Correlation functions for random involutions

Our interest is in the scaled joint distribution associated with $k$-increasing subsequences for random involutions with a prescribed number of fixed points. We proceed by specifying in terms of correlation functions the same distribution for a Poissonized model in which both the number of symbols in the involution, and the number of fixed points, are random variables. From this, a de-Poissonization argument yields the scaled correlations and distribution function for the random involutions. These are found to coincide with the same quantities known in random matrix theory from the study of ensembles interpolating between the orthogonal and symplectic universality classes at the soft edge, the interpolation being due to a rank 1 perturbation.Comment: 27 pages, 1 figure, minor corrections mad

Importance of Acid–Base Equilibrium in Electrocatalytic Oxidation of Formic Acid on Platinum

This work was supported by Japanese Society for the Promotion of Science (JSPS) KAKENHI Grants Nos. 24550143 and 24750117 and MEXT Project of Integrated Research on Chemical Synthesis. M.T.M.K. gratefully acknowledges the award of Long-Term Fellowship of JSPS (No. L-11527) and Visiting Professorship of Hokkaido University. T.U. acknowledges Grants-in-Aid for Regional R&D Proposal-Based Program from Northern Advancement Center for Science & Technology of Hokkaido, Japan. J.J. acknowledges scholarship of Asian Graduate School, Hokkaido University.Peer reviewedPostprin

Analytic Approach to the Cloud-in-cloud Problem for Non-Gaussian Density Fluctuations

We revisit the cloud-in-cloud problem for non-Gaussian density fluctuations. We show that the extended Press-Schechter (EPS) formalism for non-Gaussian fluctuations has a flaw in describing mass functions regardless of type of filtering. As an example, we consider non-Gaussian models in which density fluctuations at a point obeys a \chi^2 distribution with \nu degrees of freedom. We find that mass functions predicted by using an integral formula proposed by Jedamzik, and Yano, Nagashima and Gouda, properly taking into account correlation between objects at different scales, deviate from those predicted by using the EPS formalism, especially for strongly non-Gaussian fluctuations. Our results for the mass function at large mass scales are consistent with those by Avelino and Viana obtained from numerical simulations.Comment: 10 pages, 7 EPS files, submitted to Ap

Local Voids as the Origin of Large-angle Cosmic Microwave Background Anomalies: The Effect of a Cosmological Constant

We explore the large angular scale temperature anisotropies in the cosmic microwave background (CMB) due to homogeneous local dust-filled voids in a flat Friedmann-Robertson-Walker universe with a cosmological constant. In comparison with the equivalent dust-filled void model in the Einstein-de Sitter background, we find that the anisotropy for compensated asymptotically expanding local voids can be larger because second-order effects enhance the linear integrated Sachs-Wolfe (ISW) effect. However, for local voids that expand sufficiently faster than the asymptotic velocity of the wall, the second-order effect can suppress the fluctuation due to the linear ISW effect. A pair of quasi-linear compensated asymptotic local voids with radius (2-3)*10^2 ~h^{-1} Mpc and a matter density contrast ~-0.3 can be observed as cold spots with a temperature anisotropy Delta T/T~O(10^{-5}) that might help explain the observed large-angle CMB anomalies. We predict that the associated anisotropy in the local Hubble constant in the direction of the voids could be as large as a few percent.Comment: 23 pages, 5 figures, version accepted for publication in ApJ with minor revisio

Flow-chart proofs with open problems as scaffolds for learning about geometrical proofs

AcceptedArticleCopyright © FIZ Karlsruhe 2015The final publication is available at Springer via http://dx.doi.org/10.1007/s11858-015-0712-5Recent research on the scaffolding of instruction has widened the use of the term to include forms of support for learners provided by, amongst other things, artefacts and computer-based learning environments. This paper tackles the important and under-researched issue of how mathematics lessons in lower secondary school can be designed to scaffold students’ initial understanding of geometrical proofs. In order to scaffold the process of understanding the structure of introductory proofs, we show how flow-chart proofs with multiple solutions in ‘open problem’ situations are a useful form of scaffold. We do this by identifying the ‘scaffolding functions’ of flow-chart proofs with open problems through analysis of classroom-based data from a class of Grade 8 students (aged 13-14 years old) and quantitative data from three classes. We found that using flow-chart proofs with open problems supported the students’ development of a structural understanding of proof by giving them a range of opportunities to connect proof assumptions with conclusions. The implication is that such scaffolds are useful to enrich students’ understanding of introductory mathematical proofs.Grant-in-Aid for Scientific Research, Ministry of Education, Culture, Sports, Science, and Technology, Japan

Voter model with non-Poissonian interevent intervals

Recent analysis of social communications among humans has revealed that the interval between interactions for a pair of individuals and for an individual often follows a long-tail distribution. We investigate the effect of such a non-Poissonian nature of human behavior on dynamics of opinion formation. We use a variant of the voter model and numerically compare the time to consensus of all the voters with different distributions of interevent intervals and different networks. Compared with the exponential distribution of interevent intervals (i.e., the standard voter model), the power-law distribution of interevent intervals slows down consensus on the ring. This is because of the memory effect; in the power-law case, the expected time until the next update event on a link is large if the link has not had an update event for a long time. On the complete graph, the consensus time in the power-law case is close to that in the exponential case. Regular graphs bridge these two results such that the slowing down of the consensus in the power-law case as compared to the exponential case is less pronounced as the degree increases.Comment: 18 pages, 8 figure

Chaotic Transport in the Symmetry Crossover Regime with a Spin-orbit Interaction

We study a chaotic quantum transport in the presence of a weak spin-orbit interaction. Our theory covers the whole symmetry crossover regime between time-reversal invariant systems with and without a spin-orbit interaction. This situation is experimentally realizable when the spin-orbit interaction is controlled in a conductor by applying an electric field. We utilize a semiclassical approach which has recently been developed. In this approach, the non-Abelian nature of the spin diffusion along a classical trajectory plays a crucial role. New analytical expressions with one crossover parameter are semiclassically derived for the average conductance, conductance variance and shot noise. Moreover numerical results on a random matrix model describing the crossover from the GOE (Gaussian Orthogonal Ensemble) to the GSE (Gaussian Symplectic Ensemble) are compared with the semiclassical expressions.Comment: 13 pages, 7 figure

Probing violation of the Copernican principle via the integrated Sachs-Wolfe effect

Recent observational data of supernovae indicate that we may live in an underdense region, which challenges the Copernican principle. We show that the integrated Sachs-Wolfe (ISW) effect is an excellent discriminator between anti-Copernican inhomogeneous models and the standard Copernican models. As a reference model, we consider an anti-Copernican inhomogeneous model that consists of two inner negatively curved underdense regions and an outer flat Einstein-de Sitter region. We assume that these regions are connected by two thin-walls at redshifts z = 0.067 and z=0.45. In the inner two regions, the first-order ISW effect is dominant and comparable to that in the concordant flat-Lambda models. In the outer Einstein-de Sitter region, the first-order ISW effect vanishes but the second-order ISW effect plays a dominant role, while the first-order ISW effect is dominant in the flat-Lambda models at moderate redshifts. This difference can discrimate the anti-Copernican models from the concordant flat-Lambda model. At high redshits, the second-order ISW effect is dominant both in our inhomogeneous model and the concordant model. In the outer region, moreover, the ISW effect due to large-scale density perturbations with a present matter density contrast much less than 0.37 is negligible, while the effect due to small-scale density perturbations (such as clusters of galaxies, superclusters and voids) with matter density contrast much larger than 0.37 would generate anisotropies which are larger than those generated by the ISW effect in the concordant model.Comment: 9 pages, 2 figure

Komposisi Tubuh dan Kesegaran Kardiovaskuler yang Diukur dengan Harvard Step Test dan 20m Shuttle Run Test pada Anak Obesitas

Body composition and cardiovascular fitness measured by Harvard step test and 20m shuttle run test in obese childrenBackground: One of the impacts of obesity are physical and cardiovascular problems. Harvard step test and 20m shuttle run test can be used to measure cardiovascular fitness. Objective of this research is to determine the association between body composition with cardiovascular fitness in obese children measured by Harvard step test (HST) and 20m shuttle run test (SRT).Method: Cross sectional study was conducted to 31 students of Bernardus Elementary School Semarang in August 2010. Body composition (body mass index/BMI and fat percentage) was measured by Tanita BC545. Cardiovascular fitness was measured by HST and 20m SRT. During the step test Polar Vantage? Heart Rate (HR) monitor was attached to the subjects. Data were analyzed with Spearman correlation.Result: The average age was 10.7 (0.68) years. Only 17 children finished level III of Harvard test. The HR recovery never met the normal limit. There was no difference of physical fitness index (PFI) level I, II, and III (p=0.130) but the HR recovery decreased significantly (p=0.020). The mean of VO2max measured by 20m SRT was 20.5 (1.2) ml/kg/min, significantly lower compared with HST 24.2 (2.27) ml/kg/min. There were negative correlation between PFI and BMI (r=-0.381; p=0.034) and VO2max and BMI(r=-0.448; p=0.012).Conclusion: There are negative correlation between body mass index and cardiovascular fitness. However there are difference result of VO2max from Harvard step test comparing with 20m shuttle run test