Monotone graph limits and quasimonotone graphs

The recent theory of graph limits gives a powerful framework for understanding the properties of suitable (convergent) sequences $(G_n)$ of graphs in terms of a limiting object which may be represented by a symmetric function $W$ on $[0,1]$, i.e., a kernel or graphon. In this context it is natural to wish to relate specific properties of the sequence to specific properties of the kernel. Here we show that the kernel is monotone (i.e., increasing in both variables) if and only if the sequence satisfies a `quasi-monotonicity' property defined by a certain functional tending to zero. As a tool we prove an inequality relating the cut and $L^1$ norms of kernels of the form $W_1-W_2$ with $W_1$ and $W_2$ monotone that may be of interest in its own right; no such inequality holds for general kernels.Comment: 38 page

beta-Cu2V2O7: a spin-1/2 honeycomb lattice system

We report on band structure calculations and a microscopic model of the low-dimensional magnet beta-Cu2V2O7. Magnetic properties of this compound can be described by a spin-1/2 anisotropic honeycomb lattice model with the averaged coupling \bar J1=60-66 K. The low symmetry of the crystal structure leads to two inequivalent couplings J1 and J1', but this weak spatial anisotropy does not affect the essential physics of the honeycomb spin lattice. The structural realization of the honeycomb lattice is highly non-trivial: the leading interactions J1 and J1' run via double bridges of VO4 tetrahedra between spatially separated Cu atoms, while the interactions between structural nearest neighbors are negligible. The non-negligible inter-plane coupling Jperp~15 K gives rise to the long-range magnetic ordering at TN~26 K. Our model simulations improve the fit of the magnetic susceptibility data, compared to the previously assumed spin-chain models. Additionally, the simulated ordering temperature of 27 K is in remarkable agreement with the experiment. Our study evaluates beta-Cu2V2O7 as the best available experimental realization of the spin-1/2 Heisenberg model on the honeycomb lattice. We also provide an instructive comparison of different band structure codes and computational approaches to the evaluation of exchange couplings in magnetic insulators.Comment: 11 pages, 10 figures, 2 tables: revised version, extended description of simulation result

The quantum origins of skyrmions and half-skyrmions in Cu2OSeO3

The Skyrme-particle, the $skyrmion$, was introduced over half a century ago and used to construct field theories for dense nuclear matter. But with skyrmions being mathematical objects - special types of topological solitons - they can emerge in much broader contexts. Recently skyrmions were observed in helimagnets, forming nanoscale spin-textures that hold promise as information carriers. Extending over length-scales much larger than the inter-atomic spacing, these skyrmions behave as large, classical objects, yet deep inside they are of quantum origin. Penetrating into their microscopic roots requires a multi-scale approach, spanning the full quantum to classical domain. By exploiting a natural separation of exchange energy scales, we achieve this for the first time in the skyrmionic Mott insulator Cu$_2$OSeO$_3$. Atomistic ab initio calculations reveal that its magnetic building blocks are strongly fluctuating Cu$_4$ tetrahedra. These spawn a continuum theory with a skyrmionic texture that agrees well with reported experiments. It also brings to light a decay of skyrmions into half-skyrmions in a specific temperature and magnetic field range. The theoretical multiscale approach explains the strong renormalization of the local moments and predicts further fingerprints of the quantum origin of magnetic skyrmions that can be observed in Cu$_2$OSeO$_3$, like weakly dispersive high-energy excitations associated with the Cu$_4$ tetrahedra, a weak antiferromagnetic modulation of the primary ferrimagnetic order, and a fractionalized skyrmion phase.Comment: 5 pages, 3 figure

Data driven optimal filtering for phase and frequency of noisy oscillations: application to vortex flowmetering

A new method for extracting the phase of oscillations from noisy time series is proposed. To obtain the phase, the signal is filtered in such a way that the filter output has minimal relative variation in the amplitude (MIRVA) over all filters with complex-valued impulse response. The argument of the filter output yields the phase. Implementation of the algorithm and interpretation of the result are discussed. We argue that the phase obtained by the proposed method has a low susceptibility to measurement noise and a low rate of artificial phase slips. The method is applied for the detection and classification of mode locking in vortex flowmeters. A novel measure for the strength of mode locking is proposed.Comment: 12 pages, 10 figure

Decrease in alarm call response among tufted capuchins in competitive feeding contexts: possible evidence for counterdeception

Animal signals function to elicit behaviors in receivers that ultimately benefit the signaler, while receivers should respond in a way that maximizes their own fitness. However, the best response may be difficult for receivers to determine when unreliable signaling is common. “Deceptive” alarm calling is common among tufted capuchins (Cebus apella nigritus) in competitive feeding contexts, and responding to these calls is costly. Receivers should thus vary their responses based on whether a call is likely to be reliable. If capuchins are indeed able to assess reliability, I predicted that receivers will be less likely to respond to alarms that are given during competitive feeding contexts than in noncompetitive contexts, and, within feeding contexts, that individuals inside or adjacent to a food patch will be less likely to respond to alarms than those further from the resource. I tested these predictions in a group of wild capuchins by observing the reactions of focal animals to alarm calls in both noncompetitive contexts and experimental feeding contexts. Antipredator escape reactions, but not vigilance reactions, occurred significantly less often in competitive feeding contexts than in noncompetitive contexts and individuals adjacent to food patches were more likely to respond to alarm calls than were those inside or further from food patches. Although not all predictions were fully supported, the findings demonstrate that receivers vary their behavior in a way that minimizes the costs associated with “deceptive” alarms, but further research is needed to determine whether or not this can be attributed to counterdeception

Connectivity of Growing Random Networks

A solution for the time- and age-dependent connectivity distribution of a growing random network is presented. The network is built by adding sites which link to earlier sites with a probability A_k which depends on the number of pre-existing links k to that site. For homogeneous connection kernels, A_k ~ k^gamma, different behaviors arise for gamma1, and gamma=1. For gamma<1, the number of sites with k links, N_k, varies as stretched exponential. For gamma>1, a single site connects to nearly all other sites. In the borderline case A_k ~ k, the power law N_k ~k^{-nu} is found, where the exponent nu can be tuned to any value in the range 2<nu<infinity.Comment: 4 pages, 2 figures, 2 column revtex format final version to appear in PRL; contains additional result

Solubility limit and precipitate formation in Al-doped 4H-SiC epitaxial material

Heavily Al-doped 4H–SiC structures have been prepared by vapor phase epitaxy. Subsequent anneals have been carried out in an Ar atmosphere in a rf-heated furnace between 1500 °C and 2000 °C for 0.5 to 3 h. Secondary ion mass spectrometry has been utilized to obtain Al concentration versus depth as well as lateral distributions (ion images). Transmission electron microscopy(TEM) has been employed to study the crystallinity and determine phase composition after heat treatment. A solubility limit of ∼2×10²⁰ Al/cm³ (1900 °C) is extracted. Three-dimensional ion images show that the Al distribution does not remain homogeneous in layers heat treated at 1700 °C or above when the Al concentration exceeds 2×10²⁰ cm⁻³. Al-containing precipitates are identified by energy-filtered TEM.Financial support was partly received from the Swedish Foundation for Strategic Research (SSF) SiCEP program

Efficiency of Class I and Class II malocclusion treatment with four premolar extractions

Four premolar extractions is a successful protocol to treat Class I malocclusion, but it is a less efficient way when compared with other Class II treatment protocols. Objective: The objective of this study was to evaluate the influence of anteroposterior discrepancy on the success of four premolar extractions protocol. For that, treatment efficiency of Class I and complete Class II malocclusions, treated with four premolar extractions were compared. Methods: A sample of 107 records from 75 Class I (mean age of 13.98 years - group 1) and 32 Class II (mean age of 13.19 years - group 2) malocclusion patients treated with four premolar extractions was selected. The initial and final occlusal status of each patient was evaluated on dental casts with the PAR index. The treatment time was calculated based on the clinical charts, and the treatment efficiency was obtained by the ratio between the percentage of PAR reduction and treatment time. The PAR index and its components, the treatment time and the treatment efficiency of the groups were statistically compared with t tests and Mann-Whitney U-test. Results: The Class II malocclusion patients had a greater final PAR index than Class I malocclusion patients, and similar duration (Class I - 28.95 mo. and Class II - 28.10 mo.) and treatment efficiency. Conclusion: The treatment of the complete Class II malocclusion with four premolar extractions presented worse occlusal results than Class I malocclusion owing to incomplete molar relationship correction

The monomer-dimer problem and moment Lyapunov exponents of homogeneous Gaussian random fields

We consider an "elastic" version of the statistical mechanical monomer-dimer problem on the n-dimensional integer lattice. Our setting includes the classical "rigid" formulation as a special case and extends it by allowing each dimer to consist of particles at arbitrarily distant sites of the lattice, with the energy of interaction between the particles in a dimer depending on their relative position. We reduce the free energy of the elastic dimer-monomer (EDM) system per lattice site in the thermodynamic limit to the moment Lyapunov exponent (MLE) of a homogeneous Gaussian random field (GRF) whose mean value and covariance function are the Boltzmann factors associated with the monomer energy and dimer potential. In particular, the classical monomer-dimer problem becomes related to the MLE of a moving average GRF. We outline an approach to recursive computation of the partition function for "Manhattan" EDM systems where the dimer potential is a weighted l1-distance and the auxiliary GRF is a Markov random field of Pickard type which behaves in space like autoregressive processes do in time. For one-dimensional Manhattan EDM systems, we compute the MLE of the resulting Gaussian Markov chain as the largest eigenvalue of a compact transfer operator on a Hilbert space which is related to the annihilation and creation operators of the quantum harmonic oscillator and also recast it as the eigenvalue problem for a pantograph functional-differential equation.Comment: 24 pages, 4 figures, submitted on 14 October 2011 to a special issue of DCDS-