89 research outputs found
Characteristic length of random knotting for cylindrical self-avoiding polygons
We discuss the probability of random knotting for a model of self-avoiding
polygons whose segments are given by cylinders of unit length with radius .
We show numerically that the characteristic length of random knotting is
roughly approximated by an exponential function of the chain thickness .Comment: 5 pages, 4 figure
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
Winding of planar gaussian processes
We consider a smooth, rotationally invariant, centered gaussian process in
the plane, with arbitrary correlation matrix . We study the winding
angle around its center. We obtain a closed formula for the variance
of the winding angle as a function of the matrix . For most stationary
processes the winding angle exhibits diffusion at large time
with diffusion coefficient .
Correlations of with integer , the distribution of the
angular velocity , and the variance of the algebraic area are also
obtained. For smooth processes with stationary increments (random walks) the
variance of the winding angle grows as , with proper
generalizations to the various classes of fractional Brownian motion. These
results are tested numerically. Non integer is studied numerically.Comment: 12 pages, 6 figure
Functionals of the Brownian motion, localization and metric graphs
We review several results related to the problem of a quantum particle in a
random environment.
In an introductory part, we recall how several functionals of the Brownian
motion arise in the study of electronic transport in weakly disordered metals
(weak localization).
Two aspects of the physics of the one-dimensional strong localization are
reviewed : some properties of the scattering by a random potential (time delay
distribution) and a study of the spectrum of a random potential on a bounded
domain (the extreme value statistics of the eigenvalues).
Then we mention several results concerning the diffusion on graphs, and more
generally the spectral properties of the Schr\"odinger operator on graphs. The
interest of spectral determinants as generating functions characterizing the
diffusion on graphs is illustrated.
Finally, we consider a two-dimensional model of a charged particle coupled to
the random magnetic field due to magnetic vortices. We recall the connection
between spectral properties of this model and winding functionals of the planar
Brownian motion.Comment: Review article. 50 pages, 21 eps figures. Version 2: section 5.5 and
conclusion added. Several references adde
Placement and orientation of individual DNA shapes on lithographically patterned surfaces
Artificial DNA nanostructures show promise for the organization of functional materials to create nanoelectronic or nano-optical devices. DNA origami, in which a long single strand of DNA is folded into a shape using shorter 'staple strands', can display 6-nm-resolution patterns of binding sites, in principle allowing complex arrangements of carbon nanotubes, silicon nanowires, or quantum dots. However, DNA origami are synthesized in solution and uncontrolled deposition results in random arrangements; this makes it difficult to measure the properties of attached nanodevices or to integrate them with conventionally fabricated microcircuitry. Here we describe the use of electron-beam lithography and dry oxidative etching to create DNA origami-shaped binding sites on technologically useful materials, such as SiO_2 and diamond-like carbon. In buffer with ~ 100 mM MgCl_2, DNA origami bind with high selectivity and good orientation: 70â95% of sites have individual origami aligned with an angular dispersion (±1 s.d.) as low as ±10° (on diamond-like carbon) or ±20° (on SiO_2)
Nonlinear Optical Microscopy for Histology of Fresh Normal and Cancerous Pancreatic Tissues
BACKGROUND: Pancreatic cancer is a lethal disease with a 5-year survival rate of only 1-5%. The acceleration of intraoperative histological examination would be beneficial for better management of pancreatic cancer, suggesting an improved survival. Nonlinear optical methods based on two-photon excited fluorescence (TPEF) and second harmonic generation (SHG) of intrinsic optical biomarkers show the ability to visualize the morphology of fresh tissues associated with histology, which is promising for real-time intraoperative evaluation of pancreatic cancer. METHODOLOGY/PRINCIPAL FINDINGS: In order to investigate whether the nonlinear optical imaging methods have the ability to characterize pancreatic histology at cellular resolution, we studied different types of pancreatic tissues by using label-free TPEF and SHG. Compared with other routine methods for the preparation of specimens, fresh tissues without processing were found to be most suitable for nonlinear optical imaging of pancreatic tissues. The detailed morphology of the normal rat pancreas was observed and related with the standard histological images. Comparatively speaking, the preliminary images of a small number of chemical-induced pancreatic cancer tissues showed visible neoplastic differences in the morphology of cells and extracellular matrix. The subcutaneous pancreatic tumor xenografts were further observed using the nonlinear optical microscopy, showing that most cells are leucocytes at 5 days after implantation, the tumor cells begin to proliferate at 10 days after implantation, and the extracellular collagen fibers become disordered as the xenografts grow. CONCLUSIONS/SIGNIFICANCE: In this study, nonlinear optical imaging was used to characterize the morphological details of fresh pancreatic tissues for the first time. We demonstrate that it is possible to provide real-time histological evaluation of pancreatic cancer by the nonlinear optical methods, which present an opportunity for the characterization of the progress of spontaneous pancreatic cancer and further application in a non-invasive manner
The lateral septum mediates kinship behavior in the rat
Kinship behavior in rodents has been documented in the laboratory setting but the neural mechanisms that mediate kinship behavior are not known. Here, the authors show that the lateral septum has a key role in organizing mammalian kinship behavior
On the Tree-Like Structure of Rings in Dense Solutions
One of the most challenging problems in polymer physics is providing a
theoretical description for the behaviour of rings in dense solutions and
melts. Although it is nowadays well established that the overall size of a ring
in these conditions scales like that of a collapsed globule, there is
compelling evidence that rings may exhibit ramified and tree-like
conformations. In this work I show how to characterise these local tree-like
structures by measuring the local writhing of the rings' segments and by
identifying the patterns of intra-chain contacts. These quantities reveal two
major topological structures: loops and terminal branches which strongly
suggest that the strictly double-folded "lattice animal" picture for rings in
the melt may be replaced by a more relaxed tree-like structure accommodating
loops. In particular, I show that one can identify hierarchically looped
structures whose degree increases linearly with the size of a ring, and that
terminal branches are found to store about 30% of the whole ring mass,
irrespectively of its length. Finally, I draw an analogy between rings in the
melt and slip-linked chains, where contact points are enforced by mobile
slip-links and for which a field-theoretic treatment can be employed to get
some insight into their typical conformations. These findings are ultimately
discussed in the light of recent works on the static structure of rings and on
the existence of inter-ring threadings.Comment: Accepted version. To appear in RSC Soft Matter. Suppl. Movie can be
found at http://www2.ph.ed.ac.uk/~dmichiel
Hi-C-constrained physical models of human chromosomes recover functionally-related properties of genome organization
Combining genome-wide structural models with phenomenological data is at the forefront of efforts to understand the organizational principles regulating the human genome. Here, we use chromosome-chromosome contact data as knowledge-based constraints for large-scale three-dimensional models of the human diploid genome. The resulting models remain minimally entangled and acquire several functional features that are observed in vivo and that were never used as input for the model. We find, for instance, that gene-rich, active regions are drawn towards the nuclear center, while gene poor and lamina associated domains are pushed to the periphery. These and other properties persist upon adding local contact constraints, suggesting their compatibility with non-local constraints for the genome organization. The results show that suitable combinations of data analysis and physical modelling can expose the unexpectedly rich functionally-related properties implicit in chromosome-chromosome contact data. Specific directions are suggested for further developments based on combining experimental data analysis and genomic structural modelling
Invertebrate population genetics across Earth's largest habitat: The deep-sea floor
Despite the deep sea being the largest habitat on Earth, there are just 77 population genetic studies of invertebrates (115 species) inhabiting non-chemosynthetic ecosystems on the deep-sea floor (below 200 m depth). We review and synthesize the results of these papers. Studies reveal levels of genetic diversity comparable to shallow-water species. Generally, populations at similar depths were well connected over 100sâ1,000s km, but studies that sampled across depth ranges reveal population structure at much smaller scales (100sâ1,000s m) consistent with isolation by adaptation across environmental gradients, or the existence of physical barriers to connectivity with depth. Few studies were ocean-wide (under 4%), and 48% were Atlantic-focused. There is strong emphasis on megafauna and commercial species with research into meiofauna, âecosystem engineersâ and other ecologically important species lacking. Only nine papers account for ~50% of the planet's surface (depths below 3,500 m). Just two species were studied below 5,000 m, a quarter of Earth's seafloor. Most studies used single-locus mitochondrial genes revealing a common pattern of non-neutrality, consistent with demographic instability or selective sweeps; similar to deep-sea hydrothermal vent fauna. The absence of a clear difference between vent and non-vent could signify that demographic instability is common in the deep sea, or that selective sweeps render single-locus mitochondrial studies demographically uninformative. The number of population genetics studies to date is miniscule in relation to the size of the deep sea. The paucity of studies constrains meta-analyses where broad inferences about deep-sea ecology could be made
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