Unions of 3-punctured spheres in hyperbolic 3-manifolds

We classify the topological types for the unions of the totally geodesic 3-punctured spheres in orientable hyperbolic 3-manifolds. General types of the unions appear in various hyperbolic 3-manifolds. Each of the special types of the unions appears only in a single hyperbolic 3-manifold or Dehn fillings of a single hyperbolic 3-manifold. Furthermore, we investigate bounds of the moduli of adjacent cusps for the union of linearly placed 3-punctured spheres.Comment: 40 pages, 32 figures. v2: Section 5 extended, references added, v3: Theorem 1.3 added, which concerns infinitely many 3-punctured spheres, v4: reference added; to appear in Communications in Analysis and Geometr

Degeneration of 3-dimensional hyperbolic cone structures with decreasing cone angles

For deformation of 3-dimensional hyperbolic cone structures about cone angles $\theta$, the local rigidity is known for $0 \leq \theta < 2\pi$, but the global rigidity is known only for $0 \leq \theta \leq \pi$. The proof of the global rigidity by Kojima is based on the fact that hyperbolic cone structures do not degenerate in deformation with decreasing cone angles at most $\pi$. In this paper, we give an example of degeneration of hyperbolic cone structures with decreasing cone angles less than $2\pi$. These cone structures are constructed on a certain alternating link in the thickened torus by gluing four copies of a certain polyhedra. For this construction, we explicitly describe the isometry types on such a hyperbolic polyhedron. Cone loci intersect in our example of degeneration. In order to avoid such degeneration, we generalize a cone metric to a holed cone metric.Comment: 11pages, 4 figures. v2: Section 4 adde

RIGIDITY AND DEGENERATION OF 3-DIMENSIONAL HYPERBOLIC CONE STRUCTURES (Geometry of discrete groups and hyperbolic spaces)

In this note, we survey rigidity of hyperbolic cone structures and give an example of degeneration with decreasing cone angles. This example is constructed by gluing four copies of a certain polyhedron. We can explicitly describe the isometry types of such hyperbolic polyhedra. Furthermore, we introduce a generalization of cone structure to avoid intersection of cone loci

Pole inflation in Jordan frame supergravity

We investigate inflation models in Jordan frame supergravity, in which an inflaton non-minimally couples to the scalar curvature. By imposing the condition that an inflaton would have the canonical kinetic term in the Jordan frame, we construct inflation models with asymptotically flat potential through pole inflation technique and discuss their relation to the models based on Einstein frame supergravity. We also show that the model proposed by Ferrara et al. has special position and the relation between the K\"ahler potential and the frame function is uniquely determined by requiring that scalars take the canonical kinetic terms in the Jordan frame and that a frame function consists only of a holomorphic term (and its anti-holomorphic counterpart) for symmetry breaking terms. Our case corresponds to relaxing the latter condition.Comment: 27 pages, 1 figure; revised version of the manuscript, accepted for publication in JCA

CLIP: concept learning from inference patterns

AbstractA new concept-learning method called CLIP (concept learning from inference patterns) is proposed that learns new concepts from inference patterns, not from positive/negative examples that most conventional concept learning methods use. The learned concepts enable an efficient inference on a more abstract level. We use a colored digraph to represent inference patterns. The graph representation is expressive enough and enables the quantitative analysis of the inference pattern frequency. The learning process consists of the following two steps: (1) Convert the original inference patterns to a colored digraph, and (2) Extract a set of typical patterns which appears frequently in the digraph. The basic idea is that the smaller the digraph becomes, the smaller the amount of data to be handled becomes and, accordingly, the more efficient the inference process that uses these data. Also, we can reduce the size of the graph by replacing each frequently appearing graph pattern with a single node, and each reduced node represents a new concept. Experimentally, CLIP automatically generates multilevel representations from a given physical/single-level representation of a carry-chain circuit. These representations involve abstract descriptions of the circuit, such as mathematical and logical descriptions

A mathematical approach to mechanical properties of networks in thermoplastic elastomers

We employ a mathematical model to analyze stress chains in thermoplastic elastomers (TPEs) with a microphase-separated spherical structure composed of triblock copolymers. The model represents stress chains during uniaxial and biaxial extensions using networks of spherical domains connected by bridges. We advance previous research and discuss permanent strain and other aspects of the network. It explores the dependency of permanent strain on the extension direction, using the average of tension tensors to represent isotropic material behavior. The concept of deviation angle is introduced to measure network anisotropy and is shown to play an essential role in predicting permanent strain when a network is extended in a specific direction. The paper also discusses methods to create a new network structure using various polymers.Comment: 24 pages, 35 figure