The Spectra of Small Oscillations of Thin Disk Galactic Models

This paper gives a survey of the spectral properties of the frequencies of small oscillations, both in and perpendicular to their plane, of cold thin disk galactic models. The spectra can have discrete and continuous parts, with two quite distinct types of continua arising. One type occurs with both kinds of oscillation when the density at the outer edge of the disk becomes sufficiently rarified. It is associated with rapid fluctuations in the outer region. The other type of continuum occurs for non-axisymmetric oscillations in the plane of non-uniformly rotating disks. Some significant discrete oscillations of fundamental type are found that exist in addition to the various continua.     

Stellar Hydrodynamic Equations for a Thin Disk Galaxy

Assuming that the motions of stars depart only slightly from circular, finite closed systems of stellar hydrodynamic equations are obtained for a disk galaxy by taking moments of the collisionless Boltzmann equation. The usual closure problem is avoided in that explicit expressions are obtained for the highest moments arising.     

A minimum covariance basis for diatomic vibrational constants

An alternative semianalytical representation of diatomic vibrational energy levels to the Dunham expansion, is presented in the form of an expansion over Newton polynomials. This latter representation produces smaller variances and correlation coefficients than Dunham's representation, especially for light molecules. The method is illustrated by application to the vibrational levels of the ground state of the H₂ molecule. Extension of the method to vibrational-rotational levels is discussed briefly.     

The classification of Hamiltonian stationary Lagrangian tori in {{\mathbb {CP}}^2} by their spectral data

It is known that all weakly conformal Hamiltonian stationary Lagrangian immersions of tori in ${{\mathbb {CP}}^2}$ may be constructed by methods from integrable systems theory. This article describes the precise details of a construction which leads to a form of classification. The immersion is encoded as spectral data in a similar manner to the case of minimal Lagrangian tori in ${{\mathbb {CP}}^2}$ , but the details require a careful treatment of both the ??dressing construction?? and the spectral data to deal with a loop of flat connexions which is quadratic in the loop parameter.     

The numerical evaluation of the error term in a quadrature formula of Clenshaw-Curtis type for the Gegenbauer weight function

A method is derived for the numerical evaluation of the error term arising in a quadrature formula of Clenshaw-Curtis type for functions of the form (1-x²)^{l- frac12}f(x)(1-x^{2})^{lambda - frac{1}{2}}f(x) over the interval [−1,1]. The method is illustrated by an example.     

Coupling and mixing times in a Markov chain

The derivation of the expected time to coupling in a Markov chain and its relation to the expected time to mixing (as introduced by the author [J.J. Hunter, Mixing times with applications to perturbed Markov chains, Linear Algebra Appl. 417 (2006) 108-123] are explored. The two-state cases and three-state cases are examined in detail.     

Vectorial Approach to Fast Correlation Attacks

A new, vectorial approach to fast correlation attacks on binary memoryless combiners is proposed. Instead of individual input sequences or their linear combinations, the new attack is targeting subsets of input sequences as a whole thus exploiting the full correlation between the chosen subset and the output sequence. In particular, the set of all the input sequences can be chosen as the target. The attack is based on a novel iterative probabilistic algorithm which is also applicable to general memoryless combiners over finite fields or finite rings. To illustrate the effectiveness of the introduced approach, experimental results obtained for random balanced combining functions are presentedMost of this work was done while he was with Rome CryptoDesign Center, Gemplus, Italy     

An Approximation Method for Improving Dynamic Network Model Fitting

There has been a great deal of interest recently in the modeling and simulation of dynamic networks, that is, networks that change over time. One promising model is the separable temporal exponential-family random graph model (ERGM) of Krivitsky and Handcock, which treats the formation and dissolution of ties in parallel at each time step as independent ERGMs. However, the computational cost of fitting these models can be substantial, particularly for large, sparse networks. Fitting cross-sectional models for observations of a network at a single point in time, while still a nonnegligible computational burden, is much easier. This article examines model fitting when the available data consist of independent measures of cross-sectional network structure and the duration of relationships under the assumption of stationarity. We introduce a simple approximation to the dynamic parameters for sparse networks with relationships of moderate or long duration and show that the approximation method works best in precisely those cases where parameter estimation is most likely to fail—networks with very little change at each time step. We consider a variety of cases: Bernoulli formation and dissolution of ties, independent-tie formation and Bernoulli dissolution, independent-tie formation and dissolution, and dependent-tie formation models.