Innovative Research Solutions

Exploring geometric and topological anomalies through advanced mathematical frameworks and algorithm development for enhanced understanding.

A geometric sphere composed of intersecting thin white lines forms a mesh pattern against a black background. The lines create a symmetrical, grid-like structure with a sense of depth and dimensionality.
A geometric sphere composed of intersecting thin white lines forms a mesh pattern against a black background. The lines create a symmetrical, grid-like structure with a sense of depth and dimensionality.
A geometric pattern composed of interconnected hexagonal shapes with a three-dimensional appearance. The structure appears metallic and features alternating light and dark surfaces, creating a play of light and shadow.
A geometric pattern composed of interconnected hexagonal shapes with a three-dimensional appearance. The structure appears metallic and features alternating light and dark surfaces, creating a play of light and shadow.

Research Design

Exploring geometric and topological anomalies in manifold embeddings.

An abstract geometric pattern featuring interconnected polygons with metallic spheres at each vertex. The polygons are three-dimensional triangles and quadrilaterals creating a tiled effect. The overall design has a sleek and modern aesthetic.
An abstract geometric pattern featuring interconnected polygons with metallic spheres at each vertex. The polygons are three-dimensional triangles and quadrilaterals creating a tiled effect. The overall design has a sleek and modern aesthetic.
Hyperbolic Network

Quantifying node relationships using hyperbolic graph attention.

A geometric structure is composed of interconnected lines forming a complex pattern with bright, glowing blue lights. This intricate design creates an illusion of depth and symmetry.
A geometric structure is composed of interconnected lines forming a complex pattern with bright, glowing blue lights. This intricate design creates an illusion of depth and symmetry.
Geometry Hypothesis

Proposing decoupling of geometry and topology in anomalies.

A three-dimensional network pattern with light purple nodes connected by orange lines, creating a grid-like structure. At the center, a transparent cube contains intricate, colorful circuitry resembling a futuristic data network or processor.
A three-dimensional network pattern with light purple nodes connected by orange lines, creating a grid-like structure. At the center, a transparent cube contains intricate, colorful circuitry resembling a futuristic data network or processor.
A complex, geometric pattern formed by a grid of three-dimensional hexagonal shapes. The surface appears metallic with a variety of colors reflecting from the shapes, creating an illusion of depth and movement. Some hexagons have distinct blue-tinted centers that resemble eyes.
A complex, geometric pattern formed by a grid of three-dimensional hexagonal shapes. The surface appears metallic with a variety of colors reflecting from the shapes, creating an illusion of depth and movement. Some hexagons have distinct blue-tinted centers that resemble eyes.
Algorithm Design

Developing advanced algorithms for heterogeneous graph attention.

Anomaly Metrics

Defining metrics for sensitivity in geometric anomalies.

Research

Innovative frameworks for anomaly detection in graphs.

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