Hyperbolic Vertex Research Articles

A two parameter family of lightcone-like hyperbolic string vertices

We introduce a two parameter family of string field theory vertices, which we refer to as hyperbolic Kaku vertices. It is defined in terms of hyperbolic metrics on the Riemann surface, but the geometry is allowed to depend on inputs of the states. The vertices are defined for both open and closed strings. In either case, the family contains the hyperbolic vertices. Then we show that the open string lightcone vertex is obtained as the flat limit of the hyperbolic Kaku vertices. The open string Kaku vertices, which interpolate between the Witten vertex and the open string lightcone vertex, is also obtained as a flat limit. We use the same limit on the case of closed strings to define the closed string Kaku vertices: a one parameter family of vertices that interpolates between the polyhedral vertices — which are covariant, but not cubic — and the closed string lightcone vertex — which is cubic, but not Lorentz covariant.

Complexity of word problems for HNN-extensions

The computational complexity of the word problem in HNN-extension of groups is studied. HNN-extension is a fundamental construction in combinatorial group theory. It is shown that the word problem for an ascending HNN-extension of a group H is logspace reducible to the so-called compressed word problem for H. The main result of the paper states that the word problem for an HNN-extension of a hyperbolic group H with cyclic associated subgroups can be solved in polynomial time. This result can be easily extended to fundamental groups of graphs of groups with hyperbolic vertex groups and cyclic edge groups.

Explicit kinematic equationsfor degree-4 rigid origami vertices, Euclidean and non-Euclidean.

We derive algebraic equationsfor the folding angle relationships in completely general degree-4 rigid-foldable origami vertices, including both Euclidean (developable) and non-Euclidean cases. These equationsin turn lead to elegant equationsfor the general developable degree-4 case. We compare our equationsto previous results in the literature and provide two examples of how the equationscan be used: in analyzing a family of square twist pouches with discrete configuration spaces, and for proving that a folding table design made with hyperbolic vertices has a single folding mode.

Hyperbolic string vertices

The string vertices of closed string field theory are subsets of the moduli spaces of punctured Riemann surfaces that satisfy a geometric version of the Batalin-Vilkovisky master equation. We present a homological proof of existence of string vertices and their uniqueness up to canonical transformations. Using hyperbolic metrics on surfaces with geodesic boundaries we give an exact construction of string vertices as sets of surfaces with systole greater than or equal to L with L ≤ 2 arcsinh 1. Intrinsic hyperbolic collars prevent the appearance of short geodesics upon sewing. The surfaces generated by Feynman diagrams are naturally endowed with Thurston metrics: hyperbolic on the vertices and flat on the propagators. For the classical theory the length L is arbitrary and, as L → ∞ hyperbolic vertices become the minimal-area vertices of closed string theory.

Real-Time Pattern-Recognition of GPR Images with YOLO v3 Implemented by Tensorflow.

Artificial intelligence (AI) is widely used in pattern recognition and positioning. In most of the geological exploration applications, it needs to locate and identify underground objects according to electromagnetic wave characteristics from the ground-penetrating radar (GPR) images. Currently, a few robust AI approach can detect targets by real-time with high precision or automation for GPR images recognition. This paper proposes an approach that can be used to identify parabolic targets with different sizes and underground soil or concrete structure voids based on you only look once (YOLO) v3. With the TensorFlow 1.13.0 developed by Google, we construct YOLO v3 neural network to realize real-time pattern recognition of GPR images. We propose the specific coding method for the GPR image samples in Yolo V3 to improve the prediction accuracy of bounding boxes. At the same time, K-means algorithm is also applied to select anchor boxes to improve the accuracy of positioning hyperbolic vertex. For some instances electromagnetic-vacillated signals may occur, which refers to multiple parabolic electromagnetic waves formed by strong conductive objects among soils or overlapping waveforms. This paper deals with the vacillating signal similarity intersection over union (IoU) (V-IoU) methods. Experimental result shows that the V-IoU combined with non-maximum suppression (NMS) can accurately frame targets in GPR image and reduce the misidentified boxes as well. Compared with the single shot multi-box detector (SSD), YOLO v2, and Faster-RCNN, the V-IoU YOLO v3 shows its superior performance even when implemented by CPU. It can meet the real-time output requirements by an average 12 fps detected speed. In summary, this paper proposes a simple and high-precision real-time pattern recognition method for GPR imagery, and promoted the application of artificial intelligence or deep learning in the field of the geophysical science.

Open-closed hyperbolic string vertices

We construct a family of hyperbolic string vertices in the oriented open-closed string field theory, generalizing the recent result on hyperbolic closed string vertices by Costello and Zwiebach. The vertices are described by certain bordered hyperbolic surfaces and we explain relevant collar theorems which provide restrictions on the systolic conditions for the hyperbolic vertices. We also give explicit descriptions of the vertices for all zero and one-dimensional moduli spaces.

Height in splittings of hyperbolic groups

SupposeH is a hyperbolic subgroup of a hyperbolic groupG. Assume there existsn > 0 such that the intersection ofn essentially distinct conjugates ofH is always finite. Further assumeG splits overH with hyperbolic vertex and edge groups and the two inclusions ofH are quasi-isometric embeddings. ThenH is quasiconvex inG. This answers a question of Swarup and provides a partial converse to the main theorem of [23].

Cyclicity of Infinite Contour around Certain Reversible Quadratic Center

The paper deals with quadratic vector fields on the Poincairé sphere with center of the reversible kind.x=y(1−2x),y=−x+ay2+bx2. In this case there is a 2-cycle with hyperbolic vertices at infinity. We show that the cyclicity of this 2-cycle is 2 or 3. The last possibility takes place along some curve in the (a, b) plane.

On the (2 k + 2)-vertex and (2 k + 2)-flattening theorems in higher dimensional Lobatchevskian space

A generalization of the classical four-vertex theorem is given for convex curves in the Lobatchevskian spaces. This generalization states that a convex curve in the Lobatchevskian space H 2k has at least 2 k + 2 hyperbolic vertices. Moreover, we show that a strictly convex curve in H 2k+1 has at least 2 k + 2 hyperbolic flattenings.