8,436 research outputs found
On homotopies with triple points of classical knots
We consider a knot homotopy as a cylinder in 4-space. An ordinary triple
point of the cylinder is called {\em coherent} if all three branches
intersect at pairwise with the same index. A {\em triple unknotting} of a
classical knot is a homotopy which connects with the trivial knot and
which has as singularities only coherent triple points. We give a new formula
for the first Vassiliev invariant by using triple unknottings. As a
corollary we obtain a very simple proof of the fact that passing a coherent
triple point always changes the knot type. As another corollary we show that
there are triple unknottings which are not homotopic as triple unknottings even
if we allow more complicated singularities to appear in the homotopy of the
homotopy.Comment: 10 pages, 13 figures, bugs in figures correcte
Random Walks Along the Streets and Canals in Compact Cities: Spectral analysis, Dynamical Modularity, Information, and Statistical Mechanics
Different models of random walks on the dual graphs of compact urban
structures are considered. Analysis of access times between streets helps to
detect the city modularity. The statistical mechanics approach to the ensembles
of lazy random walkers is developed. The complexity of city modularity can be
measured by an information-like parameter which plays the role of an individual
fingerprint of {\it Genius loci}.
Global structural properties of a city can be characterized by the
thermodynamical parameters calculated in the random walks problem.Comment: 44 pages, 22 figures, 2 table
Quantum information analysis of electronic states at different molecular structures
We have studied transition metal clusters from a quantum information theory
perspective using the density-matrix renormalization group (DMRG) method. We
demonstrate the competition between entanglement and interaction localization.
We also discuss the application of the configuration interaction based
dynamically extended active space procedure which significantly reduces the
effective system size and accelerates the speed of convergence for complicated
molecular electronic structures to a great extent. Our results indicate the
importance of taking entanglement among molecular orbitals into account in
order to devise an optimal orbital ordering and carry out efficient
calculations on transition metal clusters. We propose a recipe to perform DMRG
calculations in a black-box fashion and we point out the connections of our
work to other tensor network state approaches
Mesospheric anomalous diffusion during noctilucent clouds
The Andenes specular meteor radar shows meteor-trail diffusion rates increasing on average by ~ 20% at times and locations where a lidar observes noctilucent clouds (NLCs). This high-latitude effect has been attributed to the presence of charged NLC but this study shows that such behaviors result predominantly from thermal tides. To make this claim, the current study evaluates data from three stations, at high-, mid-, and low-latitudes, for the years 2012 to 2016, comparing diffusion to show that thermal tides correlate strongly with the presence of NLCs. This data also shows that the connection between meteor-trail diffusion and thermal tide occurs at all altitudes in the mesosphere, while the NLC influence exists only at high-latitudes and at around peak of NLC layer. This paper discusses a number of possible explanations for changes in the regions with NLCs and leans towards the hypothesis that relative abundance of background electron density plays the leading role. A more accurate model of the meteor trail diffusion around NLC particles would help researchers determine mesospheric temperature and neutral density profiles from meteor radars.Public versio
Identification of the Staphylococcus sciuri Species Group with EcoRI Fragments Containing rRNA Sequences and Description of Staphylococcus vitulus sp. nov.
Prenatal mechanistic target of rapamycin complex 1 (mTORC1) inhibition by rapamycin treatment of pregnant mice causes intrauterine growth restriction and alters postnatal cardiac growth, morphology, and function
BACKGROUND: Fetal growth impacts cardiovascular health throughout postnatal life in humans. Various animal models of intrauterine growth restriction exhibit reduced heart size at birth, which negatively influences cardiac function in adulthood. The mechanistic target of rapamycin complex 1 (mTORC1) integrates nutrient and growth factor availability with cell growth, thereby regulating organ size. This study aimed at elucidating a possible involvement of mTORC1 in intrauterine growth restriction and prenatal heart growth.
METHODS AND RESULTS: We inhibited mTORC1 in fetal mice by rapamycin treatment of pregnant dams in late gestation. Prenatal rapamycin treatment reduces mTORC1 activity in various organs at birth, which is fully restored by postnatal day 3. Rapamycin-treated neonates exhibit a 16% reduction in body weight compared with vehicle-treated controls. Heart weight decreases by 35%, resulting in a significantly reduced heart weight/body weight ratio, smaller left ventricular dimensions, and reduced cardiac output in rapamycin- versus vehicle-treated mice at birth. Although proliferation rates in neonatal rapamycin-treated hearts are unaffected, cardiomyocyte size is reduced, and apoptosis increased compared with vehicle-treated neonates. Rapamycin-treated mice exhibit postnatal catch-up growth, but body weight and left ventricular mass remain reduced in adulthood. Prenatal mTORC1 inhibition causes a reduction in cardiomyocyte number in adult hearts compared with controls, which is partially compensated for by an increased cardiomyocyte volume, resulting in normal cardiac function without maladaptive left ventricular remodeling.
CONCLUSIONS: Prenatal rapamycin treatment of pregnant dams represents a new mouse model of intrauterine growth restriction and identifies an important role of mTORC1 in perinatal cardiac growth
On phenomenon of scattering on resonances associated with discretisation of systems with fast rotating phase
Numerical integration of ODEs by standard numerical methods reduces a
continuous time problems to discrete time problems. Discrete time problems have
intrinsic properties that are absent in continuous time problems. As a result,
numerical solution of an ODE may demonstrate dynamical phenomena that are
absent in the original ODE. We show that numerical integration of system with
one fast rotating phase lead to a situation of such kind: numerical solution
demonstrate phenomenon of scattering on resonances that is absent in the
original system.Comment: 10 pages, 5 figure
Gershgorin disks for multiple eigenvalues of non-negative matrices
Gershgorin's famous circle theorem states that all eigenvalues of a square
matrix lie in disks (called Gershgorin disks) around the diagonal elements.
Here we show that if the matrix entries are non-negative and an eigenvalue has
geometric multiplicity at least two, then this eigenvalue lies in a smaller
disk. The proof uses geometric rearrangement inequalities on sums of higher
dimensional real vectors which is another new result of this paper
Mining Top-K Large Structural Patterns in a Massive Network
With ever-growing popularity of social networks, web and bio-networks, mining large frequent patterns from a single huge network has become increasingly important. Yet the existing pattern mining methods cannot offer the efficiency desirable for large pattern discovery. We propose Spider- Mine, a novel algorithm to efficiently mine top-K largest frequent patterns from a single massive network with any user-specified probability of 1-??. Deviating from the existing edge-by-edge (i.e., incremental) pattern-growth framework, SpiderMine achieves its efficiency by unleashing the power of small patterns of a bounded diameter, which we call 'spiders'. With the spider structure, our approach adopts a probabilistic mining framework to find the top-k largest patterns by (i) identifying an affordable set of promising growth paths toward large patterns, (ii) generating large patterns with much lower combinatorial complexity, and finally (iii) greatly reducing the cost of graph isomorphism tests with a new graph pattern representation by a multi-set of spiders. Extensive experimental studies on both synthetic and real data sets show that our algorithm outperforms existing methods. ? 2011 VLDB Endowment.EI011807-818
Molecular Clock on a Neutral Network
The number of fixed mutations accumulated in an evolving population often
displays a variance that is significantly larger than the mean (the
overdispersed molecular clock). By examining a generic evolutionary process on
a neutral network of high-fitness genotypes, we establish a formalism for
computing all cumulants of the full probability distribution of accumulated
mutations in terms of graph properties of the neutral network, and use the
formalism to prove overdispersion of the molecular clock. We further show that
significant overdispersion arises naturally in evolution when the neutral
network is highly sparse, exhibits large global fluctuations in neutrality, and
small local fluctuations in neutrality. The results are also relevant for
elucidating the topological structure of a neutral network from empirical
measurements of the substitution process.Comment: 10 page
- …