Density matrix for the kink ground state of the ferromagnetic XXZ chain

The exact expression for the density matrix of the kink ground state of the ferromagnetic XXZ chain is obtained. Utilizing this, we exactly calculate various correlation functions such as the longitudinal and transverse spin-spin correlation functions, and the ferromagnetic and antiferromagnetic string formation probabilities. The asymptotic behaviors of these correlation functions are also analyzed. As a consequence, we find that the spin-spin correlation functions decay exponentially for large distances, while the string formation probabilities exhibit Gaussian decay for large strings. We also evaluate the entanglement entropy, which shows interesting behaviors due to the lack of the translational invariance of the state.Comment: 7 pages, 9 figure

Reflection equation for the N=3 Cremmer-Gervais R-matrix

We consider the reflection equation of the N=3 Cremmer-Gervais R-matrix. The reflection equation is shown to be equivalent to 38 equations which do not depend on the parameter of the R-matrix, q. Solving those 38 equations. the solution space is found to be the union of two types of spaces, each of which is parametrized by the algebraic variety $\mathbb{P}^1(\mathbb{C}) \times \mathbb{P}^1(\mathbb{C}) \times \mathbb{P}^2(\mathbb{C})$ and $\mathbb{C} \times \mathbb{P}^1(\mathbb{C}) \times \mathbb{P}^2(\mathbb{C})$.Comment: 28 pages, revised versio

TPXL-1 activates Aurora A to clear contractile ring components from the polar cortex during cytokinesis

During cytokinesis, a signal from the central spindle that forms between the separating anaphase chromosomes promotes the accumulation of contractile ring components at the cell equator, while a signal from the centrosomal microtubule asters inhibits accumulation of contractile ring components at the cell poles. However, the molecular identity of the inhibitory signal has remained unknown. To identify molecular components of the aster-based inhibitory signal, we developed a means to monitor the removal of contractile ring proteins from the polar cortex after anaphase onset. Using this assay, we show that polar clearing is an active process that requires activation of Aurora A kinase by TPXL-1. TPXL-1 concentrates on astral microtubules coincident with polar clearing in anaphase, and its ability to recruit Aurora A and activate its kinase activity are essential for clearing. In summary, our data identify Aurora A kinase as an aster-based inhibitory signal that restricts contractile ring components to the cell equator during cytokinesis.We thank the Caenorhabditis Genetic Center (funded by the National Institutes of Health Office of Research Infrastructure Programs P40 OD010440) for strains. This work was supported by grants to K. Oegema (National Institutes of Health; GM074207), E. Zanin (Deutsche Forschungsgemeinschaft, ZA619/3-1), and A.X. Carvalho (European Research Council; 640553–ACTOMYO). T. Kim was supported by a grant to Arshad Desai (National Institutes of Health; GM074215). K. Oegema receives salary and other support from the Ludwig Institute for Cancer Research. S. Mangal is a member of International Max Planck Research School for Molecular Life Sciences, and J. Sacher is a member of the Life Science Munich graduate program; both thank their programs for support

On the problem of calculation of correlation functions in the six-vertex model with domain wall boundary conditions

The problem of calculation of correlation functions in the six-vertex model with domain wall boundary conditions is addressed by considering a particular nonlocal correlation function, called row configuration probability. This correlation function can be used as building block for computing various (both local and nonlocal) correlation functions in the model. The row configuration probability is calculated using the quantum inverse scattering method; the final result is given in terms of a multiple integral. The connection with the emptiness formation probability, another nonlocal correlation function which was computed elsewhere using similar methods, is also discussed.Comment: 15 pages, 2 figure

Loss of DLX3 tumor suppressive function promotes progression of SCC through EGFR-ERBB2 pathway

Cutaneous squamous cell carcinoma (cSCC) ranks second in the frequency of all skin cancers. The balance between keratinocyte proliferation and differentiation is disrupted in the pathological development of cSCC. DLX3 is a homeobox transcription factor which plays pivotal roles in embryonic development and epidermal homeostasis. To investigate the impact of DLX3 expression on cSCC prognosis, we carried out clinicopathologic analysis of DLX3 expression which showed statistical correlation between tumors of higher pathologic grade and levels of DLX3 protein expression. Further, Kaplan-Meier survival curve analysis demonstrated that low DLX3 expression correlated with poor patient survival. To model the function of Dlx3 in skin tumorigenesis, a two-stage dimethylbenzanthracene (DMBA)/12-O-tetradecanoylphorbol 13-acetate (TPA) study was performed on mice genetically depleted of Dlx3 in skin epithelium (Dlx3cKO). Dlx3cKO mice developed significantly more tumors, with more rapid tumorigenesis compared to control mice. In Dlx3cKO mice treated only with DMBA, tumors developed after similar to 16 weeks suggesting that loss of Dlx3 has a tumor promoting effect. Whole transcriptome analysis of tumor and skin tissue from our mouse model revealed spontaneous activation of the EGFR-ERBB2 pathway in the absence of Dlx3. Together, our findings from human and mouse model system support a tumor suppressive function for DLX3 in skin and underscore the efficacy of therapeutic approaches that target EGFR-ERBB2 pathway

Multiply-refined enumeration of alternating sign matrices

Four natural boundary statistics and two natural bulk statistics are considered for alternating sign matrices (ASMs). Specifically, these statistics are the positions of the 1's in the first and last rows and columns of an ASM, and the numbers of generalized inversions and -1's in an ASM. Previously-known and related results for the exact enumeration of ASMs with prescribed values of some of these statistics are discussed in detail. A quadratic relation which recursively determines the generating function associated with all six statistics is then obtained. This relation also leads to various new identities satisfied by generating functions associated with fewer than six of the statistics. The derivation of the relation involves combining the Desnanot-Jacobi determinant identity with the Izergin-Korepin formula for the partition function of the six-vertex model with domain-wall boundary conditions.Comment: 62 pages; v3 slightly updated relative to published versio

Simultaneous disruption of two DNA polymerases, Polη and Polζ, in Avian DT40 cells unmasks the role of Polη in cellular response to various DNA lesions

Replicative DNA polymerases are frequently stalled by DNA lesions. The resulting replication blockage is released by homologous recombination (HR) and translesion DNA synthesis (TLS). TLS employs specialized TLS polymerases to bypass DNA lesions. We provide striking in vivo evidence of the cooperation between DNA polymerase η, which is mutated in the variant form of the cancer predisposition disorder xeroderma pigmentosum (XP-V), and DNA polymerase ζ by generating POLη−/−/POLζ−/− cells from the chicken DT40 cell line. POLζ−/− cells are hypersensitive to a very wide range of DNA damaging agents, whereas XP-V cells exhibit moderate sensitivity to ultraviolet light (UV) only in the presence of caffeine treatment and exhibit no significant sensitivity to any other damaging agents. It is therefore widely believed that Polη plays a very specific role in cellular tolerance to UV-induced DNA damage. The evidence we present challenges this assumption. The phenotypic analysis of POLη−/−/POLζ−/− cells shows that, unexpectedly, the loss of Polη significantly rescued all mutant phenotypes of POLζ−/− cells and results in the restoration of the DNA damage tolerance by a backup pathway including HR. Taken together, Polη contributes to a much wide range of TLS events than had been predicted by the phenotype of XP-V cells

An application of incomplete pairwise comparison matrices for ranking top tennis players

Pairwise comparison is an important tool in multi-attribute decision making. Pairwise comparison matrices (PCM) have been applied for ranking criteria and for scoring alternatives according to a given criterion. Our paper presents a special application of incomplete PCMs: ranking of professional tennis players based on their results against each other. The selected 25 players have been on the top of the ATP rankings for a shorter or longer period in the last 40 years. Some of them have never met on the court. One of the aims of the paper is to provide ranking of the selected players, however, the analysis of incomplete pairwise comparison matrices is also in the focus. The eigenvector method and the logarithmic least squares method were used to calculate weights from incomplete PCMs. In our results the top three players of four decades were Nadal, Federer and Sampras. Some questions have been raised on the properties of incomplete PCMs and remains open for further investigation.Comment: 14 pages, 2 figure

Importance of individual events in temporal networks

Records of time-stamped social interactions between pairs of individuals (e.g., face-to-face conversations, e-mail exchanges, and phone calls) constitute a so-called temporal network. A remarkable difference between temporal networks and conventional static networks is that time-stamped events rather than links are the unit elements generating the collective behavior of nodes. We propose an importance measure for single interaction events. By generalizing the concept of the advance of event proposed by [Kossinets G, Kleinberg J, and Watts D J (2008) Proceeding of the 14th ACM SIGKDD International conference on knowledge discovery and data mining, p 435], we propose that an event is central when it carries new information about others to the two nodes involved in the event. We find that the proposed measure properly quantifies the importance of events in connecting nodes along time-ordered paths. Because of strong heterogeneity in the importance of events present in real data, a small fraction of highly important events is necessary and sufficient to sustain the connectivity of temporal networks. Nevertheless, in contrast to the behavior of scale-free networks against link removal, this property mainly results from bursty activity patterns and not heterogeneous degree distributions.Comment: 36 pages, 13 figures, 2 table

REV1 restrains DNA polymerase ζ to ensure frame fidelity during translesion synthesis of UV photoproducts in vivo

Exposure to ultraviolet light induces a number of forms of damage in DNA, of which (6–4) photoproducts present the most formidable challenge to DNA replication. No single DNA polymerase has been shown to bypass these lesions efficiently in vitro suggesting that the coordinate use of a number of different enzymes is required in vivo. To further understand the mechanisms and control of lesion bypass in vivo, we have devised a plasmid-based system to study the replication of site-specific T–T(6–4) photoproducts in chicken DT40 cells. We show that DNA polymerase ζ is absolutely required for translesion synthesis (TLS) of this lesion, while loss of DNA polymerase η has no detectable effect. We also show that either the polymerase-binding domain of REV1 or ubiquitinated PCNA is required for the recruitment of Polζ as the catalytic TLS polymerase. Finally, we demonstrate a previously unappreciated role for REV1 in ensuring bypass synthesis remains in frame with the template. Our data therefore suggest that REV1 not only helps to coordinate the delivery of DNA polymerase ζ to a stalled primer terminus but also restrains its activity to ensure that nucleotides are incorporated in register with the template strand