258 research outputs found
Blocking Coloured Point Sets
This paper studies problems related to visibility among points in the plane.
A point \emph{blocks} two points and if is in the interior of
the line segment . A set of points is \emph{-blocked} if each
point in is assigned one of colours, such that distinct points are assigned the same colour if and only if some other point in blocks
and . The focus of this paper is the conjecture that each -blocked
set has bounded size (as a function of ). Results in the literature imply
that every 2-blocked set has at most 3 points, and every 3-blocked set has at
most 6 points. We prove that every 4-blocked set has at most 12 points, and
that this bound is tight. In fact, we characterise all sets
such that some 4-blocked set has exactly points in
the -th colour class. Amongst other results, for infinitely many values of
, we construct -blocked sets with points
The mitotic-spindle-associated protein astrin is essential for progression through mitosis
Astrin is a mitotic-spindle-associated protein expressed in most human cell lines and tissues. However, its functions in spindle organization and mitosis have not yet been determined. Sequence analysis revealed that astrin has an N-terminal globular domain and an extended coiled-coil domain. Recombinant astrin was purified and characterized by CD spectroscopy and electron microscopy. Astrin showed parallel dimers with head- stalk structures reminiscent of motor proteins, although no sequence similarities to known motor proteins were found. In physiological buffers, astrin dimers oligomerized via their globular head domains and formed aster-like structures. Silencing of astrin in HeLa cells by RNA interference resulted in growth arrest, with formation of multipolar and highly disordered spindles. Chromosomes did not congress to the spindle equator and remained dispersed. Cells depleted of astrin were normal during interphase but were unable to progress through mitosis and finally ended in apoptotic cell death. Possible functions of astrin in mitotic spindle organization are discussed
On the Maximum Crossing Number
Research about crossings is typically about minimization. In this paper, we
consider \emph{maximizing} the number of crossings over all possible ways to
draw a given graph in the plane. Alpert et al. [Electron. J. Combin., 2009]
conjectured that any graph has a \emph{convex} straight-line drawing, e.g., a
drawing with vertices in convex position, that maximizes the number of edge
crossings. We disprove this conjecture by constructing a planar graph on twelve
vertices that allows a non-convex drawing with more crossings than any convex
one. Bald et al. [Proc. COCOON, 2016] showed that it is NP-hard to compute the
maximum number of crossings of a geometric graph and that the weighted
geometric case is NP-hard to approximate. We strengthen these results by
showing hardness of approximation even for the unweighted geometric case and
prove that the unweighted topological case is NP-hard.Comment: 16 pages, 5 figure
Triangle-Free Penny Graphs: Degeneracy, Choosability, and Edge Count
We show that triangle-free penny graphs have degeneracy at most two, list
coloring number (choosability) at most three, diameter , and
at most edges.Comment: 10 pages, 2 figures. To appear at the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017
Nucleoplasmic LAP2 alpha-lamin A complexes are required to maintain a proliferative state in human fibroblasts
In human diploid fibroblasts (HDFs), expression of lamina-associated polypeptide 2 (LAP2) upon entry and exit from G0 is tightly correlated with phosphorylation and subnuclear localization of retinoblastoma protein (Rb). Phosphoisoforms of Rb and LAP2 are down-regulated in G0. Although RbS780 phosphoform and LAP2 are up-regulated upon reentry into G1 and colocalize in the nucleoplasm, RbS795 migrates between nucleoplasmic and speckle compartments. In HDFs, which are null for lamins A/C, LAP2 is mislocalized within nuclear aggregates, and this is correlated with cell cycle arrest and accumulation of Rb within speckles. Nuclear retention of nucleoplasmic Rb during G1 phase but not of speckle-associated Rb depends on lamin A/C. siRNA knock down of LAP2 or lamin A/C in HDFs leads to accumulation of Rb in speckles and G1 arrest, probably because of activation of a cell cycle checkpoint. Our results suggest that LAP2 and lamin A/C are involved in controlling Rb localization and phosphorylation, and a lack or mislocalization of either protein leads to cell cycle arrest in HDFs
Comprehensive analysis of NuMA variation in breast cancer
<p>Abstract</p> <p>Background</p> <p>A recent genome wide case-control association study identified <it>NuMA </it>region on 11q13 as a candidate locus for breast cancer susceptibility. Specifically, the variant Ala794Gly was suggested to be associated with increased risk of breast cancer.</p> <p>Methods</p> <p>In order to evaluate the <it>NuMa </it>gene for breast cancer susceptibility, we have here screened the entire coding region and exon-intron boundaries of <it>NuMa </it>in 92 familial breast cancer patients and constructed haplotypes of the identified variants. Five missense variants were further screened in 341 breast cancer cases with a positive family history and 368 controls. We examined the frequency of Ala794Gly in an extensive series of familial (n = 910) and unselected (n = 884) breast cancer cases and controls (n = 906), with a high power to detect the suggested breast cancer risk. We also tested if the variant is associated with histopathologic features of breast tumors.</p> <p>Results</p> <p>Screening of <it>NuMA </it>resulted in identification of 11 exonic variants and 12 variants in introns or untranslated regions. Five missense variants that were further screened in breast cancer cases with a positive family history and controls, were each carried on a unique haplotype. None of the variants, or the haplotypes represented by them, was associated with breast cancer risk although due to low power in this analysis, very low risk alleles may go unrecognized. The <it>NuMA </it>Ala794Gly showed no difference in frequency in the unselected breast cancer case series or familial case series compared to control cases. Furthermore, Ala794Gly did not show any significant association with histopathologic characteristics of the tumors, though Ala794Gly was slightly more frequent among unselected cases with lymph node involvement.</p> <p>Conclusion</p> <p>Our results do not support the role of <it>NuMA </it>variants as breast cancer susceptibility alleles.</p
Contact numbers for congruent sphere packings in Euclidean 3-space
Continuing the investigations of Harborth (1974) and the author (2002) we
study the following two rather basic problems on sphere packings. Recall that
the contact graph of an arbitrary finite packing of unit balls (i.e., of an
arbitrary finite family of non-overlapping unit balls) in Euclidean 3-space is
the (simple) graph whose vertices correspond to the packing elements and whose
two vertices are connected by an edge if the corresponding two packing elements
touch each other. One of the most basic questions on contact graphs is to find
the maximum number of edges that a contact graph of a packing of n unit balls
can have in Euclidean 3-space. Our method for finding lower and upper estimates
for the largest contact numbers is a combination of analytic and combinatorial
ideas and it is also based on some recent results on sphere packings. Finally,
we are interested also in the following more special version of the above
problem. Namely, let us imagine that we are given a lattice unit sphere packing
with the center points forming the lattice L in Euclidean 3-space (and with
certain pairs of unit balls touching each other) and then let us generate
packings of n unit balls such that each and every center of the n unit balls is
chosen from L. Just as in the general case we are interested in finding good
estimates for the largest contact number of the packings of n unit balls
obtained in this way.Comment: 18 page
String Matching and 1d Lattice Gases
We calculate the probability distributions for the number of occurrences
of a given letter word in a random string of letters. Analytical
expressions for the distribution are known for the asymptotic regimes (i) (Gaussian) and such that is finite
(Compound Poisson). However, it is known that these distributions do now work
well in the intermediate regime . We show that the
problem of calculating the string matching probability can be cast into a
determining the configurational partition function of a 1d lattice gas with
interacting particles so that the matching probability becomes the
grand-partition sum of the lattice gas, with the number of particles
corresponding to the number of matches. We perform a virial expansion of the
effective equation of state and obtain the probability distribution. Our result
reproduces the behavior of the distribution in all regimes. We are also able to
show analytically how the limiting distributions arise. Our analysis builds on
the fact that the effective interactions between the particles consist of a
relatively strong core of size , the word length, followed by a weak,
exponentially decaying tail. We find that the asymptotic regimes correspond to
the case where the tail of the interactions can be neglected, while in the
intermediate regime they need to be kept in the analysis. Our results are
readily generalized to the case where the random strings are generated by more
complicated stochastic processes such as a non-uniform letter probability
distribution or Markov chains. We show that in these cases the tails of the
effective interactions can be made even more dominant rendering thus the
asymptotic approximations less accurate in such a regime.Comment: 44 pages and 8 figures. Major revision of previous version. The
lattice gas analogy has been worked out in full, including virial expansion
and equation of state. This constitutes the main part of the paper now.
Connections with existing work is made and references should be up to date
now. To be submitted for publicatio
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