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Neumann-Lara and Škrekovski conjectured that every planar digraph is 2-colourable. We show that this conjecture is equivalent to the more general statement that all oriented K_5-minor-free graphs are 2-colourable.

We give sharp point-wise bounds in the weight-aspect on fourth moments of modular forms on arithmetic hyperbolic surfaces associated to Eichler orders. Thereby, we strengthen a result of Xia and extend it to co-compact lattices. We realize this fourth moment by constructing a holomorphic theta kernel on $\\mathbf {G} \\times \\mathbf {G} \\times \\mathbf {SL}_{2}$, for $\\mathbf {G}$ an indefinite inner form of $\\mathbf {SL}_2$ over $\\mathbb {Q}$, based on the Bergman kernel, and considering its $L^2$-norm in the Weil variable. The constructed theta kernel further gives rise to new elementary theta series for integral quadratic forms of signature $(2,2)$.

Increasing evidence suggests that the gut microbiome may modulate the efficacy of cancer immunotherapy. In a B cell lymphoma patient cohort from five centers in Germany and the United States (Germany, n  = 66; United States, n  = 106; total, n  = 172), we demonstrate that wide-spectrum antibiotics treatment (‘high-risk antibiotics’) prior to CD19-targeted chimeric antigen receptor (CAR)-T cell therapy is associated with adverse outcomes, but this effect is likely to be confounded by an increased pretreatment tumor burden and systemic inflammation in patients pretreated with high-risk antibiotics. To resolve this confounding effect and gain insights into antibiotics-masked microbiome signals impacting CAR-T efficacy, we focused on the high-risk antibiotics non-exposed patient population. Indeed, in these patients, significant correlations were noted between pre-CAR-T infusion Bifidobacterium longum and microbiome-encoded peptidoglycan biosynthesis, and CAR-T treatment-associated 6-month survival or lymphoma progression. Furthermore, predictive pre-CAR-T treatment microbiome-based machine learning algorithms trained on the high-risk antibiotics non-exposed German cohort and validated by the respective US cohort robustly segregated long-term responders from non-responders. Bacteroides , Ruminococcus , Eubacterium and Akkermansia were most important in determining CAR-T responsiveness, with Akkermansia also being associated with pre-infusion peripheral T cell levels in these patients. Collectively, we identify conserved microbiome features across clinical and geographical variations, which may enable cross-cohort microbiome-based predictions of outcomes in CAR-T cell immunotherapy. Conserved microbiome features across clinical and geographical variations may enable microbiome-based predictions of outcomes in CD19-targeted CAR-T cell immunotherapy

We establish several new results on the existence of probability distributions on the independent sets in triangle-free graphs where each vertex is present with a given probability. This setting was introduced and studied under the name of “fractional coloring with local demands” by Kelly and Postle and is closely related to the well-studied fractional chromatic number of graphs. Our first main result strengthens Shearer’s classic bound on independence number, proving that for every triangle-free graph G there exists a distribution over independent sets where each vertex v appears with probability $(1-o(1))\\frac {\\ln d_G(v)}{d_G(v)}$ , resolving a conjecture by Kelly and Postle. This in turn implies new upper bounds on the fractional chromatic number of triangle-free graphs with a prescribed number of vertices or edges, which resolves a conjecture by Cames van Batenburg et al. and addresses yet another one by the same authors. Our second main result resolves Harris’ conjecture on triangle-free d-degenerate graphs, showing that such graphs have fractional chromatic number at most $(4+o(1))\\frac {d}{\\ln d}$ . As previously observed by various authors, this in turn has several interesting consequences. A notable example is that every triangle-free graph with minimum degree d contains a bipartite induced subgraph of minimum degree $\\Omega (\\log d)$ . This settles a conjecture by Esperet, Kang, and Thomassé. The main technique employed to obtain our results is the analysis of carefully designed random processes on vertex-weighted triangle-free graphs that preserve weights in expectation. The analysis of these processes yields weighted generalizations of the aforementioned results that may be of independent interest.

Let f be an $L^2$ -normalized holomorphic newform of weight k on $\\Gamma _0(N) \\backslash \\mathbb {H}$ with N squarefree or, more generally, on any hyperbolic surface $\\Gamma \\backslash \\mathbb {H}$ attached to an Eichler order of squarefree level in an indefinite quaternion algebra over $\\mathbb {Q}$ . Denote by V the hyperbolic volume of said surface. We prove the sup-norm estimate $$\\begin{align*}\\| \\Im(\\cdot)^{\\frac{k}{2}} f \\|_{\\infty} \\ll_{\\varepsilon} (k V)^{\\frac{1}{4}+\\varepsilon} \\end{align*}$$ with absolute implied constant. For a cuspidal Maaß newform $\\varphi $ of eigenvalue $\\lambda $ on such a surface, we prove that $$\\begin{align*}\\|\\varphi \\|_{\\infty} \\ll_{\\lambda,\\varepsilon} V^{\\frac{1}{4}+\\varepsilon}. \\end{align*}$$ We establish analogous estimates in the setting of definite quaternion algebras.

Carfilzomib is a proteasome inhibitor that binds selectively and irreversibly to the 20S proteasome, the proteolytic core particle within the 26S proteasome, resulting in the accumulation of proteasome substrates and ultimately growth arrest and apoptosis of tumor cells. The development and ultimate approval of this medication by regulatory agencies has been an important step toward improving clinical outcomes in multiple myeloma. Although initially approved as a single agent for the treatment of multiply relapsed and/or refractory myeloma, in the USA, it is now widely used in the early relapse setting in combination with lenalidomide and dexamethasone. Carfilzomib has also been studied in combination with second-generation immunomodulatory drugs, histone deacetylase inhibitors, alkylating agents and other novel medications. In this review article, we will discuss the efficacy, safety, tolerability and quality of life of carfilzomib-based combination therapies, as well as novel agents, for relapsed multiple myeloma.

The mechanisms driving therapeutic resistance and poor outcomes of mantle cell lymphoma (MCL) are incompletely understood. We characterize the cellular and molecular heterogeneity within and across patients and delineate the dynamic evolution of tumor and immune cell compartments at single cell resolution in longitudinal specimens from ibrutinib-sensitive patients and non-responders. Temporal activation of multiple cancer hallmark pathways and acquisition of 17q are observed in a refractory MCL. Multi-platform validation is performed at genomic and cellular levels in PDX models and larger patient cohorts. We demonstrate that due to 17q gain, BIRC5/survivin expression is upregulated in resistant MCL tumor cells and targeting BIRC5 results in marked tumor inhibition in preclinical models. In addition, we discover notable differences in the tumor microenvironment including progressive dampening of CD8+ T cells and aberrant cell-to-cell communication networks in refractory MCLs. This study reveals diverse and dynamic tumor and immune programs underlying therapy resistance in MCL. Mantle cell lymphoma can be refractory to treatment. Here, the authors used single cell sequencing to study the tumours of patients that were responsive and resistant to treatment and find gains of 17q in resistant tumours, which they attribute to increased expression of Birc5 and validate these findings in mouse models of the disease.

Conditioning chemotherapy (CCT) has been shown to be essential for optimal efficacy of chimeric antigen receptor (CAR) T-cell therapy. Here, we determined whether the change in absolute lymphocyte count, referred to as delta lymphocyte index (DLIx), may serve as a surrogate marker for pharmacodynamic effects of CCT and whether it associated with germline genetic variants in patients with large B-cell lymphoma (LBCL). One-hundred and seventy-one patients were included, of which 86 (50%) received bridging therapy post-leukapheresis. Median DLIx was 0.5 × 109/L (range, 0.01–2.75 × 109/L) and was significantly higher in patients who achieved complete response (p = 0.04). On multivariate analysis, low DLIx was associated only with use of bridging therapy (odds ratio 0.4, 95% CI 0.2–0.8, p = 0.007). Low DLIx was independently associated with shorter progression-free (p = 0.02) and overall survival (p = 0.02). DLIx was associated with genetic variations related to drug metabolism and macrophage biology such as ABCB1, MISP and CPVL. The impact of CCT on lymphocyte count is affected by use of bridging therapy but change in lymphocyte count is independently associated with efficacy. Studies aimed at investigating macrophage biology in this setting may suggest strategies to increase the efficacy of CCT and improve outcomes.

Hadwiger’s conjecture asserts that every graph without a \\(K_t\\)-minor is \\((t-1)\\)-colourable. It is known that the exact version of Hadwiger’s conjecture does not extend to list colouring, but it has been conjectured by Kawarabayashi and Mohar (2007) that there exists a constant \\(c\\) such that every graph with no \\(K_t\\)-minor has list chromatic number at most \\(ct\\). More specifically, they also conjectured that this holds for \\(c=\\frac{3}{2}\\).Refuting the latter conjecture, we show that the maximum list chromatic number of graphs with no \\(K_t\\)-minor is at least \\((2-o(1))t\\), and hence \\(c \\ge 2\\) in the above conjecture is necessary. This improves the previous best lower bound by Barát, Joret and Wood (2011), who proved that \\(c \\ge \\frac{4}{3}\\). Our lower-bound examples are obtained via the probabilistic method.

Nodular lymphocyte-predominant Hodgkin lymphoma (NLPHL) is a rare cancer, and few studies have comprehensively investigated the immune microenvironment and rare lymphocyte-predominant (LP) cells. Here we develop a NLPHL specific lymphocyte-predominant ecotype (LPE) model to identify 34 distinct cell states across 14 cell types that co-occur within 3 LPEs for 171 cases. LPE1 and LPE2 were characterized by immunosuppressive microenvironments with high expression of B2M on LP cells, CD8 T-cell exhaustion, immune checkpoint genes expressed by follicular T-cells, and an improved freedom from progression compared to LPE3 in training ( n  = 109, with 65% LPE1/2) and validation cohorts ( n  = 62, with 61% LPE1/2). We validate the co-occurrence and co-localization of cell states using spatial transcriptomics. Protein expression of HLA-I and HLA-II on LP cells and SSTR2 on dendritic cells was predictive of LPE1 (C-statistic=0.69), LPE2 (C-statistic=0.79), and LPE3 (C-statistic=0.60). This study establishes a clinically relevant biologic categorization for NLPHL. Nodular lymphocyte-predominant Hodgkin lymphoma (NLPHL) is a rare cancer. Here, the authors develop a NLPHL specific model to identify 34 distinct cell states across 14 cell types that co-occur within 3 lymphocyte predominant ecotypes (LPEs) for 171 cases.