Spin Models, Association Schemes and the Nakanishi–Montesinos Conjecture

AbstractA 3-transformation of a link is a local change which replaces two strings that are three times half twisted around each other by two untwisted strings (and vice versa). The Nakanishi–Montesinos (NM) conjecture asserts that this 3-transformation can unknot any link. We introduce the notion of the NM-spin model, which gives a link invariant preserved by 3-transformation. We try to classify such spin models and determine the corresponding link invariant. It is proved that the dimension of the Bose–Mesner algebra generated by the spin model is ≤4. For dimension 1 and 2, there is no such spin model, but for dimension 3, there exists a unique one. Its link invariant is a non-trivial specialization of the Kauffman polynomial, but does not distinguish trivial links from the others, and hence cannot disprove the NM conjecture. For dimension 4, we give a family of NM-spin models. The corresponding link invariant is identified and does not distinguish trivial links from the others. Strong regularity and triple regularity of the Bose–Mesner algebra and its fusions are studied

An innovative plasmacytoid dendritic cell line-based cancer vaccine primes and expands antitumor T-cells in melanoma patients in a first-in-human trial.

The efficacy of immune checkpoint inhibitors has been shown to depend on preexisting antitumor immunity; thus, their combination with cancer vaccines is an attractive therapeutic approach. Plasmacytoid dendritic cells (PDC) are strong inducers of antitumor responses and represent promising vaccine candidates. We developed a cancer vaccine approach based on an allogeneic PDC line that functioned as a very potent antigen-presenting cell in pre-clinical studies. In this phase Ib clinical trial, nine patients with metastatic stage IV melanoma received up to 60 million irradiated PDC line cells loaded with 4 melanoma antigens, injected subcutaneously at weekly intervals. The primary endpoints were safety and tolerability. The vaccine was well tolerated and no serious vaccine-induced side effects were recorded. Strikingly, there was no allogeneic response toward the vaccine, but a significant increase in the frequency of circulating anti-tumor specific T lymphocytes was observed in two patients, accompanied by a switch from a naïve to memory phenotype, thus demonstrating priming of antigen-specific T-cells. Signs of clinical activity were observed, including four stable diseases according to IrRC and vitiligoïd lesions. Four patients were still alive at week 48. We also demonstrate the in vitro enhancement of specific T cell expansion induced by the synergistic combination of peptide-loaded PDC line with anti-PD-1, as compared to peptide-loaded PDC line alone. Taken together, these clinical observations demonstrate the ability of the PDC line based-vaccine to prime and expand antitumor CD8+ responses in cancer patients. Further trials should test the combination of this vaccine with immune checkpoint inhibitors