Hilbert schemeIn algebraic geometry, a branch of mathematics, a Hilbert scheme is a scheme that is the parameter space for the closed subschemes of some projective space (or a more general projective scheme), refining the Chow variety. The Hilbert scheme is a disjoint union of projective subschemes corresponding to Hilbert polynomials. The basic theory of Hilbert schemes was developed by . Hironaka's example shows that non-projective varieties need not have Hilbert schemes.
Data qualityData quality refers to the state of qualitative or quantitative pieces of information. There are many definitions of data quality, but data is generally considered high quality if it is "fit for [its] intended uses in operations, decision making and planning". Moreover, data is deemed of high quality if it correctly represents the real-world construct to which it refers. Furthermore, apart from these definitions, as the number of data sources increases, the question of internal data consistency becomes significant, regardless of fitness for use for any particular external purpose.
Spontaneous symmetry breakingSpontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state spontaneously ends up in an asymmetric state. In particular, it can describe systems where the equations of motion or the Lagrangian obey symmetries, but the lowest-energy vacuum solutions do not exhibit that same symmetry. When the system goes to one of those vacuum solutions, the symmetry is broken for perturbations around that vacuum even though the entire Lagrangian retains that symmetry.
Data lakeA data lake is a system or repository of data stored in its natural/raw format, usually object blobs or files. A data lake is usually a single store of data including raw copies of source system data, sensor data, social data etc., and transformed data used for tasks such as reporting, visualization, advanced analytics and machine learning. A data lake can include structured data from relational databases (rows and columns), semi-structured data (CSV, logs, XML, JSON), unstructured data (emails, documents, PDFs) and binary data (images, audio, video).
Raw dataRaw data, also known as primary data, are data (e.g., numbers, instrument readings, figures, etc.) collected from a source. In the context of examinations, the raw data might be described as a raw score (after test scores). If a scientist sets up a computerized thermometer which records the temperature of a chemical mixture in a test tube every minute, the list of temperature readings for every minute, as printed out on a spreadsheet or viewed on a computer screen are "raw data".
Group schemeIn mathematics, a group scheme is a type of object from algebraic geometry equipped with a composition law. Group schemes arise naturally as symmetries of schemes, and they generalize algebraic groups, in the sense that all algebraic groups have group scheme structure, but group schemes are not necessarily connected, smooth, or defined over a field. This extra generality allows one to study richer infinitesimal structures, and this can help one to understand and answer questions of arithmetic significance.
X-ray crystallographyX-ray crystallography is the experimental science determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to diffract into many specific directions. By measuring the angles and intensities of these diffracted beams, a crystallographer can produce a three-dimensional picture of the density of electrons within the crystal. From this electron density, the mean positions of the atoms in the crystal can be determined, as well as their chemical bonds, their crystallographic disorder, and various other information.
Data and information visualizationData and information visualization (data viz or info viz) is the practice of designing and creating easy-to-communicate and easy-to-understand graphic or visual representations of a large amount of complex quantitative and qualitative data and information with the help of static, dynamic or interactive visual items.
SymmetrySymmetry () in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term has a more precise definition and is usually used to refer to an object that is invariant under some transformations, such as translation, reflection, rotation, or scaling. Although these two meanings of the word can sometimes be told apart, they are intricately related, and hence are discussed together in this article.
Microcrystal electron diffractionMicrocrystal electron diffraction, or MicroED, is a CryoEM method that was developed by the Gonen laboratory in late 2013 at the Janelia Research Campus of the Howard Hughes Medical Institute. MicroED is a form of electron crystallography where thin 3D crystals are used for structure determination by electron diffraction. Prior to this demonstration, macromolecular (protein) electron crystallography was only used on 2D crystals, for example.
