We introduce symmetry hierarchy of man-made objects, a high-level structural representation of a 3D model providing a symmetry-induced, hierarchical organization of the model’s constituent parts. Given an input mesh, we segment it into primitive parts and build an initial graph which encodes inter-part symmetries and connectivity relations, as well as self-symmetries in individual parts. The sy...

Recently it was suggested that the dark energy maybe related to the well-known hierarchy between the Planck scale (∼ 10GeV) and the TeV scale. The same brane-world setup to address this hierarchy problem may also in principle address the smallness problem of dark energy. Specifically, the Planck-SM hierarchy ratio was viewed as a quantum gravity-related, dimensionless fine structure constant wh...

Cosmological probes are steadily reducing the total neutrino mass window, resulting in constraints on the neutrino-mass degeneracy as the most significant outcome. In this work we explore the discovery potential of cosmological probes to constrain the neutrino hierarchy, and point out some subtleties that could yield spurious claims of detection. This has an important implication for next gener...

The central limit theorem, the invariance principle and the Poisson limit theorem for the hierarchy of freeness are studied. We show that for given m ∈ IN the limit laws can be expressed in terms of non-crossing partitions of depth smaller or equal to m. For A = I C[x], we solve the associated moment problems and find explicitly the discrete limit measures.

Applying two definitions of the union of IF-events, P. Grzegorzewski gave two generalizations of the inclusion-exclusion principle for IF-events.In this paper we prove an inclusion-exclusion principle for IF-states based on a method which can also be used to prove Grzegorzewski's inclusion-exclusion principle for probabilities on IF-events.Finally, we give some applications of this principle by...

We present a reflection principle of the form “If pφq is provable, then φ” implemented in the HOL4 theorem prover, assuming the existence of a large cardinal. We use the large-cardinal assumption to construct a model of HOL within HOL, and show how to ensure φ has the same meaning both inside and outside of this model. Soundness of HOL implies that if pφq is provable, then it is true in this mo...

The principle of multiresolution segmentation was represented in detail in this study, and the canny algorithm was applied for edge-detection of a remotely sensed image based on this principle. The target image was divided into regions based on object-oriented multiresolution segmentation and edge-detection. Furthermore, object hierarchy was created, and a series of features (water bodies, vege...

We define a new NP search problem, the “local improvement” principle, about labellings of an acyclic, bounded-degree graph. We show that, provably in PV, it characterizes the ∀Σb1 consequences of V 1 2 and that natural restrictions of it characterize the ∀Σb1 consequences of U 1 2 and of the bounded arithmetic hierarchy. We also show that over V 0 it characterizes the ∀ΣB0 consequences of V 1 a...

We show that the complex modified KdV (cmKdV) equation and generalized nonlinear Schrödinger (GNLS) equation belong to the Ablowitz, Kaup, Newell and Segur or so-called AKNS hierarchy. Both equations do not follow from the action principle and are nonintegrable. By introducing some auxiliary fields we obtain the variational principle for them and study their canonical structures. We make use of...