An algebraic differential equation is a type of differential equation that involves algebraic expressions in the unknown function and its derivatives, but does not involve any transcendental functions like exponentials, logarithms, or trigonometric functions. Essentially, it is a differential equation where the relationship between the function and its derivatives can be expressed entirely in terms of polynomials or rational functions.

The Axiom of Determinacy (AD) is a principle in set theory that relates to the behavior of certain games and the existence of winning strategies in those games. More specifically, the Axiom of Determinacy posits that for certain kinds of infinite games involving two players, one player can always have a winning strategy.

The Runge-Gross theorem is a fundamental result in the field of many-body quantum mechanics, specifically in the context of time-dependent density functional theory (TDDFT). It establishes a mathematical connection between the time-dependent electron density of a system and the external potential acting on it.

pytorch.org/vision/0.13/models.html has a minimal runnable example adapted to python/pytorch/resnet_demo.py.

That example uses a ResNet pre-trained on the COCO dataset to do some inference, tested on Ubuntu 22.10:This first downloads the model, which is currently 167 MB.

We know it is COCO because of the docs: pytorch.org/vision/0.13/models/generated/torchvision.models.detection.fasterrcnn_resnet50_fpn_v2.html which explains that is an alias for:

The runtime is relatively slow on P51, about 4.7s.

After it finishes, the program prints the recognized classes:so we get the expected bird, but also the more intriguing banana.

By looking at the output image with bounding boxes, we understand where the banana came from!

Pulay stress is a phenomenon that arises in electronic structure calculations, particularly in the context of density functional theory (DFT) and other wavefunction-based methods. It occurs due to the finite basis set used to represent the electronic wavefunctions in these calculations. When performing electronic structure calculations, especially for periodic systems (such as crystals), one typically uses a finite basis set (like plane waves or localized atomic orbitals) to approximate the electronic wavefunctions.

The Harris functional, often referred to in the context of mathematical analysis and calculus of variations, is associated with a certain type of energy integral. It was introduced by the mathematician C. A. Harris in the context of studying minimal surfaces and surface area functionals. In simple terms, the Harris functional represents a mathematical tool used for characterizing energy configurations, particularly for problems involving surfaces or interfaces in variational calculus.

Density Functional Theory (DFT) software refers to computational tools and programs used to perform quantum mechanical calculations based on DFT principles. DFT is a widely used method in physics, chemistry, and materials science for studying the electronic structure of many-body systems, particularly atoms, molecules, and the condensed phases of matter.

The Demidov Prize is a prestigious award in the field of science, primarily recognizing outstanding achievements in the fields of natural sciences and engineering. Established in 1884, the prize is named after the Demidov family, notable patrons of science and industry in Russia. The award is presented by the Russian Academy of Sciences and is typically given to researchers and scientists for their significant contributions to advancing knowledge and innovation.

Sydney Chapman (1888–1970) was a notable British mathematician and geophysicist, renowned for his work in the fields of mathematics, astrophysics, and atmospheric science. He made significant contributions to the understanding of atmospheric physics, especially in areas related to the Earth's ionosphere, gas dynamics, and the behavior of gases in the atmosphere.

E. W. Hobson refers to Edward William Hobson, a prominent British mathematician known for his contributions to various fields within mathematics, particularly in the areas of analysis and mathematical physics. He is often associated with the study of series, potential theory, and the theory of functions. Hobson's work includes important texts and research papers that have influenced both theoretical mathematics and its applications. If you're referring to a different context for "E.W. Hobson," please provide more details for clarification!

A Weakly Interacting Massive Particle (WIMP) is a hypothetical elementary particle that is a candidate for dark matter, which makes up a significant fraction of the universe's mass-energy content. WIMPs are predicted to have mass and interact primarily through the weak nuclear force and gravity, but not through electromagnetic interactions, which means they do not emit, absorb, or reflect light, making them difficult to detect directly.

Warm dark matter (WDM) is a theoretical form of dark matter that falls in energy and mass characteristics between cold dark matter (CDM) and hot dark matter (HDM). The primary distinctions among these categories relate to the speed of the particles and their thermal properties during the early universe.

In particle physics, WISP stands for "Weakly Interacting Slim Particle." Wisps are hypothetical particles that are considered as candidates for dark matter. They are characterized by their weak interactions with standard model particles, making them difficult to detect directly. WISPs usually include particles like axions, hidden photons, or other similar entities that could constitute non-baryonic matter in the universe.

Self-interacting dark matter (SIDM) is a theoretical alternative to the more commonly discussed weakly interacting massive particles (WIMPs) as a candidate for dark matter. The key feature of SIDM is that the particles making up dark matter can interact with each other through a force other than gravity, which is not the case for most traditional dark matter models.