Periodic patterns and symmetries are striking visual properties that have been used decoratively around the world throughout human history. Periodic patterns can be mathematically classi ed into one of 17 differentWallpaper groups, and while computational models have been developed which can extract an image's symmetry group, very little work has been done on how humans perceive these patterns....

We study multi-level multivariate normal distribution with self similar compound symmetry covariance structure for k different levels of the multivariate data. Both maximum likelihood and unbiased estimates of the matrix parameters are obtained. The spectral decomposition of the new covariance structure are discussed and are demonstrated with a real dataset from medical studies.

The response to perturbations of a simplified transport model is studied. The model is used as a paradigmatic example of transport controlled by a critical gradient. Long-time system behaviour is diffusive when most of the system is sub-critical. However, when the critical mechanism becomes significant, it is observed to dominate the system behaviour at both short and long time scales. While th...

We obtain an intertwining relation between some Riemann-Liouville operators of order α ∈ (1, 2), connecting through a certain multiplicative identity in law the one-dimensional marginals of reflected completely asymmetric α−stable Lévy processes. An alternative approach based on recurrent extensions of positive self-similar Markov processes and exponential functionals of Lévy processes is also ...

In many instances, both voters and politicians are imperfectly informed about which policies are optimal. We analyze politicians’ policy choice in such situations. A distinctive element of our analysis is that we investigate how the strategic sophistication of voters’ beliefs about politicians’ behavior affects policy choice. This provides a novel approach in political economy that leads to a n...

Since the 20 century, timbre has become an important factor in music composition. However, no effective timbre theory for music composition has been yet developed. In this paper, firstly standpoints are described for previous timbre theories. Then the requirements for a new timbre theory are discussed: 1) How timbre should be categorized, 2) hierarchical structure and its self-similar represent...

of the Dissertation Almost-Kähler Anti-Self-Dual Metrics by Inyoung Kim Doctor of Philosophy in Mathematics Stony Brook University 2014 We show the existence of strictly almost-Kähler anti-self-dual metrics on certain 4-manifolds by deforming a scalar-flat Kähler metric. On the other hand, we prove the non-existence of such metrics on certain other 4-manifolds by means of SeibergWitten theory. ...

A method is given for the extraction of large numbers of semantic classes along with their corresponding instances. Based on the recombination of elements clustered through distributional similarity, experimental results show the procedure allows for a parametric trade-off between high precision and expanded recall.

In this paper we give, for the first time, a complete description of the late-time evolution of non-tilted spatially homogeneous cosmologies of Bianchi type VIII. The source is assumed to be a perfect fluid with equation of state p = (γ − 1)µ, where γ is a constant which satisfies 1 γ 2. Using the orthonormal frame formalism and Hubble-normalized variables, we rigorously establish the limiting ...

While it is known previously that the cycle lengths of individual components of the AES round function are very small, we demonstrate here that the cycle length of the S-box combined with the ShiftRow and MixColumn transformation is at least 10. This result is obtained by providing new invariances of the complete AES round function without the key addition. Furthermore, we consider self-duality...