ICB vs TT) was not independently prognostic. As second-line therapy BRAF+MEK showed the best survival outcome compared with ICB and other therapies (HR for CTLA-4+PD-1 compared with BRAF+MEK: 13.964, 95% CI 3.6 to 54.4, p<0.001; for PD-1 vs BRAF+MEK: 4.587 95% CI 1.3 to 16.8, p=0.022 for OS). Regarding therapy sequencing, patients treated with ICB as first-line therapy and BRAF+MEK as second-line therapy showed an improved OS (HR for CTLA-4+PD-1 followed by BRAF+MEK: 0.370, 95% CI 0.157 to 0.934, p=0.035; HR for PD-1 followed by BRAF+MEK: 0.290, 95% CI 0.092 to 0.918, p=0.035) compared with patients starting with BRAF+MEK in first-line therapy. There was no significant survival difference when comparing first-line therapy with CTLA-4+PD-1 ICB with PD-1 ICB. CONCLUSIONS: In patients with MBM, the addition of radiotherapy resulted in a favorable OS on systemic therapy. In BRAF-mutated MBM patients, ICB as first-line therapy and BRAF+MEK as second-line therapy were associated with a significantly prolonged OS

Brain metastasis and survival outcomes after first-line therapy in metastatic melanoma: a multicenter DeCOG study on 1704 patients from the prospective skin cancer registry ADOREG

Background Despite the availability of effective systemic therapies, a significant number of advanced melanoma patients develops brain metastases. This study investigated differences in incidence and time to diagnosis of brain metastasis and survival outcomes dependent on the type of first-line therapy.Methods Patients with metastatic, non-resectable melanoma (AJCCv8 stage IIIC–V) without brain metastasis at start of first-line therapy (1L-therapy) were identified from the prospective multicenter real-world skin cancer registry ADOREG. Study endpoints were incidence of brain metastasis, brain metastasis-free survival (BMFS), progression-free survival (PFS), and overall survival (OS).Results Of 1704 patients, 916 were BRAF wild-type (BRAFwt) and 788 were BRAF V600 mutant (BRAFmut). Median follow-up time after start of 1L-therapy was 40.4 months. BRAFwt patients received 1L-therapy with immune checkpoint inhibitors (ICI) against CTLA-4+PD-1 (n=281) or PD-1 (n=544). In BRAFmut patients, 1L-therapy was ICI in 415 patients (CTLA-4+PD-1, n=108; PD-1, n=264), and BRAF+MEK targeted therapy (TT) in 373 patients. After 24 months, 1L-therapy with BRAF+MEK resulted in a higher incidence of brain metastasis compared with PD-1±CTLA-4 (BRAF+MEK, 30.3%; CTLA-4+PD-1, 22.2%; PD-1, 14.0%). In multivariate analysis, BRAFmut patients developed brain metastases earlier on 1L-therapy with BRAF+MEK than with PD-1±CTLA-4 (CTLA-4+PD-1: HR 0.560, 95% CI 0.332 to 0.945, p=0.030; PD-1: HR 0.575, 95% CI 0.372 to 0.888, p=0.013). Type of 1L-therapy, tumor stage, and age were independent prognostic factors for BMFS in BRAFmut patients. In BRAFwt patients, tumor stage was independently associated with longer BMFS; ECOG Performance status (ECOG-PS), lactate dehydrogenase (LDH), and tumor stage with OS. CTLA-4+PD-1 did not result in better BMFS, PFS, or OS than PD-1 in BRAFwt patients. For BRAFmut patients, multivariate Cox regression revealed ECOG-PS, type of 1L-therapy, tumor stage, and LDH as independent prognostic factors for PFS and OS. 1L-therapy with CTLA-4+PD-1 led to longer OS than PD-1 (HR 1.97, 95% CI 1.122 to 3.455, p=0.018) or BRAF+MEK (HR 2.41, 95% CI 1.432 to 4.054, p=0.001), without PD-1 being superior to BRAF+MEK.Conclusions In BRAFmut patients 1L-therapy with PD-1±CTLA-4 ICI resulted in a delayed and less frequent development of brain metastasis compared with BRAF+MEK TT. 1L-therapy with CTLA-4+PD-1 showed superior OS compared with PD-1 and BRAF+MEK. In BRAFwt patients, no differences in brain metastasis and survival outcomes were detected for CTLA-4+PD-1 compared with PD-1