Topological entropy of a stiff ring polymer and its connection to DNA knots

We discuss the entropy of a circular polymer under a topological constraint. We call it the {\it topological entropy} of the polymer, in short. A ring polymer does not change its topology (knot type) under any thermal fluctuations. Through numerical simulations using some knot invariants, we show that the topological entropy of a stiff ring polymer with a fixed knot is described by a scaling formula as a function of the thickness and length of the circular chain. The result is consistent with the viewpoint that for stiff polymers such as DNAs, the length and diameter of the chains should play a central role in their statistical and dynamical properties. Furthermore, we show that the new formula extends a known theoretical formula for DNA knots.Comment: 14pages,11figure

COnstructing Proxy Records from Age models (COPRA)

Reliable age models are fundamental for any palaeoclimate reconstruction. Available interpolation procedures between age control points are often inadequately reported, and very few translate age uncertainties to proxy uncertainties. Most available modeling algorithms do not allow incorporation of layer counted intervals to improve the confidence limits of the age model in question. We present a framework that allows detection and interactive handling of age reversals and hiatuses, depth-age modeling, and proxy-record reconstruction. Monte Carlo simulation and a translation procedure are used to assign a precise time scale to climate proxies and to translate dating uncertainties to uncertainties in the proxy values. The presented framework allows integration of incremental relative dating information to improve the final age model. The free software package COPRA1.0 facilitates easy interactive usage

The Hopf Algebra of Renormalization, Normal Coordinates and Kontsevich Deformation Quantization

Using normal coordinates in a Poincar\'e-Birkhoff-Witt basis for the Hopf algebra of renormalization in perturbative quantum field theory, we investigate the relation between the twisted antipode axiom in that formalism, the Birkhoff algebraic decomposition and the universal formula of Kontsevich for quantum deformation.Comment: 21 pages, 15 figure

Persistent northward North Atlantic tropical cyclone track migration over the past five centuries

Accurately predicting future tropical cyclone risk requires understanding the fundamental controls on tropical cyclone dynamics. Here we present an annually-resolved 450-year reconstruction of western Caribbean tropical cyclone activity developed using a new coupled carbon and oxygen isotope ratio technique in an exceptionally well-dated stalagmite from Belize. Western Caribbean tropical cyclone activity peaked at 1650 A.D., coincident with maximum Little Ice Age cooling, and decreased gradually until the end of the record in 1983. Considered with other reconstructions, the new record suggests that the mean track of Cape Verde tropical cyclones shifted gradually north-eastward from the western Caribbean toward the North American east coast over the last 450 years. Since ~1870 A.D., these shifts were largely driven by anthropogenic greenhouse gas and sulphate aerosol emissions. Our results strongly suggest that future emission scenarios will result in more frequent tropical cyclone impacts on the financial and population centres of the northeastern United States

The Pure Virtual Braid Group Is Quadratic

If an augmented algebra K over Q is filtered by powers of its augmentation ideal I, the associated graded algebra grK need not in general be quadratic: although it is generated in degree 1, its relations may not be generated by homogeneous relations of degree 2. In this paper we give a sufficient criterion (called the PVH Criterion) for grK to be quadratic. When K is the group algebra of a group G, quadraticity is known to be equivalent to the existence of a (not necessarily homomorphic) universal finite type invariant for G. Thus the PVH Criterion also implies the existence of such a universal finite type invariant for the group G. We apply the PVH Criterion to the group algebra of the pure virtual braid group (also known as the quasi-triangular group), and show that the corresponding associated graded algebra is quadratic, and hence that these groups have a (not necessarily homomorphic) universal finite type invariant.Comment: 53 pages, 15 figures. Some clarifications added and inaccuracies corrected, reflecting suggestions made by the referee of the published version of the pape

Gyration radius of a circular polymer under a topological constraint with excluded volume

It is nontrivial whether the average size of a ring polymer should become smaller or larger under a topological constraint. Making use of some knot invariants, we evaluate numerically the mean square radius of gyration for ring polymers having a fixed knot type, where the ring polymers are given by self-avoiding polygons consisting of freely-jointed hard cylinders. We obtain plots of the gyration radius versus the number of polygonal nodes for the trivial, trefoil and figure-eight knots. We discuss possible asymptotic behaviors of the gyration radius under the topological constraint. In the asymptotic limit, the size of a ring polymer with a given knot is larger than that of no topological constraint when the polymer is thin, and the effective expansion becomes weak when the polymer is thick enough.Comment: 12pages,3figure

Derivation of Myoepithelial Progenitor Cells from Bipotent Mammary Stem/Progenitor Cells

There is increasing evidence that breast and other cancers originate from and are maintained by a small fraction of stem/progenitor cells with self-renewal properties. Recent molecular profiling has identified six major subtypes of breast cancer: basal-like, ErbB2-overexpressing, normal breast epithelial-like, luminal A and B, and claudin-low subtypes. To help understand the relationship among mammary stem/progenitor cells and breast cancer subtypes, we have recently derived distinct hTERT-immortalized human mammary stem/progenitor cell lines: a K5+/K19− type, and a K5+/K19+ type. Under specific culture conditions, bipotent K5+/K19− stem/progenitor cells differentiated into stable clonal populations that were K5−/K19− and exhibit self-renewal and unipotent myoepithelial differentiation potential in contrast to the parental K5+/K19− cells which are bipotent. These K5−/K19− cells function as myoepithelial progenitor cells and constitutively express markers of an epithelial to mesenchymal transition (EMT) and show high invasive and migratory abilities. In addition, these cells express a microarray signature of claudin-low breast cancers. The EMT characteristics of an un-transformed unipotent mammary myoepithelial progenitor cells together with claudin-low signature suggests that the claudin-low breast cancer subtype may arise from myoepithelial lineage committed progenitors. Availability of immortal MPCs should allow a more definitive analysis of their potential to give rise to claudin-low breast cancer subtype and facilitate biological and molecular/biochemical studies of this disease

Breast-Lesion Characterization using Textural Features of Quantitative Ultrasound Parametric Maps

© 2017 The Author(s). This study evaluated, for the first time, the efficacy of quantitative ultrasound (QUS) spectral parametric maps in conjunction with texture-analysis techniques to differentiate non-invasively benign versus malignant breast lesions. Ultrasound B-mode images and radiofrequency data were acquired from 78 patients with suspicious breast lesions. QUS spectral-analysis techniques were performed on radiofrequency data to generate parametric maps of mid-band fit, spectral slope, spectral intercept, spacing among scatterers, average scatterer diameter, and average acoustic concentration. Texture-analysis techniques were applied to determine imaging biomarkers consisting of mean, contrast, correlation, energy and homogeneity features of parametric maps. These biomarkers were utilized to classify benign versus malignant lesions with leave-one-patient-out cross-validation. Results were compared to histopathology findings from biopsy specimens and radiology reports on MR images to evaluate the accuracy of technique. Among the biomarkers investigated, one mean-value parameter and 14 textural features demonstrated statistically significant differences (p < 0.05) between the two lesion types. A hybrid biomarker developed using a stepwise feature selection method could classify the legions with a sensitivity of 96%, a specificity of 84%, and an AUC of 0.97. Findings from this study pave the way towards adapting novel QUS-based frameworks for breast cancer screening and rapid diagnosis in clinic

Geometrical complexity of conformations of ring polymers under topological constraints

One measure of geometrical complexity of a spatial curve is the number of crossings in a planar projection of the curve. For $N$-noded ring polymers with a fixed knot type, we evaluate numerically the average of the crossing number over some directions. We find that the average crossing number under the topological constraint are less than that of no topological constraint for large $N$. The decrease of the geometrical complexity is significant when the thickness of polymers is small. The simulation with or without a topological constraint also shows that the average crossing number and the average size of ring polymers are independent measures of conformational complexity.Comment: 8 pages, 4figure