158 research outputs found
An infinitesimally nonrigid polyhedron with nonstationary volume in the Lobachevsky 3-space
We give an example of an infinitesimally nonrigid polyhedron in the
Lobachevsky 3-space and construct an infinitesimal flex of that polyhedron such
that the volume of the polyhedron isn't stationary under the flex.Comment: 10 pages, 2 Postscript figure
From Hurwitz numbers to Kontsevich-Witten tau-function: a connection by Virasoro operators
In this letter,we present our conjecture on the connection between the
Kontsevich--Witten and the Hurwitz tau-functions. The conjectural formula
connects these two tau-functions by means of the group element. An
important feature of this group element is its simplicity: this is a group
element of the Virasoro subalgebra of . If proved, this conjecture
would allow to derive the Virasoro constraints for the Hurwitz tau-function,
which remain unknown in spite of existence of several matrix model
representations, as well as to give an integrable operator description of the
Kontsevich--Witten tau-function.Comment: 13 page
Rigidity and volume preserving deformation on degenerate simplices
Given a degenerate -simplex in a -dimensional space
(Euclidean, spherical or hyperbolic space, and ), for each , , Radon's theorem induces a partition of the set of -faces into two
subsets. We prove that if the vertices of the simplex vary smoothly in
for , and the volumes of -faces in one subset are constrained only to
decrease while in the other subset only to increase, then any sufficiently
small motion must preserve the volumes of all -faces; and this property
still holds in for if an invariant of
the degenerate simplex has the desired sign. This answers a question posed by
the author, and the proof relies on an invariant we discovered
for any -stress on a cell complex in . We introduce a
characteristic polynomial of the degenerate simplex by defining
, and prove that the roots
of are real for the Euclidean case. Some evidence suggests the same
conjecture for the hyperbolic case.Comment: 27 pages, 2 figures. To appear in Discrete & Computational Geometr
A discrete Laplace-Beltrami operator for simplicial surfaces
We define a discrete Laplace-Beltrami operator for simplicial surfaces. It
depends only on the intrinsic geometry of the surface and its edge weights are
positive. Our Laplace operator is similar to the well known finite-elements
Laplacian (the so called ``cotan formula'') except that it is based on the
intrinsic Delaunay triangulation of the simplicial surface. This leads to new
definitions of discrete harmonic functions, discrete mean curvature, and
discrete minimal surfaces. The definition of the discrete Laplace-Beltrami
operator depends on the existence and uniqueness of Delaunay tessellations in
piecewise flat surfaces. While the existence is known, we prove the uniqueness.
Using Rippa's Theorem we show that, as claimed, Musin's harmonic index provides
an optimality criterion for Delaunay triangulations, and this can be used to
prove that the edge flipping algorithm terminates also in the setting of
piecewise flat surfaces.Comment: 18 pages, 6 vector graphics figures. v2: Section 2 on Delaunay
triangulations of piecewise flat surfaces revised and expanded. References
added. Some minor changes, typos corrected. v3: fixed inaccuracies in
discussion of flip algorithm, corrected attributions, added references, some
minor revision to improve expositio
The Evolutionary Origin of Man Can Be Traced in the Layers of Defunct Ancestral Alpha Satellites Flanking the Active Centromeres of Human Chromosomes
Alpha satellite domains that currently function as centromeres of human chromosomes are flanked by layers of older alpha satellite, thought to contain dead centromeres of primate progenitors, which lost their function and the ability to homogenize satellite repeats, upon appearance of a new centromere. Using cladistic analysis of alpha satellite monomers, we elucidated complete layer patterns on chromosomes 8, 17, and X and related them to each other and to primate alpha satellites. We show that discrete and chronologically ordered alpha satellite layers are partially symmetrical around an active centromere and their succession is partially shared in non-homologous chromosomes. The layer structure forms a visual representation of the human evolutionary lineage with layers corresponding to ancestors of living primates and to entirely fossil taxa. Surprisingly, phylogenetic comparisons suggest that alpha satellite arrays went through periods of unusual hypermutability after they became “dead” centromeres. The layer structure supports a model of centromere evolution where new variants of a satellite repeat expanded periodically in the genome by rounds of inter-chromosomal transfer/amplification. Each wave of expansion covered all or many chromosomes and corresponded to a new primate taxon. Complete elucidation of the alpha satellite phylogenetic record would give a unique opportunity to number and locate the positions of major extinct taxa in relation to human ancestors shared with extant primates. If applicable to other satellites in non-primate taxa, analysis of centromeric layers could become an invaluable tool for phylogenetic studies
Head Position in Stroke Trial (HeadPoST)- sitting-up vs lying-flat positioning of patients with acute stroke: study protocol for a cluster randomised controlled trial
Background
Positioning a patient lying-flat in the acute phase of ischaemic stroke may improve recovery and reduce disability, but such a possibility has not been formally tested in a randomised trial. We therefore initiated the Head Position in Stroke Trial (HeadPoST) to determine the effects of lying-flat (0°) compared with sitting-up (≥30°) head positioning in the first 24 hours of hospital admission for patients with acute stroke.
Methods/Design
We plan to conduct an international, cluster randomised, crossover, open, blinded outcome-assessed clinical trial involving 140 study hospitals (clusters) with established acute stroke care programs. Each hospital will be randomly assigned to sequential policies of lying-flat (0°) or sitting-up (≥30°) head position as a ‘business as usual’ stroke care policy during the first 24 hours of admittance. Each hospital is required to recruit 60 consecutive patients with acute ischaemic stroke (AIS), and all patients with acute intracerebral haemorrhage (ICH) (an estimated average of 10), in the first randomised head position policy before crossing over to the second head position policy with a similar recruitment target. After collection of in-hospital clinical and management data and 7-day outcomes, central trained blinded assessors will conduct a telephone disability assessment with the modified Rankin Scale at 90 days. The primary outcome for analysis is a shift (defined as improvement) in death or disability on this scale. For a cluster size of 60 patients with AIS per intervention and with various assumptions including an intracluster correlation coefficient of 0.03, a sample size of 16,800 patients at 140 centres will provide 90 % power (α 0.05) to detect at least a 16 % relative improvement (shift) in an ordinal logistic regression analysis of the primary outcome. The treatment effect will also be assessed in all patients with ICH who are recruited during each treatment study period.
Discussion
HeadPoST is a large international clinical trial in which we will rigorously evaluate the effects of different head positioning in patients with acute stroke.
Trial registration
ClinicalTrials.gov identifier: NCT02162017 (date of registration: 27 April 2014); ANZCTR identifier: ACTRN12614000483651 (date of registration: 9 May 2014). Protocol version and date: version 2.2, 19 June 2014
Ground-State of Charged Bosons Confined in a Harmonic Trap
We study a system composed of N identical charged bosons confined in a
harmonic trap. Upper and lower energy bounds are given. It is shown in the
large N limit that the ground-state energy is determined within an accuracy of
and that the mean field theory provides a reasonable result with
relative error of less than 16% for the binding energy .Comment: 15 page
Amyloid-Mediated Sequestration of Essential Proteins Contributes to Mutant Huntingtin Toxicity in Yeast
BACKGROUND: Polyglutamine expansion is responsible for several neurodegenerative disorders, among which Huntington disease is the most well-known. Studies in the yeast model demonstrated that both aggregation and toxicity of a huntingtin (htt) protein with an expanded polyglutamine region strictly depend on the presence of the prion form of Rnq1 protein ([PIN+]), which has a glutamine/asparagine-rich domain. PRINCIPAL FINDINGS: Here, we showed that aggregation and toxicity of mutant htt depended on [PIN+] only quantitatively: the presence of [PIN+] elevated the toxicity and the levels of htt detergent-insoluble polymers. In cells lacking [PIN+], toxicity of mutant htt was due to the polymerization and inactivation of the essential glutamine/asparagine-rich Sup35 protein and related inactivation of another essential protein, Sup45, most probably via its sequestration into Sup35 aggregates. However, inhibition of growth of [PIN+] cells depended on Sup35/Sup45 depletion only partially, suggesting that there are other sources of mutant htt toxicity in yeast. CONCLUSIONS: The obtained data suggest that induced polymerization of essential glutamine/asparagine-rich proteins and related sequestration of other proteins which interact with these polymers represent an essential source of htt toxicity
Challenges in QCD matter physics - The Compressed Baryonic Matter experiment at FAIR
Substantial experimental and theoretical efforts worldwide are devoted to
explore the phase diagram of strongly interacting matter. At LHC and top RHIC
energies, QCD matter is studied at very high temperatures and nearly vanishing
net-baryon densities. There is evidence that a Quark-Gluon-Plasma (QGP) was
created at experiments at RHIC and LHC. The transition from the QGP back to the
hadron gas is found to be a smooth cross over. For larger net-baryon densities
and lower temperatures, it is expected that the QCD phase diagram exhibits a
rich structure, such as a first-order phase transition between hadronic and
partonic matter which terminates in a critical point, or exotic phases like
quarkyonic matter. The discovery of these landmarks would be a breakthrough in
our understanding of the strong interaction and is therefore in the focus of
various high-energy heavy-ion research programs. The Compressed Baryonic Matter
(CBM) experiment at FAIR will play a unique role in the exploration of the QCD
phase diagram in the region of high net-baryon densities, because it is
designed to run at unprecedented interaction rates. High-rate operation is the
key prerequisite for high-precision measurements of multi-differential
observables and of rare diagnostic probes which are sensitive to the dense
phase of the nuclear fireball. The goal of the CBM experiment at SIS100
(sqrt(s_NN) = 2.7 - 4.9 GeV) is to discover fundamental properties of QCD
matter: the phase structure at large baryon-chemical potentials (mu_B > 500
MeV), effects of chiral symmetry, and the equation-of-state at high density as
it is expected to occur in the core of neutron stars. In this article, we
review the motivation for and the physics programme of CBM, including
activities before the start of data taking in 2022, in the context of the
worldwide efforts to explore high-density QCD matter.Comment: 15 pages, 11 figures. Published in European Physical Journal
Fused eco29kIR- and M genes coding for a fully functional hybrid polypeptide as a model of molecular evolution of restriction-modification systems
<p>Abstract</p> <p>Background</p> <p>The discovery of restriction endonucleases and modification DNA methyltransferases, key instruments of genetic engineering, opened a new era of molecular biology through development of the recombinant DNA technology. Today, the number of potential proteins assigned to type II restriction enzymes alone is beyond 6000, which probably reflects the high diversity of evolutionary pathways. Here we present experimental evidence that a new type IIC restriction and modification enzymes carrying both activities in a single polypeptide could result from fusion of the appropriate genes from preexisting bipartite restriction-modification systems.</p> <p>Results</p> <p>Fusion of <it>eco29kIR </it>and <it>M </it>ORFs gave a novel gene encoding for a fully functional hybrid polypeptide that carried both restriction endonuclease and DNA methyltransferase activities. It has been placed into a subclass of type II restriction and modification enzymes - type IIC. Its MTase activity, 80% that of the M.Eco29kI enzyme, remained almost unchanged, while its REase activity decreased by three times, concurrently with changed reaction optima, which presumably can be caused by increased steric hindrance in interaction with the substrate. <it>In vitro </it>the enzyme preferentially cuts DNA, with only a low level of DNA modification detected. <it>In vivo </it>new RMS can provide a 10<sup>2</sup>-fold less protection of host cells against phage invasion.</p> <p>Conclusions</p> <p>We propose a molecular mechanism of appearing of type IIC restriction-modification and M.SsoII-related enzymes, as well as other multifunctional proteins. As shown, gene fusion could play an important role in evolution of restriction-modification systems and be responsible for the enzyme subclass interconversion. Based on the proposed approach, hundreds of new type IIC enzymes can be generated using head-to-tail oriented type I, II, and III restriction and modification genes. These bifunctional polypeptides can serve a basis for enzymes with altered recognition specificities. Lastly, this study demonstrates that protein fusion may change biochemical properties of the involved enzymes, thus giving a starting point for their further evolutionary divergence.</p
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