Geometric

The management of the Geometric Power Plant has confirmed the percentage of equity stake purchased by the Abia State Government in the company’s power plant in Aba. Controversy There was speculation that the Abia State Government contributed a five per cent equity stake in the power plant during the administration of Okezie Ikpeazu who served as the governor of the state from 2015 to 2023. Data from the Abia State Accountant General’s 2022 financial report indicated that the state government invested N1.41…

Underneath a temple in the ancient ruined city of Taposiris Magna on the Egyptian coast, archaeologists uncovered a vast, spectacular tunnel that experts are referring to as a "geometric miracle".During ongoing excavations and exploration of the temple, Kathleen Martinez of the University of Santo Domingo in the Dominican Republic and colleagues uncovered the structure 13 meters (43 feet) below the ground. The 2-meter tall tunnel had been hewn through an incredible 1,305 meters (4,281 feet) of sandstone.Its design,…

State-of-the-Art DigestGraph & Geometric ML in 2024: Where We Are and What’s Next (Part II — Applications)Following the tradition from previous years, we interviewed a cohort of distinguished and prolific academic and industrial experts in an attempt to summarise the highlights of the past year and predict what is in store for 2024. Past 2023 was so ripe with results that we had to break this post into two parts. This is Part II focusing on applications, see also Part I for theory & new architectures.Image by…

State-of-the-Art DigestGraph & Geometric ML in 2024: Where We Are and What’s Next (Part I — Theory & Architectures)Following the tradition from previous years, we interviewed a cohort of distinguished and prolific academic and industrial experts in an attempt to summarise the highlights of the past year and predict what is in store for 2024. Past 2023 was so ripe with results that we had to break this post into two parts. This is Part I focusing on theory & new architectures, see also Part II on…

Underneath a temple in the ancient ruined city of Taposiris Magna on the Egyptian coast, archaeologists discovered a vast, spectacular tunnel in 2022, a tunnel that experts called a "geometric miracle".During ongoing excavations and exploration of the temple, Kathleen Martinez of the University of Santo Domingo in the Dominican Republic and colleagues uncovered the structure 13 meters (43 feet) below the ground. The 2-meter tall tunnel had been hewn through an incredible 1,305 meters (4,281 feet) of sandstone.Its design,…

The gray “hat” polykite tile is an “einstein”, an aperiodic monotile. In other words, copies of this tile may be assembled into tilings of the plane (the tile “admits” tilings), yet copies of the tile cannot form periodic tilings, tilings that have translational symmetry. In fact, the tile admits uncountably many tilings. Credit: arXiv (2023). DOI: 10.48550/arxiv.2303.10798 A quartet of mathematicians from Yorkshire…

Scalable and equivariant spherical CNNs by DISCO convolutionsNo existing spherical convolutional neural network (CNN) framework is both computationally scalable and rotationally equivariant. Continuous approaches capture rotational equivariance but are often prohibitively computationally demanding. Discrete approaches offer more favorable computational performance but at the cost of equivariance. We develop a hybrid discrete-continuous (DISCO) group convolution that is simultaneously equivariant and computationally…

Continuous vs discrete approaches on the sphereIdeally geometric deep learning techniques on groups would encode equivariance to group transformations, to provide well-behaved representation spaces and excellent performance, while also being computationally efficient. However, no single approach provides both of these desirable properties. Continuous approaches offer excellent equivariance but with a very large computational cost. Discrete approaches are typically relatively computationally efficient but sacrifice…

Although autism spectrum disorder (ASD) can be diagnosed at any age, symptoms generally appear in the first two years of a child’s life. The earlier ASD is diagnosed, the sooner treatment and access to relevant services can start. A new study has found that checking toddlers’ visual attention to geometric images is a reliable biomarker for the early identification of autism.Led by Karen Pierce, PhD, from the University of California, San Diego, the study expanded upon Pierce’s previous research, which had examined the…

Underneath a temple in the ancient ruined city of Taposiris Magna on the Egyptian coast, archaeologists have uncovered a vast, spectacular tunnel that experts are referring to as a "geometric miracle".During ongoing excavations and exploration of the temple, Kathleen Martinez of the University of Santo Domingo in the Dominican Republic and colleagues uncovered the structure 13 meters (43 feet) below the ground. The 2-meter tall tunnel had been hewn through an incredible 1,305 meters (4,281 feet) of sandstone.Its design,…