Universality in the merging dynamics of parametric active contours: a study in MRI-based lung segmentation

Measurement of lung ventilation is one of the most reliable techniques of diagnosing pulmonary diseases. The time consuming and bias prone traditional methods using hyperpolarized H${}^{3}$He and ${}^{1}$H magnetic resonance imageries have recently been improved by an automated technique based on multiple active contour evolution. Mapping results from an equivalent thermodynamic model, here we analyse the fundamental dynamics orchestrating the active contour (AC) method. We show that the numerical method is inherently connected to the universal scaling behavior of a classical nucleation-like dynamics. The favorable comparison of the exponent values with the theoretical model render further credentials to our claim.Comment: 4 pages, 4 figure

Multiparticle Schrodinger operators with point interactions in the plane

We study a system of N bosons in the plane interacting with delta function potentials. After a coupling constant renormalization we show that the Hamiltonian defines a self-adjoint operator and obtain a lower bound for the energy. The same results hold if one includes a regular inter-particle potential.Comment: 17 pages, Late

Zero Energy Bound States in Many--Particle Systems

It is proved that the eigenvalues in the N--particle system are absorbed at zero energy threshold, if none of the subsystems has a bound state with $E \leq 0$ and none of the particle pairs has a zero energy resonance. The pair potentials are allowed to take both signs

Bound States at Threshold resulting from Coulomb Repulsion

The eigenvalue absorption for a many-particle Hamiltonian depending on a parameter is analyzed in the framework of non-relativistic quantum mechanics. The long-range part of pair potentials is assumed to be pure Coulomb and no restriction on the particle statistics is imposed. It is proved that if the lowest dissociation threshold corresponds to the decay into two likewise non-zero charged clusters then the bound state, which approaches the threshold, does not spread and eventually becomes the bound state at threshold. The obtained results have applications in atomic and nuclear physics. In particular, we prove that atomic ion with atomic critical charge $Z_{cr}$ and $N_e$ electrons has a bound state at threshold given that $Z_{cr} \in (N_e -2, N_e -1)$, whereby the electrons are treated as fermions and the mass of the nucleus is finite.Comment: This is a combined and updated version of the manuscripts arXiv:math-ph/0611075v2 and arXiv:math-ph/0610058v

Comparative Seed Strike of Temperate, Sub-Tropical and Native Grasses and Herb Species Under Contrasting Environments in Southern Australia

The role of deep-rooted perennials in reducing recharge to mitigate dryland salinity has been recognised widely in Australia recently. Poor seedling establishment is a key limiting factor for the expression of genetic merit for some perennial pasture species. Nie et al. (2004) investigated seedling establishment, and its relationship with rainfall and temperature, of a range of perennial grass and herb species in southern Australia. This paper reports seed strike of a range of perennial pasture species in 2 contrasting environments. There was significant interaction between species and site on seed strike. Environmental conditions caused different establishment outcomes within a diverse set of perennial forage species

Entropy production rates of bistochastic strictly contractive quantum channels on a matrix algebra

We derive, for a bistochastic strictly contractive quantum channel on a matrix algebra, a relation between the contraction rate and the rate of entropy production. We also sketch some applications of our result to the statistical physics of irreversible processes and to quantum information processing.Comment: 7 pages; revised version submitted to J. Phys.

Hilbert space for quantum mechanics on superspace

In superspace a realization of sl2 is generated by the super Laplace operator and the generalized norm squared. In this paper, an inner product on superspace for which this representation is skew-symmetric is considered. This inner product was already defined for spaces of weighted polynomials (see [K. Coulembier, H. De Bie and F. Sommen, Orthogonality of Hermite polynomials in superspace and Mehler type formulae, arXiv:1002.1118]). In this article, it is proven that this inner product can be extended to the super Schwartz space, but not to the space of square integrable functions. Subsequently, the correct Hilbert space corresponding to this inner product is defined and studied. A complete basis of eigenfunctions for general orthosymplectically invariant quantum problems is constructed for this Hilbert space. Then the integrability of the sl2-representation is proven. Finally the Heisenberg uncertainty principle for the super Fourier transform is constructed

On the unitarity of higher-dervative and nonlocal theories

We consider two simple models of higher-derivative and nonlocal quantu systems.It is shown that, contrary to some claims found in literature, they can be made unitary.Comment: 8 pages, no figure

Density matrix renormalisation group study of the correlation function of the bilinear-biquadratic spin-1 chain

Using the recently developed density matrix renormalization group approach, we study the correlation function of the spin-1 chain with quadratic and biquadratic interactions. This allows us to define and calculate the periodicity of the ground state which differs markedly from that in the classical analogue. Combining our results with other studies, we predict three phases in the region where the quadratic and biquadratic terms are both positive.Comment: 13 pages, Standard Latex File + 5 PostScript figures in separate (New version with SUBSTANTIAL REVISIONS to appear in J Phys A

Parametrizations of density matrices

This article gives a brief overview of some recent progress in the characterization and parametrization of density matrices of finite dimensional systems. We discuss in some detail the Bloch-vector and Jarlskog parametrizations and mention briefly the coset parametrization. As applications of the Bloch parametrization we discuss the trace invariants for the case of time dependent Hamiltonians and in some detail the dynamics of three-level systems. Furthermore, the Bloch vector of two-qubit systems as well as the use of the polarization operator basis is indicated. As the main application of the Jarlskog parametrization we construct density matrices for composite systems. In addition, some recent related articles are mentioned without further discussion.Comment: 31 pages. v2: 32 pages, Abstract and Introduction rewritten and Conclusion section added, references adde