Abstract: Procedural noise functions are fundamental tools in computer graphics used for synthesizing virtual geometry and texture patterns. Ideally, a procedural noise function should be compact, ...

This is a small collection of formally verified junk theorems provable in Lean 4 + Mathlib that, in my experience, are quite surprising and upsetting to mathematicians who are not familiar with type ...

The central dogma of molecular biology suggests that the primary role of RNA is to convert the information stored in DNA into proteins. In reality, there is much more to the RNA story. However, in the ...

Lysosomes are dynamic organelles that receive membrane traffic input from the secretory, endocytic, autophagic and phagocytic pathways. They can also fuse with the plasma membrane. Live-cell imaging ...

Established in 1945 under the Charter of the United Nations, the General Assembly occupies a central position as the chief deliberative, policymaking and representative organ of the United Nations.

The firebase-functions package provides an SDK for defining Cloud Functions for Firebase. Cloud Functions is a hosted, private, and scalable Node.js environment where you can run JavaScript code. The ...

The trigeminal nerve is the largest of the 12 cranial nerves and has both sensory and motor functions. The trigeminal nerve has three parts: the ophthalmic, maxillary, and mandibular nerves which ...

The cervix produces mucus during ovulation to help sperm travel to the uterus. During labor, the cervix opens to allow the baby to pass through the birth canal. Changes in the cervix during menopause ...

The endocrine system is a complex network of glands and organs. It uses hormones to control and coordinate your body's metabolism, energy level, reproduction, growth and development, and response to ...

Persistent Link: https://ieeexplore.ieee.org/servlet/opac?punumber=9970761 ...

Haglund recently proposed a combinatorial interpretation of the modified Macdonald polynomials H̃μ. We give a combinatorial proof of this conjecture, which establishes the existence and integrality of ...