Twist operator correlation functions in O(n) loop models

Using conformal field theoretic methods we calculate correlation functions of geometric observables in the loop representation of the O(n) model at the critical point. We focus on correlation functions containing twist operators, combining these with anchored loops, boundaries with SLE processes and with double SLE processes. We focus further upon n=0, representing self-avoiding loops, which corresponds to a logarithmic conformal field theory (LCFT) with c=0. In this limit the twist operator plays the role of a zero weight indicator operator, which we verify by comparison with known examples. Using the additional conditions imposed by the twist operator null-states, we derive a new explicit result for the probabilities that an SLE_{8/3} wind in various ways about two points in the upper half plane, e.g. that the SLE passes to the left of both points. The collection of c=0 logarithmic CFT operators that we use deriving the winding probabilities is novel, highlighting a potential incompatibility caused by the presence of two distinct logarithmic partners to the stress tensor within the theory. We provide evidence that both partners do appear in the theory, one in the bulk and one on the boundary and that the incompatibility is resolved by restrictive bulk-boundary fusion rules.Comment: 18 pages, 8 figure

Virasoro Module Structure of Local Martingales of SLE Variants

Martingales often play an important role in computations with Schramm-Loewner evolutions (SLEs). The purpose of this article is to provide a straightforward approach to the Virasoro module structure of the space of local martingales for variants of SLEs. In the case of ordinary chordal SLE, it has been shown in Bauer & Bernard: Phys.Lett.B 557 that polynomial local martingales form a Virasoro module. We will show for more general variants that the module of local martingales has a natural submodule M that has the same interpretation as the module of polynomial local martingales of chordal SLE, but it is in many cases easy to find more local martingales than that. We discuss the surprisingly rich structure of the Virasoro module M and construction of the ``SLE state'' or ``martingale generating function'' by Coulomb gas formalism. In addition, Coulomb gas or Feigin-Fuchs integrals will be shown to transparently produce candidates for multiple SLE pure geometries.Comment: 48 pages, 3 figures. v4: Completely reorganized, with new results, erroneous corollary 4 (in v3) correcte

Abelian Sandpile Model on the Honeycomb Lattice

We check the universality properties of the two-dimensional Abelian sandpile model by computing some of its properties on the honeycomb lattice. Exact expressions for unit height correlation functions in presence of boundaries and for different boundary conditions are derived. Also, we study the statistics of the boundaries of avalanche waves by using the theory of SLE and suggest that these curves are conformally invariant and described by SLE2.Comment: 24 pages, 5 figure

Machine Learning of Bone Marrow Histopathology Identifies Genetic and Clinical Determinants in Patients with MDS

Publisher Copyright: ©2021 American Association for Cancer Research.In myelodysplastic syndrome (MDS) and myeloproliferative neoplasm (MPN), bone marrow (BM) histopathology is assessed to identify dysplastic cellular morphology, cellularity, and blast excess. Yet, other morphologic findings may elude the human eye. We used convolutional neural networks to extract morphologic features from 236 MDS, 87 MDS/MPN, and 11 control BM biopsies. These features predicted genetic and cytogenetic aberrations, prognosis, age, and gender in multivariate regression models. Highest prediction accuracy was found for TET2 [area under the receiver operating curve (AUROC) = 0.94] and spliceosome mutations (0.89) and chromosome 7 monosomy (0.89). Mutation prediction probability correlated with variant allele frequency and number of affected genes per pathway, demonstrating the algorithms' ability to identify relevant morphologic patterns. By converting regression models to texture and cellular composition, we reproduced the classical del(5q) MDS morphology consisting of hypolobulated megakaryocytes. In summary, this study highlights the potential of linking deep BM histopathology with genetics and clinical variables. SIGNIFICANCE: Histopathology is elementary in the diagnostics of patients with MDS, but its high-dimensional data are underused. By elucidating the association of morphologic features with clinical variables and molecular genetics, this study highlights the vast potential of convolutional neural networks in understanding MDS pathology and how genetics is reflected in BM morphology.See related commentary by Elemento, p. 195.Peer reviewe

MGMT Promoter Methylation and Parathyroid Carcinoma

Peer reviewe

Gene fusions and oncogenic mutations in MLH1 deficient and BRAFV600E wild-type colorectal cancers

Gene fusions can act as oncogenic drivers and offer targets for cancer therapy. Since fusions are rare in colorectal cancer (CRC), their universal screening seems impractical. Our aim was to investigate gene fusions in 62 CRC cases with deficient MLH1 (dMLH1) and BRAFV600E wild-type (wt) status from a consecutive real-life series of 2079 CRCs. First, gene fusions were analysed using a novel FusionPlex Lung v2 RNA-based next-generation sequencing (NGS) panel, and these results were compared to a novel Idylla GeneFusion assay and pan-TRK immunohistochemistry (IHC). NGS detected seven (7/62, 11%) NTRK1 fusions (TPM3::NTRK1, PLEKHA6::NTRK1 and LMNA::NTRK1, each in two cases, and IRF2BP2::NTRK1 in one case). In addition, two ALK, four RET and seven BRAF fusions were identified. Idylla detected seven NTRK1 expression imbalances, in line with the NGS results (overall agreement 100%). Furthermore, Idylla detected the two NGS-identified ALK rearrangements as one specific ALK fusion and one ALK expression imbalance, whilst only two of the four RET fusions were discovered. However, Idylla detected several expression imbalances of ALK (n = 7) and RET (n = 1) that were found to be fusion negative with the NGS. Pan-TRK IHC showed clearly detectable, fusion partner-dependent staining patterns in the seven NTRK1 fusion cases. Overall agreement for pan-TRK antibody clone EPR17341 was 98% and for A7H6R 100% when compared to the NGS. Of the 62 CRCs, 43 were MLH1 promoter hypermethylated (MLH1ph) and 39 were RASwt. All fusion cases were both MLH1ph and RASwt. Our results show that kinase fusions (20/30, 67%) and most importantly targetable NTRK1 fusions (7/30, 23%) are frequent in CRCs with dMLH1/BRAFV600Ewt/MLH1ph/RASwt. NGS was the most comprehensive method in finding the fusions, of which a subset can be screened by Idylla or IHC, provided that the result is confirmed by NGS

Associative algebraic approach to logarithmic CFT in the bulk: the continuum limit of the gl(1|1) periodic spin chain, Howe duality and the interchiral algebra

We develop in this paper the principles of an associative algebraic approach to bulk logarithmic conformal field theories (LCFTs). We concentrate on the closed $gl(1|1)$ spin-chain and its continuum limit - the $c=-2$ symplectic fermions theory - and rely on two technical companion papers, "Continuum limit and symmetries of the periodic gl(1|1) spin chain" [Nucl. Phys. B 871 (2013) 245-288] and "Bimodule structure in the periodic gl(1|1) spin chain" [Nucl. Phys. B 871 (2013) 289-329]. Our main result is that the algebra of local Hamiltonians, the Jones-Temperley-Lieb algebra JTL_N, goes over in the continuum limit to a bigger algebra than the product of the left and right Virasoro algebras. This algebra, S - which we call interchiral, mixes the left and right moving sectors, and is generated, in the symplectic fermions case, by the additional field $S(z,\bar{z})=S_{ab}\psi^a(z)\bar{\psi}^b(\bar{z})$, with a symmetric form $S_{ab}$ and conformal weights (1,1). We discuss in details how the Hilbert space of the LCFT decomposes onto representations of this algebra, and how this decomposition is related with properties of the finite spin-chain. We show that there is a complete correspondence between algebraic properties of finite periodic spin chains and the continuum limit. An important technical aspect of our analysis involves the fundamental new observation that the action of JTL_N in the $gl(1|1)$ spin chain is in fact isomorphic to an enveloping algebra of a certain Lie algebra, itself a non semi-simple version of $sp(N-2)$. The semi-simple part of JTL_N is represented by $Usp(N-2)$, providing a beautiful example of a classical Howe duality, for which we have a non semi-simple version in the full JTL image represented in the spin-chain. On the continuum side, simple modules over the interchiral algebra S are identified with "fundamental" representations of $sp(\infty)$.Comment: 69 pp., 10 figs, v2: the paper has been substantially modified - new proofs, new refs, new App C with inductive limits construction, et

Fusion rules and boundary conditions in the c=0 triplet model

The logarithmic triplet model W_2,3 at c=0 is studied. In particular, we determine the fusion rules of the irreducible representations from first principles, and show that there exists a finite set of representations, including all irreducible representations, that closes under fusion. With the help of these results we then investigate the possible boundary conditions of the W_2,3 theory. Unlike the familiar Cardy case where there is a consistent boundary condition for every representation of the chiral algebra, we find that for W_2,3 only a subset of representations gives rise to consistent boundary conditions. These then have boundary spectra with non-degenerate two-point correlators.Comment: 50 pages; v2: changed formulation in section 1.2.1 and corrected typos, version to appear in J. Phys.