On homotopies with triple points of classical knots

We consider a knot homotopy as a cylinder in 4-space. An ordinary triple point $p$ of the cylinder is called {\em coherent} if all three branches intersect at $p$ pairwise with the same index. A {\em triple unknotting} of a classical knot $K$ is a homotopy which connects $K$ with the trivial knot and which has as singularities only coherent triple points. We give a new formula for the first Vassiliev invariant $v_2(K)$ 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

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