597 research outputs found
Colored Non-Crossing Euclidean Steiner Forest
Given a set of -colored points in the plane, we consider the problem of
finding trees such that each tree connects all points of one color class,
no two trees cross, and the total edge length of the trees is minimized. For
, this is the well-known Euclidean Steiner tree problem. For general ,
a -approximation algorithm is known, where is the
Steiner ratio.
We present a PTAS for , a -approximation algorithm
for , and two approximation algorithms for general~, with ratios
and
Quarter-Filled Honeycomb Lattice with a Quantized Hall Conductance
We study a generic two-dimensional hopping model on a honeycomb lattice with
strong spin-orbit coupling, without the requirement that the half-filled
lattice be a Topological Insulator. For quarter-(or three-quarter) filling, we
show that a state with a quantized Hall conductance generically arises in the
presence of a Zeeman field of sufficient strength. We discuss the influence of
Hubbard interactions and argue that spontaneous ferromagnetism (which breaks
time-reversal) will occur, leading to a quantized anomalous Hall effect.Comment: 4 pages, 3 figure
A local families index formula for d-bar operators on punctured Riemann surfaces
Using heat kernel methods developed by Vaillant, a local index formula is
obtained for families of d-bar operators on the Teichmuller universal curve of
Riemann surfaces of genus g with n punctures. The formula also holds on the
moduli space M{g,n} in the sense of orbifolds where it can be written in terms
of Mumford-Morita-Miller classes. The degree two part of the formula gives the
curvature of the corresponding determinant line bundle equipped with the
Quillen connection, a result originally obtained by Takhtajan and Zograf.Comment: 47 page
Bounded-Angle Spanning Tree: Modeling Networks with Angular Constraints
We introduce a new structure for a set of points in the plane and an angle
, which is similar in flavor to a bounded-degree MST. We name this
structure -MST. Let be a set of points in the plane and let be an angle. An -ST of is a spanning tree of the
complete Euclidean graph induced by , with the additional property that for
each point , the smallest angle around containing all the edges
adjacent to is at most . An -MST of is then an
-ST of of minimum weight. For , an -ST does
not always exist, and, for , it always exists. In this paper,
we study the problem of computing an -MST for several common values of
.
Motivated by wireless networks, we formulate the problem in terms of
directional antennas. With each point , we associate a wedge of
angle and apex . The goal is to assign an orientation and a radius
to each wedge , such that the resulting graph is connected and its
MST is an -MST. (We draw an edge between and if , , and .) Unsurprisingly, the problem of computing an
-MST is NP-hard, at least for and . We
present constant-factor approximation algorithms for .
One of our major results is a surprising theorem for ,
which, besides being interesting from a geometric point of view, has important
applications. For example, the theorem guarantees that given any set of
points in the plane and any partitioning of the points into triplets,
one can orient the wedges of each triplet {\em independently}, such that the
graph induced by is connected. We apply the theorem to the {\em antenna
conversion} problem
Enhanced chondrogenic phenotype of primary bovine articular chondrocytes in Fibrin-Hyaluronan hydrogel by multi-axial mechanical loading and FGF18
Current treatments for cartilage lesions are often associated with fibrocartilage formation and donor site morbidity. Mechanical and biochemical stimuli play an important role in hyaline cartilage formation. Biocompatible scaffolds capable of transducing mechanical loads and delivering bioactive instructive factors may better support cartilage regeneration. In this study we aimed to test the interplay between mechanical and FGF-18 mediated biochemical signals on the proliferation and differentiation of primary bovine articular chondrocytes embedded in a chondro-conductive Fibrin-Hyaluronan (FB/HA) based hydrogel. Chondrocytes seeded in a Fibrin-HA hydrogel, with or without a chondro-inductive, FGFR3 selective FGF18 variant (FGF-18v) were loaded into a joint-mimicking bioreactor applying controlled, multi-axial movements, simulating the natural movements of articular joints. Samples were evaluated for DNA content, sulphated glycosaminoglycan (sGAG) accumulation, key chondrogenic gene expression markers and histology. Under moderate loading, samples produced particularly significant amounts of sGAG/DNA compared to unloaded controls. Interestingly there was no significant effect of FGF-18v on cartilage gene expression at rest. Following moderate multi-axial loading, FGF-18v upregulated the expression of Aggrecan (ACAN), Cartilage Oligomeric Matrix Protein (COMP), type II collagen (COL2) and Lubricin (PRG4). Moreover, the combination of load and FGF-18v, significantly downregulated Matrix Metalloproteinase-9 (MMP-9) and Matrix Metaloproteinase-13 (MMP-13), two of the most important factors contributing to joint destruction in OA. Biomimetic mechanical signals and FGF-18 may work in concert to support hyaline cartilage regeneration and repair. Statement of significance: Articular cartilage has very limited repair potential and focal cartilage lesions constitute a challenge for current standard clinical procedures. The aim of the present research was to explore novel procedures and constructs, based on biomaterials and biomechanical algorithms that can better mimic joints mechanical and biochemical stimulation to promote regeneration of damaged cartilage. Using a hydrogel-based platform for chondrocyte 3D culture revealed a synergy between mechanical forces and growth factors. Exploring the mechanisms underlying this mechano-biochemical interplay may enhance our understanding of cartilage remodeling and the development of new strategies for cartilage repair and regeneration
Harris criterion on hierarchical lattices: Rigorous inequalities and counterexamples in Ising systems
Random bond Ising systems on a general hierarchical lattice are considered.
The inequality between the specific heat exponent of the pure system,
, and the crossover exponent , , gives rise to
a possibility of a negative along with a positive , leading to
random criticality in disagreement with the Harris criterion. An explicit
example where this really happens for an Ising system is presented and
discussed. In addition to that, it is shown that in presence of full long-range
correlations, the crossover exponent is larger than in the uncorrelated case.Comment: 8 pages, 3 figure
Quantum Fields in Hyperbolic Space-Times with Finite Spatial Volume
The one-loop effective action for a massive self-interacting scalar field is
investigated in -dimensional ultrastatic space-time ,
being a non-compact hyperbolic manifold with finite volume. Making
use of the Selberg trace formula, the -function related to the small
disturbance operator is constructed. For an arbitrary gravitational coupling,
it is found that has a simple pole at . The one-loop effective
action is analysed by means of proper-time regularisations and the one-loop
divergences are explicitly found. It is pointed out that, in this special case,
also -function regularisation requires a divergent counterterm, which
however is not necessary in the free massless conformal invariant coupling
case. Finite temperature effects are studied and the high-temperature expansion
is presented. A possible application to the problem of the divergences of the
entanglement entropy for a free massless scalar field in a Rindler-like
space-time is briefly discussed.Comment: 13 pages, LaTex. The contribution of hyperbolic elements has been
added. Other minor corrections and reference
Engineering Art Galleries
The Art Gallery Problem is one of the most well-known problems in
Computational Geometry, with a rich history in the study of algorithms,
complexity, and variants. Recently there has been a surge in experimental work
on the problem. In this survey, we describe this work, show the chronology of
developments, and compare current algorithms, including two unpublished
versions, in an exhaustive experiment. Furthermore, we show what core
algorithmic ingredients have led to recent successes
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