This page contains the most recent publications from the Departement of Mathematics at Stockholm University (SU), and the Department of Mathematics at The Royal Institute of Technology (KTH), are presented.
Mapping placental topology from 3D scans, the graphic display of variation in arborisation across gestation (vol 34, pg A73, 2013)
No abstract available.
Equidistributed Statistics on Matchings and Permutations
We show that the bistatistic of right nestings and right crossings in matchings without left nestings is equidistributed with the number of occurrences of two certain patterns in permutations, and furthermore that this equidistribution holds when refined to positions of these statistics in matchings and permutations. For this distribution we obtain a non-commutative generating function which specializes to Zagier's generating function for the Fishburn numbers after abelianization. As a special case we obtain proofs of two conjectures of Claesson and Linusson. Finally, we conjecture that our results can be generalized to involving left crossings of matchings too.
Measures of multivariate skewness and kurtosis in high-dimensional framework
Skewness and kurtosis characteristics of a multivariate p-dimensional distribution introduced by Mardia (1970) have been used in various testing procedures and demonstrated attractive asymptotic properties in large sample settings. However these characteristics are not designed for high-dimensional problems where the dimensionality, p can largely exceeds the sample size, N. Such type of high-dimensional data are commonly encountered in modern statistical applications. This the suggests that new measures of skewness and kurtosis that can accommodate high-dimensional settings must be derived and carefully studied. In this paper, we show that, by exploiting the dependence structure, new expressions for skewness and kurtosis are introduced as an extension of the corresponding Mardia’s measures, which uses the potential advantages that the block-diagonal covariance structure has to offer in high dimensions. Asymptotic properties of newly derived measures are investigated and the cumulant based characterizations are presented along with of applications to a mixture of multivariate normal distributions and multivariate Laplace distribution, for which the explicit expressions of skewness and kurto-sis are obtained. Test statistics based on the new measures of skewness and kurtosis are proposed for testing a distribution shape, and their limit distributions are established in the asymptotic framework where N → ∞ and p is fixed but large, including p > N. For the dependence structure learning, the gLasso based technique is explored followed by AIC step which we propose for optimization of the gLasso candidate model. Performance accuracy of the test procedures based on our estimators of skewness and kurtosis are evaluated using Monte Carlo simulations and the validity of the suggested approach is shown for a number of cases when p > N.
Guaranteed resonance enclosures and exclosures for atoms and molecules
In this paper, we confirm, with absolute certainty, a conjecture on a certain oscillatory behaviour of higher auto-ionizing resonances of atoms and molecules beyond a threshold. These results not only definitely settle a more than 30 year old controversy in Rittby et al. (1981 Phys. Rev. A 24, 1636-1639 (doi: 10.1103/PhysRevA.24.1636)) and Korsch et al. (1982 Phys. Rev. A 26, 1802-1803 (doi:10.1103/PhysRevA.26.1802)), but also provide new and reliable information on the threshold. Our interval-arithmetic-based method allows one, for the first time, to enclose and to exclude resonances with guaranteed certainty. The efficiency of our approach is demonstrated by the fact that we are able to show that the approximations in Rittby et al. (1981 Phys. Rev. A 24, 1636-1639 (doi:10.1103/PhysRevA.24.1636)) do lie near true resonances, whereas the approximations of higher resonances in Korsch et al. (1982 Phys. Rev. A 26, 1802-1803 (doi:10.1103/PhysRevA.26.1802)) do not, and further that there exist two new pairs of resonances as suggested in Abramov et al. (2001 J. Phys. A 34, 57-72 (doi:10.1088/0305-4470/34/1/304)).
Bifurcation from infinity for an asymptotically linear Schrodinger equation
We consider the asymptotically linear Schrodinger equation , and we show that if is an isolated eigenvalue for the linearization at infinity, then under some additional conditions there exists a sequence () of solutions such that and . Our results extend those by Stuart [Ann. Inst. H. Poincar, Anal. Non Lin,aire, to appear]. We use the degree theory if the multiplicity of is odd and Morse theory (or more specifically, Gromoll-Meyer theory) if it is not.