Oncology & Cancer

Blood-based biomarkers for brain tumours

Researchers at the Indian Institute of Science (IISc), along with collaborators, have identified potential blood-based biomarkers to predict disease progression and survival times in those with late-stage brain tumors.

Oncology & Cancer

New pathways to target breast cancer

A pathway helping the breast cancer protein BRCA1 repair damaged DNA has been identified by University of Queensland researchers in a study that will inform future targeted therapies.

Oncology & Cancer

Breaking through the tumor's protective shield

The immune system protects the body from cancer. To protect healthy body cells from its own immune system, they have developed a protective shield: the protein CD47 is a so called "don't eat me" signal, which tells the immune ...

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In mathematics, specifically in topology, a surface is a two-dimensional topological manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space R3 — for example, the surface of a ball or bagel. On the other hand, there are surfaces which cannot be embedded in three-dimensional Euclidean space without introducing singularities or intersecting itself — these are the unorientable surfaces.

To say that a surface is "two-dimensional" means that, about each point, there is a coordinate patch on which a two-dimensional coordinate system is defined. For example, the surface of the Earth is (ideally) a two-dimensional sphere, and latitude and longitude provide coordinates on it — except at the International Date Line and the poles, where longitude is undefined. This example illustrates that not all surfaces admits a single coordinate patch. In general, multiple coordinate patches are needed to cover a surface.

Surfaces find application in physics, engineering, computer graphics, and many other disciplines, primarily when they represent the surfaces of physical objects. For example, in analyzing the aerodynamic properties of an airplane, the central consideration is the flow of air along its surface.

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