Regular autodense languages

A regular component is either autodense or anti-autodense. Characterizations of a regular component being a pure autodense language and being a pure autodense code are obtained. A relationship between intercodes and anti-autodense languages is that for an intercode L of index m, L n is an anti-autodense language for every n > m

The Q-operator for Root-of-Unity Symmetry in Six Vertex Model

We construct the explicit $Q$-operator incorporated with the $sl_2$-loop-algebra symmetry of the six-vertex model at roots of unity. The functional relations involving the $Q$-operator, the six-vertex transfer matrix and fusion matrices are derived from the Bethe equation, parallel to the Onsager-algebra-symmetry discussion in the superintegrable $N$-state chiral Potts model. We show that the whole set of functional equations is valid for the $Q$-operator. Direct calculations in certain cases are also given here for clearer illustration about the nature of the $Q$-operator in the symmetry study of root-of-unity six-vertex model from the functional-relation aspect.Comment: Latex 26 Pages; Typos and small errors corrected, Some explanations added for clearer presentation, References updated-Journal version with modified labelling of sections and formula

The structure of quotients of the Onsager algebra by closed ideals

We study the Onsager algebra from the ideal theoretic point of view. A complete classification of closed ideals and the structure of quotient algebras are obtained. We also discuss the solvable algebra aspect of the Onsager algebra through the use of formal Lie algebras.Comment: 33 pages, Latex, small topos corrected-Journal versio

53BP1 expression is a modifier of the prognostic value of lymph node ratio and CA 19–9 in pancreatic adenocarcinoma

BACKGROUND: 53BP1 binds to the tumor suppressor p53 and has a key role in DNA damage response and repair. Low 53BP1 expression has been associated with decreased survival in breast cancer and has been shown to interact with several prognostic factors in non-small cell lung cancer. The role of 53BP1 in pancreatic ductal adenocarcinoma (PDAC) has yet to be determined. We aimed to investigate whether 53BP1 levels interact with established prognostic factors in PDAC. METHODS: 106 patients for whom there was tissue available at time of surgical resection for PDAC were included. A tissue microarray was constructed using surgical specimens, stained with antibodies to 53BP1, and scored for expression intensity. Univariate and multivariate statistical analyses were performed to investigate the association between 53BP1 and patient survival with known prognostic factors for survival. RESULTS: The association of 53BP1 with several established prognostic factors was examined, including stage, tumor grade, surgical margin, peripancreatic extension, lymph node ratio (LNR), and CA 19–9. We found that 53BP1 modified the effects of known prognostic variables including LNR and CA 19–9 on survival outcomes. When 53BP1 intensity was low, increased LNR was associated with decreased OS (HR 4.84, 95% CI (2.26, 10.37), p<0.001) and high CA19-9 was associated with decreased OS (HR 1.72, 95% CI (1.18, 2.51), p=0.005). When 53BP1 intensity was high, LNR and CA19-9 were no longer associated with OS (p=0.958 and p=0.606, respectively). CONCLUSIONS: In this study, 53BP1, a key player in DNA damage response and repair, was found to modify the prognostic value of two established prognostic factors, LNR and CA 19–9, suggesting 53BP1 may alter tumor behavior and ultimately impact how we interpret the value of other prognostic factors

Tourism, transport, and land use: a dynamic impact assessment for Kaohsiung’s Asia New Bay Area

This paper proposes a hybrid methodology for analysing the causal relations between public transportation development, tourism and land use by combining System Dynamics (SD) with Geographical Information Systems (GIS) and agent-based modelling (ABM). It is applied to illustrate the quantitative and spatial effect of the two phases Light Rail Transit (LRT) development in Asia New Bay Area, Kaohsiung, Taiwan. This paper also furthers the application of the ABM spatial information as interactive variables in the stocks-flow model. The simulation results support that development policies of LRT are significant to the future tourism in Asia New Bay Area, while the under debate second phase of LRT is estimated to raise the number of visitors in long term by alleviating the deteriorating road traffic congestion. This policy-oriented simulation can serve as a reference to the decision-makers towards the future management of LRT

On τ(2)\tau^{(2)}-model in Chiral Potts Model and Cyclic Representation of Quantum Group Uq(sl2)U_q(sl_2)

We identify the precise relationship between the five-parameter $\tau^{(2)}$-family in the $N$-state chiral Potts model and XXZ chains with $U_q (sl_2)$-cyclic representation. By studying the Yang-Baxter relation of the six-vertex model, we discover an one-parameter family of $L$-operators in terms of the quantum group $U_q (sl_2)$. When $N$ is odd, the $N$-state $\tau^{(2)}$-model can be regarded as the XXZ chain of $U_{\sf q} (sl_2)$ cyclic representations with ${\sf q}^N=1$. The symmetry algebra of the $\tau^{(2)}$-model is described by the quantum affine algebra $U_{\sf q} (\hat{sl}_2)$ via the canonical representation. In general for an arbitrary $N$, we show that the XXZ chain with a $U_q (sl_2)$-cyclic representation for $q^{2N}=1$ is equivalent to two copies of the same $N$-state $\tau^{(2)}$-model.Comment: Latex 11 pages; Typos corrected, Minor changes for clearer presentation, References added and updated-Journal versio

JASPAR 2016: a major expansion and update of the open-access database of transcription factor binding profiles.

JASPAR (http://jaspar.genereg.net) is an open-access database storing curated, non-redundant transcription factor (TF) binding profiles representing transcription factor binding preferences as position frequency matrices for multiple species in six taxonomic groups. For this 2016 release, we expanded the JASPAR CORE collection with 494 new TF binding profiles (315 in vertebrates, 11 in nematodes, 3 in insects, 1 in fungi and 164 in plants) and updated 59 profiles (58 in vertebrates and 1 in fungi). The introduced profiles represent an 83% expansion and 10% update when compared to the previous release. We updated the structural annotation of the TF DNA binding domains (DBDs) following a published hierarchical structural classification. In addition, we introduced 130 transcription factor flexible models trained on ChIP-seq data for vertebrates, which capture dinucleotide dependencies within TF binding sites. This new JASPAR release is accompanied by a new web tool to infer JASPAR TF binding profiles recognized by a given TF protein sequence. Moreover, we provide the users with a Ruby module complementing the JASPAR API to ease programmatic access and use of the JASPAR collection of profiles. Finally, we provide the JASPAR2016 R/Bioconductor data package with the data of this release

Fusion Operators in the Generalized τ(2)\tau^{(2)}-model and Root-of-unity Symmetry of the XXZ Spin Chain of Higher Spin

We construct the fusion operators in the generalized $\tau^{(2)}$-model using the fused $L$-operators, and verify the fusion relations with the truncation identity. The algebraic Bethe ansatz discussion is conducted on two special classes of $\tau^{(2)}$ which include the superintegrable chiral Potts model. We then perform the parallel discussion on the XXZ spin chain at roots of unity, and demonstrate that the $sl_2$-loop-algebra symmetry exists for the root-of-unity XXZ spin chain with a higher spin, where the evaluation parameters for the symmetry algebra are identified by the explicit Fabricius-McCoy current for the Bethe states. Parallels are also drawn to the comparison with the superintegrable chiral Potts model.Comment: Latex 33 Pages; Typos and errors corrected, New improved version by adding explanations for better presentation. Terminology in the content and the title refined. References added and updated-Journal versio