153 research outputs found
Self-Assembly of 4-sided Fractals in the Two-handed Tile Assembly Model
We consider the self-assembly of fractals in one of the most well-studied
models of tile based self-assembling systems known as the Two-handed Tile
Assembly Model (2HAM). In particular, we focus our attention on a class of
fractals called discrete self-similar fractals (a class of fractals that
includes the discrete Sierpi\'nski carpet). We present a 2HAM system that
finitely self-assembles the discrete Sierpi\'nski carpet with scale factor 1.
Moreover, the 2HAM system that we give lends itself to being generalized and we
describe how this system can be modified to obtain a 2HAM system that finitely
self-assembles one of any fractal from an infinite set of fractals which we
call 4-sided fractals. The 2HAM systems we give in this paper are the first
examples of systems that finitely self-assemble discrete self-similar fractals
at scale factor 1 in a purely growth model of self-assembly. Finally, we show
that there exists a 3-sided fractal (which is not a tree fractal) that cannot
be finitely self-assembled by any 2HAM system
Reflections on Tiles (in Self-Assembly)
We define the Reflexive Tile Assembly Model (RTAM), which is obtained from
the abstract Tile Assembly Model (aTAM) by allowing tiles to reflect across
their horizontal and/or vertical axes. We show that the class of directed
temperature-1 RTAM systems is not computationally universal, which is
conjectured but unproven for the aTAM, and like the aTAM, the RTAM is
computationally universal at temperature 2. We then show that at temperature 1,
when starting from a single tile seed, the RTAM is capable of assembling n x n
squares for n odd using only n tile types, but incapable of assembling n x n
squares for n even. Moreover, we show that n is a lower bound on the number of
tile types needed to assemble n x n squares for n odd in the temperature-1
RTAM. The conjectured lower bound for temperature-1 aTAM systems is 2n-1.
Finally, we give preliminary results toward the classification of which finite
connected shapes in Z^2 can be assembled (strictly or weakly) by a singly
seeded (i.e. seed of size 1) RTAM system, including a complete classification
of which finite connected shapes be strictly assembled by a "mismatch-free"
singly seeded RTAM system.Comment: New results which classify the types of shapes which can
self-assemble in the RTAM have been adde
Polymorphisms in the WNK1 gene are asociated with blood pressure variation and urinary potassium excretion
WNK1 - a serine/threonine kinase involved in electrolyte homeostasis and blood pressure (BP) control - is an excellent candidate gene for essential hypertension (EH). We and others have previously reported association between WNK1 and BP variation. Using tag SNPs (tSNPs) that capture 100% of common WNK1 variation in HapMap, we aimed to replicate our findings with BP and to test for association with phenotypes relating to WNK1 function in the British Genetics of Hypertension (BRIGHT) study case-control resource (1700 hypertensive cases and 1700 normotensive controls). We found multiple variants to be associated with systolic blood pressure, SBP (7/28 tSNPs min-p = 0.0005), diastolic blood pressure, DBP (7/28 tSNPs min-p = 0.002) and 24 hour urinary potassium excretion (10/28 tSNPs min-p = 0.0004). Associations with SBP and urine potassium remained significant after correction for multiple testing (p = 0.02 and p = 0.01 respectively). The major allele (A) of rs765250, located in intron 1, demonstrated the strongest evidence for association with SBP, effect size 3.14 mmHg (95%CI:1.23–4.9), DBP 1.9 mmHg (95%CI:0.7–3.2) and hypertension, odds ratio (OR: 1.3 [95%CI: 1.0–1.7]).We genotyped this variant in six independent populations (n = 14,451) and replicated the association between rs765250 and SBP in a meta-analysis (p = 7×10−3, combined with BRIGHT data-set p = 2×10−4, n = 17,851). The associations of WNK1 with DBP and EH were not confirmed. Haplotype analysis revealed striking associations with hypertension and BP variation (global permutation p10 mmHg reduction) and risk for hypertension (OR<0.60). Our data indicates that multiple rare and common WNK1 variants contribute to BP variation and hypertension, and provide compelling evidence to initiate further genetic and functional studies to explore the role of WNK1 in BP regulation and EH
The stability of axisymmetric Taylor-Couette flow in hydromagnetics
The linear marginal instability of an axisymmetric MHD Taylor-Couette flow of
infinite vertical extension is considered. The dependence of the flow stability
on magnetic Prandtl number, Pm, and gap-width between rotating cylinders is
investigated. There is an unstability for flows with resting outer cylinder
even without a magnetic field. Nevertheless, there are solutions with smaller
critical Reynolds numbers for certain (weak) magnetic fields. These solutions,
however, exist for not too small Pm or large enough gap. For hydrodynamically
stable flow, we found that a magnetic field amplitude always exsits where the
critical Reynolds number is minimal. In all calculated cases the minimal
critical Reynolds numbers are running with 1/Pm for small Pm and the critical
Reynolds numbers exceed value of 10^6 for Pm of sodium (10^{-5}) or gallium
(10^{-6}).Comment: 8 pages, 17 figure
Angular momentum transport and turbulence in laboratory models of Keplerian flows
We present angular momentum transport (torque) measurements in two recent
experimental studies of the turbulent flow between independently rotating
cylinders. In addition to these studies, we reanalyze prior torque measurements
to expand the range of control parameters for the experimental Taylor-Couette
flows. We find that the torque may be described as a product of functions that
depend only on the Reynolds number, which describes the turbulent driving
intensity, and the rotation number, which characterizes the effects of global
rotation. For a given Reynolds number, the global angular momentum transport
for Keplerian-like flow profiles is approximately 14% of the maximum achievable
transport rate. We estimate that this level of transport would produce an
accretion rate of in astrophysical disks. We
argue that this level of transport from hydrodynamics alone could be
significant.Comment: 17 pages, 7 figures, 2 tables, submitted to Astronomy & Astrophysics
(2011
Magnetohydrodynamic experiments on cosmic magnetic fields
It is widely known that cosmic magnetic fields, i.e. the fields of planets,
stars, and galaxies, are produced by the hydromagnetic dynamo effect in moving
electrically conducting fluids. It is less well known that cosmic magnetic
fields play also an active role in cosmic structure formation by enabling
outward transport of angular momentum in accretion disks via the
magnetorotational instability (MRI). Considerable theoretical and computational
progress has been made in understanding both processes. In addition to this,
the last ten years have seen tremendous efforts in studying both effects in
liquid metal experiments. In 1999, magnetic field self-excitation was observed
in the large scale liquid sodium facilities in Riga and Karlsruhe. Recently,
self-excitation was also obtained in the French "von Karman sodium" (VKS)
experiment. An MRI-like mode was found on the background of a turbulent
spherical Couette flow at the University of Maryland. Evidence for MRI as the
first instability of an hydrodynamically stable flow was obtained in the
"Potsdam Rossendorf Magnetic Instability Experiment" (PROMISE). In this review,
the history of dynamo and MRI related experiments is delineated, and some
directions of future work are discussed.Comment: 25 pages, 26 figures, to appear in ZAM
Depth, Highness and DNR Degrees
A sequence is Bennett deep [5] if every recursive approximation of the
Kolmogorov complexity of its initial segments from above satisfies that the difference
between the approximation and the actual value of the Kolmogorov complexity of
the initial segments dominates every constant function. We study for different lower
bounds r of this difference between approximation and actual value of the initial segment
complexity, which properties the corresponding r(n)-deep sets have. We prove
that for r(n) = εn, depth coincides with highness on the Turing degrees. For smaller
choices of r, i.e., r is any recursive order function, we show that depth implies either
highness or diagonally-non-recursiveness (DNR). In particular, for left-r.e. sets, order
depth already implies highness. As a corollary, we obtain that weakly-useful sets are
either high or DNR. We prove that not all deep sets are high by constructing a low
order-deep set.
Bennett's depth is defined using prefix-free Kolmogorov complexity. We show that
if one replaces prefix-free by plain Kolmogorov complexity in Bennett's depth definition,
one obtains a notion which no longer satisfies the slow growth law (which
stipulates that no shallow set truth-table computes a deep set); however, under this
notion, random sets are not deep (at the unbounded recursive order magnitude). We
improve Bennett's result that recursive sets are shallow by proving all K-trivial sets
are shallow; our result is close to optimal.
For Bennett's depth, the magnitude of compression improvement has to be achieved
almost everywhere on the set. Bennett observed that relaxing to infinitely often is
meaningless because every recursive set is infinitely often deep. We propose an alternative
infinitely often depth notion that doesn't suffer this limitation (called i.o.
depth).We show that every hyperimmune degree contains a i.o. deep set of magnitude
εn, and construct a π01- class where every member is an i.o. deep set of magnitude
εn. We prove that every non-recursive, non-DNR hyperimmune-free set is i.o. deep
of constant magnitude, and that every nonrecursive many-one degree contains such
a set
The microaerophilic microbiota of de-novo paediatric inflammatory bowel disease: the BISCUIT study
<p>Introduction: Children presenting for the first time with inflammatory bowel disease (IBD) offer a unique opportunity to study aetiological agents before the confounders of treatment. Microaerophilic bacteria can exploit the ecological niche of the intestinal epithelium; Helicobacter and Campylobacter are previously implicated in IBD pathogenesis. We set out to study these and other microaerophilic bacteria in de-novo paediatric IBD.</p>
<p>Patients and Methods: 100 children undergoing colonoscopy were recruited including 44 treatment naïve de-novo IBD patients and 42 with normal colons. Colonic biopsies were subjected to microaerophilic culture with Gram-negative isolates then identified by sequencing. Biopsies were also PCR screened for the specific microaerophilic bacterial groups: Helicobacteraceae, Campylobacteraceae and Sutterella wadsworthensis.</p>
<p>Results: 129 Gram-negative microaerophilic bacterial isolates were identified from 10 genera. The most frequently cultured was S. wadsworthensis (32 distinct isolates). Unusual Campylobacter were isolated from 8 subjects (including 3 C. concisus, 1 C. curvus, 1 C. lari, 1 C. rectus, 3 C. showae). No Helicobacter were cultured. When comparing IBD vs. normal colon control by PCR the prevalence figures were not significantly different (Helicobacter 11% vs. 12%, p = 1.00; Campylobacter 75% vs. 76%, p = 1.00; S. wadsworthensis 82% vs. 71%, p = 0.312).</p>
<p>Conclusions: This study offers a comprehensive overview of the microaerophilic microbiota of the paediatric colon including at IBD onset. Campylobacter appear to be surprisingly common, are not more strongly associated with IBD and can be isolated from around 8% of paediatric colonic biopsies. S. wadsworthensis appears to be a common commensal. Helicobacter species are relatively rare in the paediatric colon.</p>
Hydrodynamic turbulence cannot transport angular momentum effectively in astrophysical disks
The most efficient energy sources known in the Universe are accretion disks.
Those around black holes convert 5 -- 40 per cent of rest-mass energy to
radiation. Like water circling a drain, inflowing mass must lose angular
momentum, presumably by vigorous turbulence in disks, which are essentially
inviscid. The origin of the turbulence is unclear. Hot disks of electrically
conducting plasma can become turbulent by way of the linear magnetorotational
instability. Cool disks, such as the planet-forming disks of protostars, may be
too poorly ionized for the magnetorotational instability to occur, hence
essentially unmagnetized and linearly stable. Nonlinear hydrodynamic
instability often occurs in linearly stable flows (for example, pipe flows) at
sufficiently large Reynolds numbers. Although planet-forming disks have extreme
Reynolds numbers, Keplerian rotation enhances their linear hydrodynamic
stability, so the question of whether they can be turbulent and thereby
transport angular momentum effectively is controversial. Here we report a
laboratory experiment, demonstrating that non-magnetic quasi-Keplerian flows at
Reynolds numbers up to millions are essentially steady. Scaled to accretion
disks, rates of angular momentum transport lie far below astrophysical
requirements. By ruling out purely hydrodynamic turbulence, our results
indirectly support the magnetorotational instability as the likely cause of
turbulence, even in cool disks.Comment: 12 pages and 4 figures. To be published in Nature on November 16,
2006, available at
http://www.nature.com/nature/journal/v444/n7117/abs/nature05323.htm
SLC2A9 Is a High-Capacity Urate Transporter in Humans
Serum uric acid levels in humans are influenced by diet, cellular breakdown, and renal elimination, and correlate with blood pressure, metabolic syndrome, diabetes, gout, and cardiovascular disease. Recent genome-wide association scans have found common genetic variants of SLC2A9 to be associated with increased serum urate level and gout. The SLC2A9 gene encodes a facilitative glucose transporter, and it has two splice variants that are highly expressed in the proximal nephron, a key site for urate handling in the kidney. We investigated whether SLC2A9 is a functional urate transporter that contributes to the longstanding association between urate and blood pressure in man
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