1,078 research outputs found
Evaluations of topological Tutte polynomials
We find new properties of the topological transition polynomial of embedded
graphs, . We use these properties to explain the striking similarities
between certain evaluations of Bollob\'as and Riordan's ribbon graph
polynomial, , and the topological Penrose polynomial, . The general
framework provided by also leads to several other combinatorial
interpretations these polynomials. In particular, we express , ,
and the Tutte polynomial, , as sums of chromatic polynomials of graphs
derived from ; show that these polynomials count -valuations of medial
graphs; show that counts edge 3-colourings; and reformulate the Four
Colour Theorem in terms of . We conclude with a reduction formula for the
transition polynomial of the tensor product of two embedded graphs, showing
that it leads to additional relations among these polynomials and to further
combinatorial interpretations of and .Comment: V2: major revision, several new results, and improved expositio
Minimum and maximum against k lies
A neat 1972 result of Pohl asserts that [3n/2]-2 comparisons are sufficient,
and also necessary in the worst case, for finding both the minimum and the
maximum of an n-element totally ordered set. The set is accessed via an oracle
for pairwise comparisons. More recently, the problem has been studied in the
context of the Renyi-Ulam liar games, where the oracle may give up to k false
answers. For large k, an upper bound due to Aigner shows that (k+O(\sqrt{k}))n
comparisons suffice. We improve on this by providing an algorithm with at most
(k+1+C)n+O(k^3) comparisons for some constant C. The known lower bounds are of
the form (k+1+c_k)n-D, for some constant D, where c_0=0.5, c_1=23/32=0.71875,
and c_k=\Omega(2^{-5k/4}) as k goes to infinity.Comment: 11 pages, 3 figure
Disorder Potentials near Lithographically Fabricated Atom Chips
We show that previously observed large disorder potentials in magnetic
microtraps for neutral atoms are reduced by about two orders of magnitude when
using atom chips with lithographically fabricated high quality gold layers.
Using one dimensional Bose-Einstein condensates, we probe the remaining
magnetic field variations at surface distances down to a few microns.
Measurements on a 100 um wide wire imply that residual variations of the
current flow result from local properties of the wire.Comment: submitted on September 24th, 200
The RNA Helicase DDX6 Controls Cellular Plasticity by Modulating P-Body Homeostasis
Post-transcriptional mechanisms have the potential to influence complex changes in gene expression, yet their role in cell fate transitions remains largely unexplored. Here, we show that suppression of the RNA helicase DDX6 endows human and mouse primed embryonic stem cells (ESCs) with a differentiation-resistant, “hyper-pluripotent” state, which readily reprograms to a naive state resembling the preimplantation embryo. We further demonstrate that DDX6 plays a key role in adult progenitors where it controls the balance between self-renewal and differentiation in a context-dependent manner. Mechanistically, DDX6 mediates the translational suppression of target mRNAs in P-bodies. Upon loss of DDX6 activity, P-bodies dissolve and release mRNAs encoding fate-instructive transcription and chromatin factors that re-enter the ribosome pool. Increased translation of these targets impacts cell fate by rewiring the enhancer, heterochromatin, and DNA methylation landscapes of undifferentiated cell types. Collectively, our data establish a link between P-body homeostasis, chromatin organization, and stem cell potency
Illuminating spindle convex bodies and minimizing the volume of spherical sets of constant width
A subset of the d-dimensional Euclidean space having nonempty interior is
called a spindle convex body if it is the intersection of (finitely or
infinitely many) congruent d-dimensional closed balls. The spindle convex body
is called a "fat" one, if it contains the centers of its generating balls. The
core part of this paper is an extension of Schramm's theorem and its proof on
illuminating convex bodies of constant width to the family of "fat" spindle
convex bodies.Comment: 17 page
Evaluation of two interaction techniques for visualization of dynamic graphs
Several techniques for visualization of dynamic graphs are based on different
spatial arrangements of a temporal sequence of node-link diagrams. Many studies
in the literature have investigated the importance of maintaining the user's
mental map across this temporal sequence, but usually each layout is considered
as a static graph drawing and the effect of user interaction is disregarded. We
conducted a task-based controlled experiment to assess the effectiveness of two
basic interaction techniques: the adjustment of the layout stability and the
highlighting of adjacent nodes and edges. We found that generally both
interaction techniques increase accuracy, sometimes at the cost of longer
completion times, and that the highlighting outclasses the stability adjustment
for many tasks except the most complex ones.Comment: Appears in the Proceedings of the 24th International Symposium on
Graph Drawing and Network Visualization (GD 2016
Calculation of some determinants using the s-shifted factorial
Several determinants with gamma functions as elements are evaluated. This
kind of determinants are encountered in the computation of the probability
density of the determinant of random matrices. The s-shifted factorial is
defined as a generalization for non-negative integers of the power function,
the rising factorial (or Pochammer's symbol) and the falling factorial. It is a
special case of polynomial sequence of the binomial type studied in
combinatorics theory. In terms of the gamma function, an extension is defined
for negative integers and even complex values. Properties, mainly composition
laws and binomial formulae, are given. They are used to evaluate families of
generalized Vandermonde determinants with s-shifted factorials as elements,
instead of power functions.Comment: 25 pages; added section 5 for some examples of application
Quantum Hall transitions: An exact theory based on conformal restriction
We revisit the problem of the plateau transition in the integer quantum Hall
effect. Here we develop an analytical approach for this transition, based on
the theory of conformal restriction. This is a mathematical theory that was
recently developed within the context of the Schramm-Loewner evolution which
describes the stochastic geometry of fractal curves and other stochastic
geometrical fractal objects in 2D space. Observables elucidating the connection
with the plateau transition include the so-called point-contact conductances
(PCCs) between points on the boundary of the sample, described within the
language of the Chalker-Coddington network model. We show that the
disorder-averaged PCCs are characterized by classical probabilities for certain
geometric objects in the plane (pictures), occurring with positive statistical
weights, that satisfy the crucial restriction property with respect to changes
in the shape of the sample with absorbing boundaries. Upon combining this
restriction property with the expected conformal invariance at the transition
point, we employ the mathematical theory of conformal restriction measures to
relate the disorder-averaged PCCs to correlation functions of primary operators
in a conformal field theory (of central charge ). We show how this can be
used to calculate these functions in a number of geometries with various
boundary conditions. Since our results employ only the conformal restriction
property, they are equally applicable to a number of other critical disordered
electronic systems in 2D. For most of these systems, we also predict exact
values of critical exponents related to the spatial behavior of various
disorder-averaged PCCs.Comment: Published versio
Management dilemma; a woman with cystic fibrosis and severe lung disease presenting with colonic carcinoma: a case report
Introduction
There are increasing reports of bowel cancer in cystic fibrosis, suggesting a possible causal link. Individuals with cystic fibrosis who have advanced lung disease present a high operative risk, limiting curative treatment options in early bowel malignancy.
Case presentation
We describe a 41-year-old Caucasian woman with cystic fibrosis and severe lung disease who had been considered for lung transplantation, who presented with rectal bleeding and was found to have a Stage I adenocarcinoma of the sigmoid colon. After considerable discussion as to the operative risks, she underwent a laparoscopic resection and remains relatively well 1 year postoperatively with no recurrence.
Conclusion
We discuss the complexity of the management decisions for cystic fibrosis patients with severe lung disease and early stage colonic malignancy, particularly in the context of potential need for lung transplantation. The case demonstrates that cystic fibrosis patients with very severe lung function impairment may undergo laparoscopic abdominal surgical interventions without compromising postoperative airway clearance
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