A characterization of quasi-rational polygons

The aim of this paper is to study quasi-rational polygons related to the outer billiard. We compare different notions introduced, and make a synthesis of those.Comment: 15 pages, 9 figure

Enhancing noise-induced switching times in systems with distributed delays

The paper addresses the problem of calculating the noise-induced switching rates in systems with delay-distributed kernels and Gaussian noise. A general variational formulation for the switching rate is derived for any distribution kernel, and the obtained equations of motion and boundary conditions represent the most probable, or optimal, path, which maximizes the probability of escape. Explicit analytical results for the switching rates for small mean time delays are obtained for the uniform and bi-modal (or two-peak) distributions. They suggest that increasing the width of the distribution leads to an increase in the switching times even for longer values of mean time delays for both examples of the distribution kernel, and the increase is higher in the case of the two-peak distribution. Analytical predictions are compared to the direct numerical simulations and show excellent agreement between theory and numerical experiment

In-flight calibration of the Herschel-SPIRE instrument

SPIRE, the Spectral and Photometric Imaging REceiver, is the Herschel Space Observatory's submillimetre camera and spectrometer. It contains a three-band imaging photometer operating at 250, 350 and 500 μm, and an imaging Fourier-transform spectrometer (FTS) covering 194–671 μm (447-1550 GHz). In this paper we describe the initial approach taken to the absolute calibration of the SPIRE instrument using a combination of the emission from the Herschel telescope itself and the modelled continuum emission from solar system objects and other astronomical targets. We present the photometric, spectroscopic and spatial accuracy that is obtainable in data processed through the “standard” pipelines. The overall photometric accuracy at this stage of the mission is estimated as 15% for the photometer and between 15 and 50% for the spectrometer. However, there remain issues with the photometric accuracy of the spectra of low flux sources in the longest wavelength part of the SPIRE spectrometer band. The spectrometer wavelength accuracy is determined to be better than 1/10th of the line FWHM. The astrometric accuracy in SPIRE maps is found to be 2 arcsec when the latest calibration data are used. The photometric calibration of the SPIRE instrument is currently determined by a combination of uncertainties in the model spectra of the astronomical standards and the data processing methods employed for map and spectrum calibration. Improvements in processing techniques and a better understanding of the instrument performance will lead to the final calibration accuracy of SPIRE being determined only by uncertainties in the models of astronomical standards

Web ontology representation and reasoning via fragments of set theory

In this paper we use results from Computable Set Theory as a means to represent and reason about description logics and rule languages for the semantic web. Specifically, we introduce the description logic \mathcal{DL}\langle 4LQS^R\rangle(\D)--admitting features such as min/max cardinality constructs on the left-hand/right-hand side of inclusion axioms, role chain axioms, and datatypes--which turns out to be quite expressive if compared with \mathcal{SROIQ}(\D), the description logic underpinning the Web Ontology Language OWL. Then we show that the consistency problem for \mathcal{DL}\langle 4LQS^R\rangle(\D)-knowledge bases is decidable by reducing it, through a suitable translation process, to the satisfiability problem of the stratified fragment $4LQS^R$ of set theory, involving variables of four sorts and a restricted form of quantification. We prove also that, under suitable not very restrictive constraints, the consistency problem for \mathcal{DL}\langle 4LQS^R\rangle(\D)-knowledge bases is \textbf{NP}-complete. Finally, we provide a $4LQS^R$-translation of rules belonging to the Semantic Web Rule Language (SWRL)

Statistical multi-moment bifurcations in random delay coupled swarms

We study the effects of discrete, randomly distributed time delays on the dynamics of a coupled system of self-propelling particles. Bifurcation analysis on a mean field approximation of the system reveals that the system possesses patterns with certain universal characteristics that depend on distinguished moments of the time delay distribution. Specifically, we show both theoretically and numerically that although bifurcations of simple patterns, such as translations, change stability only as a function of the first moment of the time delay distribution, more complex patterns arising from Hopf bifurcations depend on all of the moments

Complement protein levels in plasma astrocyte-derived exosomes are abnormal in conversion from mild cognitive impairment to Alzheimer's disease dementia.

IntroductionLevels of complement proteins (CPs) in plasma astrocyte-derived exosomes (ADEs) that are abnormal in Alzheimer's disease (AD) have not been assessed in mild cognitive impairment (MCI).MethodsParticipants (n = 20 per group) had either MCI converting to dementia within 3 years (MCIC), MCI remaining stable over 3 years (MCIS), Alzheimer's disease, or were controls. CPs of ADEs isolated from plasmas by anti-human glutamine aspartate transporter antibody absorption were quantified by ELISAs.ResultsADE levels of C1q and C4b of the classical pathway, factor D and fragment Bb of the alternative pathway, and C5b, C3b, and C5b-C9 of both pathways were significantly higher in patients with MCIC than those with MCIS. ADE levels of inhibitory CPs decay-accelerating factor, CD46, CD59, and type 1 complement receptor were significantly lower in patients with MCIC than those with MCIS.DiscussionADE CPs are components of neurotoxic neuroinflammation that may be predictive biomarkers of MCI conversion to Alzheimer's disease

Random field Ising systems on a general hierarchical lattice: Rigorous inequalities

Random Ising systems on a general hierarchical lattice with both, random fields and random bonds, are considered. Rigorous inequalities between eigenvalues of the Jacobian renormalization matrix at the pure fixed point are obtained. These inequalities lead to upper bounds on the crossover exponents $\{\phi_i\}$.Comment: LaTeX, 13 pages, figs. 1a,1b,2. To be published in PR

Accurate Noise Projection for Reduced Stochastic Epidemic Models

We consider a stochastic Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model. Through the use of a normal form coordinate transform, we are able to analytically derive the stochastic center manifold along with the associated, reduced set of stochastic evolution equations. The transformation correctly projects both the dynamics and the noise onto the center manifold. Therefore, the solution of this reduced stochastic dynamical system yields excellent agreement, both in amplitude and phase, with the solution of the original stochastic system for a temporal scale that is orders of magnitude longer than the typical relaxation time. This new method allows for improved time series prediction of the number of infectious cases when modeling the spread of disease in a population. Numerical solutions of the fluctuations of the SEIR model are considered in the infinite population limit using a Langevin equation approach, as well as in a finite population simulated as a Markov process.Comment: 38 pages, 10 figures, new title, Final revision to appear in Chao

Switching barrier scaling near bifurcation points for non-Gaussian noise

We study noise-induced switching of a system close to bifurcation parameter values where the number of stable states changes. For non-Gaussian noise, the switching exponent, which gives the logarithm of the switching rate, displays a non-power-law dependence on the distance to the bifurcation point. This dependence is found for Poisson noise. Even weak additional Gaussian noise dominates switching sufficiently close to the bifurcation point, leading to a crossover in the behavior of the switching exponent

Building intersubjectivity in blended problem-solving tasks

This paper aims to shed light on the process of building intersubjectivity between student-student dyads in a blended educational context. Three girls and five boys, 17 to 18 years old, participated in two types of problem-solving tasks. They formed four dyads and were required to negotiate aloud what to post in a web-forum. Dyads were video recorded, with eight sessions in total. The same pairs participated in both tasks. We are interested in understanding how the intersubjective processes were affected by the tasks and by the dyads. The two tasks differ concerning the structure of the problems. The first task was based on two short papers – one pro and other con – referring to a problem close to students' real life: the use of digital devices in class. The second problem was based on perspective-taking: dyads were required to imagine “How would the school of the future look in 20 years.” Data were analysed through a purpose-built codebook, comprising five macro-categories and 21 subcategories. Altogether, our results indicate an effect of both the type of task and of dyads' specific style of interaction. Nevertheless, a five-step process featuring intersubjectivity was found. Practical implications for teachers and educators are highlighted