60,172 research outputs found
Flip Distance Between Triangulations of a Simple Polygon is NP-Complete
Let T be a triangulation of a simple polygon. A flip in T is the operation of
removing one diagonal of T and adding a different one such that the resulting
graph is again a triangulation. The flip distance between two triangulations is
the smallest number of flips required to transform one triangulation into the
other. For the special case of convex polygons, the problem of determining the
shortest flip distance between two triangulations is equivalent to determining
the rotation distance between two binary trees, a central problem which is
still open after over 25 years of intensive study. We show that computing the
flip distance between two triangulations of a simple polygon is NP-complete.
This complements a recent result that shows APX-hardness of determining the
flip distance between two triangulations of a planar point set.Comment: Accepted versio
Variational Methods for Biomolecular Modeling
Structure, function and dynamics of many biomolecular systems can be
characterized by the energetic variational principle and the corresponding
systems of partial differential equations (PDEs). This principle allows us to
focus on the identification of essential energetic components, the optimal
parametrization of energies, and the efficient computational implementation of
energy variation or minimization. Given the fact that complex biomolecular
systems are structurally non-uniform and their interactions occur through
contact interfaces, their free energies are associated with various interfaces
as well, such as solute-solvent interface, molecular binding interface, lipid
domain interface, and membrane surfaces. This fact motivates the inclusion of
interface geometry, particular its curvatures, to the parametrization of free
energies. Applications of such interface geometry based energetic variational
principles are illustrated through three concrete topics: the multiscale
modeling of biomolecular electrostatics and solvation that includes the
curvature energy of the molecular surface, the formation of microdomains on
lipid membrane due to the geometric and molecular mechanics at the lipid
interface, and the mean curvature driven protein localization on membrane
surfaces. By further implicitly representing the interface using a phase field
function over the entire domain, one can simulate the dynamics of the interface
and the corresponding energy variation by evolving the phase field function,
achieving significant reduction of the number of degrees of freedom and
computational complexity. Strategies for improving the efficiency of
computational implementations and for extending applications to coarse-graining
or multiscale molecular simulations are outlined.Comment: 36 page
Optimal competitiveness for the Rectilinear Steiner Arborescence problem
We present optimal online algorithms for two related known problems involving
Steiner Arborescence, improving both the lower and the upper bounds. One of
them is the well studied continuous problem of the {\em Rectilinear Steiner
Arborescence} (). We improve the lower bound and the upper bound on the
competitive ratio for from and to
, where is the number of Steiner
points. This separates the competitive ratios of and the Symetric-,
two problems for which the bounds of Berman and Coulston is STOC 1997 were
identical. The second problem is one of the Multimedia Content Distribution
problems presented by Papadimitriou et al. in several papers and Charikar et
al. SODA 1998. It can be viewed as the discrete counterparts (or a network
counterpart) of . For this second problem we present tight bounds also in
terms of the network size, in addition to presenting tight bounds in terms of
the number of Steiner points (the latter are similar to those we derived for
)
A role for core planar polarity proteins in cell contact-mediated orientation of planar cell division across the mammalian embryonic skin
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the articleâs Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the articleâs Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. © The Author(s) 2017. Supplementary information accompanies this paper at doi:10.1038/s41598-017-01971-2.The question of how cell division orientation is determined is fundamentally important for understanding tissue and organ shape in both healthy or disease conditions. Here we provide evidence for cell contact-dependent orientation of planar cell division in the mammalian embryonic skin. We propose a model where the core planar polarity proteins Celsr1 and Frizzled-6 (Fz6) communicate the long axis orientation of interphase basal cells to neighbouring basal mitoses so that they align their horizontal division plane along the same axis. The underlying mechanism requires a direct, cell surface, planar polarised cue, which we posit depends upon variant post-translational forms of Celsr1 protein coupled to Fz6. Our hypothesis has parallels with contact-mediated division orientation in early C. elegans embryos suggesting functional conservation between the adhesion-GPCRs Celsr1 and Latrophilin-1. We propose that linking planar cell division plane with interphase neighbour long axis geometry reinforces axial bias in skin spreading around the mouse embryo body.Peer reviewe
Kinetic theory of cluster impingement in the framework of statistical mechanics of rigid disks
The paper centres on the evaluation of the function n(theta)=N(theta)/N0,
that is the normalized number of islands as a function of coverage 0<theta<1,
given N0 initial nucleation centres (dots) having any degree of spatial
correlation. A mean field approach has been employed: the islands have the same
size at any coverage. In particular, as far as the random distribution of dots
is concerned, the problem has been solved by considering the contribution of
binary collisions between islands only. With regard to correlated dots, we
generalize a method previously applied to the random case only. In passing, we
have made use of the exclusion probability reported in [S. Torquato, B. Lu, J.
Rubinstein, Phys.Rev.A 41, 2059 (1990)], for determining the kinetics of
surface coverage in the case of correlated dots, improving our previous
calculation [M. Tomellini, M. Fanfoni, M. Volpe Phys. Rev.B 62, 11300, (2000)].Comment: 10 pages, 3 figure
T-Bet and Eomes Regulate the Balance between the Effector/Central Memory T Cells versus Memory Stem Like T Cells
Memory T cells are composed of effector, central, and memory stem cells. Previous studies have implicated that both T-bet and Eomes are involved in the generation of effector and central memory CD8 T cells. The exact role of these transcription factors in shaping the memory T cell pool is not well understood, particularly with memory stem T cells. Here, we demonstrate that both T-bet or Eomes are required for elimination of established tumors by adoptively transferred CD8 T cells. We also examined the role of T-bet and Eomes in the generation of tumor-specific memory T cell subsets upon adoptive transfer. We showed that combined T-bet and Eomes deficiency resulted in a severe reduction in the number of effector/central memory T cells but an increase in the percentage of CD62LhighCD44low Sca-1+ T cells which were similar to the phenotype of memory stem T cells. Despite preserving large numbers of phenotypic memory stem T cells, the lack of both of T-bet and Eomes resulted in a profound defect in antitumor memory responses, suggesting T-bet and Eomes are crucial for the antitumor function of these memory T cells. Our study establishes that T-bet and Eomes cooperate to promote the phenotype of effector/central memory CD8 T cell versus that of memory stem like T cells. © 2013 Li et al
Astrocytic Ion Dynamics: Implications for Potassium Buffering and Liquid Flow
We review modeling of astrocyte ion dynamics with a specific focus on the
implications of so-called spatial potassium buffering, where excess potassium
in the extracellular space (ECS) is transported away to prevent pathological
neural spiking. The recently introduced Kirchoff-Nernst-Planck (KNP) scheme for
modeling ion dynamics in astrocytes (and brain tissue in general) is outlined
and used to study such spatial buffering. We next describe how the ion dynamics
of astrocytes may regulate microscopic liquid flow by osmotic effects and how
such microscopic flow can be linked to whole-brain macroscopic flow. We thus
include the key elements in a putative multiscale theory with astrocytes
linking neural activity on a microscopic scale to macroscopic fluid flow.Comment: 27 pages, 7 figure
Level and mechanisms of perceptual learning: Learning first-order luminance and second-order texture objects
AbstractPerceptual learning is an improvement in perceptual task performance reflecting plasticity in the perceptual system. Practice effects were studied in two object orientation tasks: a first order, luminance object task and a second-order, texture object task. Perceptual learning was small or absent in the first-order task, but consistently occurred for the second-order (texture) task, where it was limited to improvements in low external noise conditions, or stimulus enhancement [Dosher, B., & Lu, Z. -L. (1998). Perceptual learning reflects external noise filtering and internal noise reduction through channel reweighting. Proceedings of the National Academy of Sciences of the United States of America, 95 (23) 13988â13993; Dosher, B., & Lu, Z. -L. (1999). Mechanisms of perceptual learning. Vision Research, 39 (19) 3197â3221], analogous to attention effects in first- and second-order motion processing [Lu, Z. -L., Liu, C. Q., & Dosher, B. (2000). Attention mechanisms for multi-location first- and second-order motion perception. Vision Research, 40 (2) 173â186]. Perceptual learning affected the later, post-rectification, stages of perceptual analysis, possibly localized at V2 or above. It serves to amplify the stimulus relative to limiting internal noise for intrinsically noisy representations of second-order stimuli
Spin-orbit coupling controlled ground states in the double perovskite iridates A2BIrO6 (A = Ba, Sr; B = Lu, Sc)
Iridates with the 5 electronic configuration have attracted recent
interest due to reports of magnetically-ordered ground states despite
longstanding expectations that their strong spin-orbit coupling would generate
a electronic ground state for each Ir ion. The major focus of
prior research has been on the double perovskite iridates BaYIrO and
SrYIrO, where the nature of the ground states (i.e. ordered vs
non-magnetic) is still controversial. Here we present neutron powder
diffraction, high energy resolution fluorescence detected x-ray absorption
spectroscopy (HERFD-XAS), resonant inelastic x-ray scattering (RIXS), magnetic
susceptibility, and muon spin relaxation data on the related double perovskite
iridates BaLuIrO, SrLuIrO, BaScIrO, and SrScIrO
that enable us to gain a general understanding of the electronic and magnetic
properties for this family of materials. Our HERFD-XAS and RIXS measurements
establish electronic ground states for the Ir ions in all cases,
with similar values for Hund's coupling and the spin-orbit coupling
constant . Our bulk susceptibility and muon spin relaxation
data find no evidence for long-range magnetic order or spin freezing, but they
do reveal weak magnetic signals that are consistent with extrinsic local
moments. Our results indicate that the large is the key
driving force behind the electronic and magnetic ground states realized in the
5 double perovskite iridates, which agrees well with conventional wisdom.Comment: 13 pages, 7 figures, accepted for publication by PR
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