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There have been exponential gains in immuno-oncology in recent times through the development of immune checkpoint inhibitors. Already approved by the U.S. Food and Drug Administration for advanced melanoma and non-small cell lung cancer, immune checkpoint inhibitors also appears to have significant antitumor activity in multiple other tumor types. An exciting component of immunotherapy is the durability of antitumor responses observed, with some patients achieving disease control for many years. Nevertheless, not all patients benefit, and efforts should thus now focus on improving the efficacy of immunotherapy through the use of combination approaches and predictive biomarkers of response and resistance. There are multiple potential rational combinations using an immunotherapy backbone, including existing treatments such as radiotherapy, chemotherapy or molecularly targeted agents, as well as other immunotherapeutics. The aim of such antitumor strategies will be to raise the tail on the survival curve by increasing the number of long term survivors, while managing any additive or synergistic toxicities that may arise with immunotherapy combinations. Rational trial designs based on a clear understanding of tumor biology and drug pharmacology remain paramount. This article reviews the biology underpinning immuno-oncology, discusses existing and novel immunotherapeutic combinations currently in development, the challenges of predictive biomarkers of response and resistance and the impact of immuno-oncology on early phase clinical trial design.

CH5126766 (also known as VS-6766, and previously named RO5126766), a novel MEK-pan-RAF inhibitor, has shown antitumour activity across various solid tumours; however, its initial development was limited by toxicity. We aimed to investigate the safety and toxicity profile of intermittent dosing schedules of CH5126766, and the antitumour activity of this drug in patients with solid tumours and multiple myeloma harbouring RAS–RAF–MEK pathway mutations. We did a single-centre, open-label, phase 1 dose-escalation and basket dose-expansion study at the Royal Marsden National Health Service Foundation Trust (London, UK). Patients were eligible for the study if they were aged 18 years or older, had cancers that were refractory to conventional treatment or for which no conventional therapy existed, and if they had a WHO performance status score of 0 or 1. For the dose-escalation phase, eligible patients had histologically or cytologically confirmed advanced or metastatic solid tumours. For the basket dose-expansion phase, eligible patients had advanced or metastatic solid tumours or multiple myeloma harbouring RAS–RAF–MEK pathway mutations. During the dose-escalation phase, we evaluated three intermittent oral schedules (28-day cycles) in patients with solid tumours: (1) 4·0 mg or 3·2 mg CH5126766 three times per week; (2) 4·0 mg CH5126766 twice per week; and (3) toxicity-guided dose interruption schedule, in which treatment at the recommended phase 2 dose (4·0 mg CH5126766 twice per week) was de-escalated to 3 weeks on followed by 1 week off if patients had prespecified toxic effects (grade 2 or worse diarrhoea, rash, or creatine phosphokinase elevation). In the basket dose-expansion phase, we evaluated antitumour activity at the recommended phase 2 dose, determined from the dose-escalation phase, in biomarker-selected patients. The primary endpoints were the recommended phase 2 dose at which no more than one out of six patients had a treatment-related dose-limiting toxicity, and the safety and toxicity profile of each dosing schedule. The key secondary endpoint was investigator-assessed response rate in the dose-expansion phase. Patients who received at least one dose of the study drug were evaluable for safety and patients who received one cycle of the study drug and underwent baseline disease assessment were evaluable for response. This trial is registered with ClinicalTrials.gov, NCT02407509. Between June 5, 2013, and Jan 10, 2019, 58 eligible patients were enrolled to the study: 29 patients with solid tumours were included in the dose-escalation cohort and 29 patients with solid tumours or multiple myeloma were included in the basket dose-expansion cohort (12 non-small-cell lung cancer, five gynaecological malignancy, four colorectal cancer, one melanoma, and seven multiple myeloma). Median follow-up at the time of data cutoff was 2·3 months (IQR 1·6–3·5). Dose-limiting toxicities included grade 3 bilateral retinal pigment epithelial detachment in one patient who received 4·0 mg CH5126766 three times per week, and grade 3 rash (in two patients) and grade 3 creatine phosphokinase elevation (in one patient) in those who received 3·2 mg CH5126766 three times per week. 4·0 mg CH5126766 twice per week (on Monday and Thursday or Tuesday and Friday) was established as the recommended phase 2 dose. The most common grade 3–4 treatment-related adverse events were rash (11 [19%] patients), creatine phosphokinase elevation (six [11%]), hypoalbuminaemia (six [11%]), and fatigue (four [7%]). Five (9%) patients had serious treatment-related adverse events. There were no treatment-related deaths. Eight (14%) of 57 patients died during the trial due to disease progression. Seven (27% [95% CI 11·6–47·8]) of 26 response-evaluable patients in the basket expansion achieved objective responses. To our knowledge, this is the first study to show that highly intermittent schedules of a RAF–MEK inhibitor has antitumour activity across various cancers with RAF–RAS–MEK pathway mutations, and that this inhibitor is tolerable. CH5126766 used as a monotherapy and in combination regimens warrants further evaluation. Chugai Pharmaceutical.

Penguins huddling in a cold wind are represented by a two-dimensional, continuum model. The huddle boundary evolves due to heat loss to the huddle exterior and through the reorganisation of penguins as they seek to regulate their heat production within the huddle. These two heat transfer mechanisms, along with area, or penguin number, conservation, gives a free boundary problem whose dynamics depend on both the dynamics interior and exterior to the huddle. Assuming the huddle shape evolves slowly compared to the advective timescale of the exterior wind, the interior temperature is governed by a Poisson equation and the exterior temperature by the steady advection-diffusion equation. The exterior, advective wind velocity is the gradient of a harmonic, scalar field. The conformal invariance of the exterior governing equations is used to convert the system to a Polubarinova-Galin type equation, with forcing depending on both the interior and exterior temperature gradients at the huddle boundary. The interior Poisson equation is not conformally invariant, so the interior temperature gradient is found numerically using a combined adaptive Antoulas-Anderson and least squares algorithm. The results show that, irrespective of the starting shape, penguin huddles evolve into an egg-like steady shape. This shape is dependent on the wind strength, parameterised by the Péclet number Pe, and a parameter β which effectively measures the strength of the interior self-generation of heat by the penguins. The numerical method developed is applicable to a further five free boundary problems.

PurposeConcomitant treatment with radium-223 and paclitaxel is a potential option for cancer patients with bone metastases; however, myelosuppression risk during coadministration is unknown. This phase Ib study in cancer patients with bone metastases evaluated the safety of radium-223 and paclitaxel.MethodsEligible patients had solid tumor malignancies with ≥2 bone metastases and were candidates for paclitaxel. Treatment included seven paclitaxel cycles (90 mg/m2 per week intravenously per local standard of care; 3 weeks on/1 week off) plus six radium-223 cycles (55 kBq/kg intravenously; one injection every 4 weeks, starting at paclitaxel cycle 2). The primary end point was percentage of patients with grade 3/4 neutropenia or thrombocytopenia during coadministration of radium-223 and paclitaxel (cycles 2, 3) versus paclitaxel alone (cycle 1).ResultsOf 22 enrolled patients, 15 were treated (safety population), with 7 completing all six radium-223 cycles. Treated patients had primary cancers of breast (n = 7), prostate (n = 4), bladder (n = 1), non–small cell lung (n = 1), myxofibrosarcoma (n = 1), and neuroendocrine (n = 1). No patients discontinued treatment from toxicity of the combination. In the 13 patients who completed cycle 3, the rates of grade 3 neutropenia in cycles 2 and 3 were 31% and 8%, respectively, versus 23% in cycle 1; there were no cases of grade 4 neutropenia or grade 3/4 thrombocytopenia. Breast cancer subgroup safety results were similar to the overall safety population.ConclusionRadium-223 was tolerated when combined with weekly paclitaxel, with no clinically relevant additive toxicities. This combination should be explored further in patients with bone metastases.

The C ∗-algebra 𝓤 nc (n) is the universal C ∗-algebra generated by n² generators u ij that make up a unitary matrix. We prove that Kirchberg’s formulation of Connes’ embedding problemhas a positive answer if and only if 𝓤 nc (2)⊗min 𝓤 nc (2) = 𝓤 nc (2)⊗max 𝓤 nc (2). Our results follow from properties of the finite-dimensional operator system 𝓥 n spanned by 1 and the generators of 𝓤 nc (n). We show that 𝓥 n is an operator system quotient of M 2n and has the OSLLP. We obtain necessary and sufficient conditions on 𝓥 n for there to be a positive answer to Kirchberg’s problem. Finally, in analogy with recent results of Ozawa, we show that a form of Tsirelson’s problem related to 𝓥 n is equivalent to Connes’ embedding problem.

We show that quantum graph parameters for finite, simple, undirected graphs encode winning strategies for all possible synchronous non-local games. Given a synchronous game \\(\\mathcal{G}=(I,O,\\lambda)\\) with \\(|I|=n\\) and \\(|O|=k\\), we demonstrate what we call a weak \\(*\\)-equivalence between \\(\\mathcal{G}\\) and a \\(3\\)-coloring game on a graph with at most \\(3+n+9n(k-2)+6|\\lambda^{-1}(\\{0\\})|\\) vertices, strengthening and simplifying work implied by Z. Ji (arXiv:1310.3794) for winning quantum strategies for synchronous non-local games. As an application, we obtain a quantum version of L. Lov\\'{a}sz's reduction (Proc. 4th SE Conf. on Comb., Graph Theory & Computing, 1973) of the \\(k\\)-coloring problem for a graph \\(G\\) with \\(n\\) vertices and \\(m\\) edges to the \\(3\\)-coloring problem for a graph with \\(3+n+9n(k-2)+6mk\\) vertices. Moreover, winning strategies for a synchronous game \\(\\mathcal{G}\\) can be transformed into winning strategies for an associated graph coloring game, where the strategies exhibit perfect zero knowledge for an honest verifier. We also show that, for ``graph of the game\" \\(X(\\mathcal{G})\\) associated to \\(\\mathcal{G}\\) from A. Atserias et al (J. Comb. Theory Series B, Vol. 136, 2019), the independence number game \\(\\text{Hom}(K_{|I|},\\overline{X(\\mathcal{G})})\\) is hereditarily \\(*\\)-equivalent to \\(\\mathcal{G}\\), so that the possibility of winning strategies is the same in both games for all models, except the game algebra. Thus, the quantum versions of the chromatic number, independence number and clique number encode winning strategies for all synchronous games in all quantum models.

Motivated by non-local games and quantum coloring problems, we introduce a graph homomorphism game between quantum graphs and classical graphs. This game is naturally cast as a \"quantum-classical game\"--that is, a non-local game of two players involving quantum questions and classical answers. This game generalizes the graph homomorphism game between classical graphs. We show that winning strategies in the various quantum models for the game is an analogue of the notion of non-commutative graph homomorphisms due to D. Stahlke [44]. Moreover, we present a game algebra in this context that generalizes the game algebra for graph homomorphisms given by J.W. Helton, K. Meyer, V.I. Paulsen and M. Satriano [22]. We also demonstrate explicit quantum colorings of all quantum complete graphs, yielding the surprising fact that the algebra of the \\(4\\)-coloring game for a quantum graph is always non-trivial, extending a result of [22].

Penguins huddling in a cold wind are represented by a two-dimensional, continuum model. The huddle boundary evolves due to heat loss to the huddle exterior and through the reorganisation of penguins as they seek to regulate their heat production within the huddle. These two heat transfer mechanisms, along with area, or penguin number, conservation, gives a free boundary problem whose dynamics depend on both the dynamics interior and exterior to the huddle. Assuming the huddle shape evolves slowly compared to the advective timescale of the exterior wind, the interior temperature is governed by a Poisson equation and the exterior temperature by the steady advection-diffusion equation. The exterior, advective wind velocity is the gradient of a harmonic, scalar field. The conformal invariance of the exterior governing equations is used to convert the system to a Polubarinova-Galin type equation, with forcing depending on both the interior and exterior temperature gradients at the huddle boundary. The interior Poisson equation is not conformally invariant, so the interior temperature gradient is found numerically using a combined adaptive Antoulas-Anderson and least squares algorithm. The results show that, irrespective of the starting shape, penguin huddles evolve into an egg-like steady shape. This shape is dependent on the wind strength, parameterised by the Péclet number Pe, and a parameter \\b{eta} which effectively measures the strength of the interior self-generation of heat by the penguins. The numerical method developed is applicable to a further five free boundary problems.

We establish several strong equivalences of synchronous non-local games, in the sense that the corresponding game algebras are \\(*\\)-isomorphic. We first show that the game algebra of any synchronous game on \\(n\\) inputs and \\(k\\) outputs is \\(*\\)-isomorphic to the game algebra of an associated bisynchronous game on \\(nk\\) inputs and \\(nk\\) outputs. As a result, we show that there are bisynchronous games with equal question and answer sets, whose optimal strategies only exist in the quantum commuting model, and not in the quantum approximate model. Moreover, we exhibit a bisynchronous game with \\(20\\) questions and \\(20\\) answers that has a non-zero game algebra, but no winning commuting strategy, resolving a problem of V.I. Paulsen and M. Rahaman. We also exhibit a \\(*\\)-isomorphism between any synchronous game algebra with \\(n\\) questions and \\(k>3\\) answers and a synchronous game algebra with \\(n(k-2)\\) questions and \\(3\\) answers.

We consider quantum XOR games, defined in [11], from the perspective of unitary correlations defined in [7]. We show that Connes' embedding problem has a positive answer if and only if every quantum XOR game has entanglement bias equal to the commuting bias. In particular, the embedding problem is equivalent to determining whether every quantum XOR game \\(G\\) with a winning strategy in the commuting model also has a winning strategy in the approximate finite-dimensional model.