SLE local martingales in logarithmic representations

A space of local martingales of SLE type growth processes forms a representation of Virasoro algebra, but apart from a few simplest cases not much is known about this representation. The purpose of this article is to exhibit examples of representations where L_0 is not diagonalizable - a phenomenon characteristic of logarithmic conformal field theory. Furthermore, we observe that the local martingales bear a close relation with the fusion product of the boundary changing fields. Our examples reproduce first of all many familiar logarithmic representations at certain rational values of the central charge. In particular we discuss the case of SLE(kappa=6) describing the exploration path in critical percolation, and its relation with the question of operator content of the appropriate conformal field theory of zero central charge. In this case one encounters logarithms in a probabilistically transparent way, through conditioning on a crossing event. But we also observe that some quite natural SLE variants exhibit logarithmic behavior at all values of kappa, thus at all central charges and not only at specific rational values.Comment: 40 pages, 7 figures. v3: completely rewritten, new title, new result

Calogero-Sutherland eigenfunctions with mixed boundary conditions and conformal field theory correlators

We construct certain eigenfunctions of the Calogero-Sutherland hamiltonian for particles on a circle, with mixed boundary conditions. That is, the behavior of the eigenfunction, as neighbouring particles collide, depend on the pair of colliding particles. This behavior is generically a linear combination of two types of power laws, depending on the statistics of the particles involved. For fixed ratio of each type at each pair of neighboring particles, there is an eigenfunction, the ground state, with lowest energy, and there is a discrete set of eigenstates and eigenvalues, the excited states and the energies above this ground state. We find the ground state and special excited states along with their energies in a certain class of mixed boundary conditions, interpreted as having pairs of neighboring bosons and other particles being fermions. These particular eigenfunctions are characterised by the fact that they are in direct correspondence with correlation functions in boundary conformal field theory. We expect that they have applications to measures on certain configurations of curves in the statistical O(n) loop model. The derivation, although completely independent from results of conformal field theory, uses ideas from the "Coulomb gas" formulation.Comment: 35 pages, 9 figure

LERW as an example of off-critical SLEs

Two dimensional loop erased random walk (LERW) is a random curve, whose continuum limit is known to be a Schramm-Loewner evolution (SLE) with parameter kappa=2. In this article we study ``off-critical loop erased random walks'', loop erasures of random walks penalized by their number of steps. On one hand we are able to identify counterparts for some LERW observables in terms of symplectic fermions (c=-2), thus making further steps towards a field theoretic description of LERWs. On the other hand, we show that it is possible to understand the Loewner driving function of the continuum limit of off-critical LERWs, thus providing an example of application of SLE-like techniques to models near their critical point. Such a description is bound to be quite complicated because outside the critical point one has a finite correlation length and therefore no conformal invariance. However, the example here shows the question need not be intractable. We will present the results with emphasis on general features that can be expected to be true in other off-critical models.Comment: 45 pages, 2 figure

Stationarity of SLE

A new method to study a stopped hull of SLE(kappa,rho) is presented. In this approach, the law of the conformal map associated to the hull is invariant under a SLE induced flow. The full trace of a chordal SLE(kappa) can be studied using this approach. Some example calculations are presented.Comment: 14 pages with 1 figur

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

Establishment of a spontaneously transformed cell line (JU-PI) from a myxoinflammatory fibroblastic sarcoma

cited By 0Myxoinflammatory fibroblastic sarcoma is a soft-tissue neoplasm most frequently found in the distal extremities of middle-aged adults. Most myxoinflammatory fibroblastic sarcoma are low-grade tumors with propensity for local recurrence after incomplete removal. We report a myxoinflammatory fibroblastic sarcoma which developed in the foot of a 41-year-old male and showed an exceptionally aggressive course with metastatic spread and fatal outcome within 16 months. We managed to establish a spontaneously transformed continuous cell line, called JU-PI, from a metastatic lesion. The JU-PI cells have a sub-tetraploid karyotype including the 1;10 chromosomal translocation and amplification of the proximal end of 3p; these features are considered genetic signatures of myxoinflammatory fibroblastic sarcoma. Both the primary tumor and the JU-PI cells showed nuclear expression of the TFE3 transcription factor but TFE3-activating chromosomal rearrangements were not found. To our knowledge, JU-PI is the first established myxoinflammatory fibroblastic sarcoma cell line. JU-PI cells offer a tool for investigating the molecular oncology of myxoinflammatory fibroblastic sarcoma. © 2018, © The Author(s) 2018.Peer reviewe

Comparative genomic hybridization reveals population-based genetic alterations in hepatoblastomas

Hepatoblastoma is a malignant paediatric liver tumour. In order to approach the genetic background of this malignancy we have screened a panel of eighteen cases from Europe and Japan for chromosomal imbalances using comparative genomic hybridization (CGH). The most frequent losses included chromosomal regions 13q21–q22 (28%) and 9p22-pter (22%), while the most frequent gains occurred on 2q23–q24 (33%), 20q (28%) and 1q24–q25 (28%). A significant difference in CGH alterations between the tumours from patients of Caucasian and Japanese was revealed where loss of 13q was found only in the Japanese samples. In conclusion, the findings indicate several candidate regions for suppressor genes and oncogenes potentially involved in the hepatoblastomas of different ethnic origin. © 2000 Cancer Research Campaig

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

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

Toward industry 4.0: Efficient and sustainable manufacturing leveraging MAESTRI total efficiency framework

© Springer International Publishing AG 2017.This paper presents an overview of the work under development within MAESTRI EU-funded collaborative project. The MAESTRI Total Efficiency Framework (MTEF) aims to advance the sustainability of manufacturing and process industries by providing a management system in the form of a flexible and scalable platform and methodology. The MTEF is based on four pillars: (a) an effective management system targeted at process continuous improvement; (b) Efficiency assessment tools to support improvements, optimisation strategies and decision support; (c) Industrial Symbiosis paradigm to gain value from waste and energy exchange; (d) an Internet-of-Things infrastructure to support easy integration and data exchange among shop-floor, business systems and tools