Proof theoryProof theory is a major branch of mathematical logic and theoretical computer science within which proofs are treated as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively-defined data structures such as lists, boxed lists, or trees, which are constructed according to the axioms and rules of inference of a given logical system. Consequently, proof theory is syntactic in nature, in contrast to model theory, which is semantic in nature.
Mathematical proofA mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference. Proofs are examples of exhaustive deductive reasoning which establish logical certainty, to be distinguished from empirical arguments or non-exhaustive inductive reasoning which establish "reasonable expectation".
Grid energy storageGrid energy storage (also called large-scale energy storage) is a collection of methods used for energy storage on a large scale within an electrical power grid. Electrical energy is stored during times when electricity is plentiful and inexpensive (especially from intermittent power sources such as renewable electricity from wind power, tidal power and solar power) or when demand is low, and later returned to the grid when demand is high, and electricity prices tend to be higher.
Energy storageEnergy storage is the capture of energy produced at one time for use at a later time to reduce imbalances between energy demand and energy production. A device that stores energy is generally called an accumulator or battery. Energy comes in multiple forms including radiation, chemical, gravitational potential, electrical potential, electricity, elevated temperature, latent heat and kinetic. Energy storage involves converting energy from forms that are difficult to store to more conveniently or economically storable forms.
Battery storage power stationA battery storage power station is a type of energy storage power station that uses a group of batteries to store electrical energy. Battery storage is the fastest responding dispatchable source of power on electric grids, and it is used to stabilise those grids, as battery storage can transition from standby to full power in under a second to deal with grid contingencies. Battery storage power stations are generally designed to be able to output at their full rated power for several hours.
CERNThe European Organization for Nuclear Research, known as CERN (sɜːrn; sɛʁn; Conseil européen pour la recherche nucléaire), is an intergovernmental organization that operates the largest particle physics laboratory in the world. Established in 1954, it is based in a northwestern suburb of Geneva, on the France–Switzerland border. It comprises 23 member states. Israel, admitted in 2013, is the only non-European full member. CERN is an official United Nations General Assembly observer.
CPU cacheA CPU cache is a hardware cache used by the central processing unit (CPU) of a computer to reduce the average cost (time or energy) to access data from the main memory. A cache is a smaller, faster memory, located closer to a processor core, which stores copies of the data from frequently used main memory locations. Most CPUs have a hierarchy of multiple cache levels (L1, L2, often L3, and rarely even L4), with different instruction-specific and data-specific caches at level 1.
Electrical gridAn electrical grid is an interconnected network for electricity delivery from producers to consumers. Electrical grids vary in size and can cover whole countries or continents. It consists of: power stations: often located near energy and away from heavily populated areas electrical substations to step voltage up or down electric power transmission to carry power long distances electric power distribution to individual customers, where voltage is stepped down again to the required service voltage(s).
Proof (truth)A proof is sufficient evidence or a sufficient argument for the truth of a proposition. The concept applies in a variety of disciplines, with both the nature of the evidence or justification and the criteria for sufficiency being area-dependent. In the area of oral and written communication such as conversation, dialog, rhetoric, etc., a proof is a persuasive perlocutionary speech act, which demonstrates the truth of a proposition.
Grid-tied electrical systemA grid-tied electrical system, also called tied to grid or grid tie system, is a semi-autonomous electrical generation or grid energy storage system which links to the mains to feed excess capacity back to the local mains electrical grid. When insufficient electricity is available, electricity drawn from the mains grid can make up the shortfall. Conversely when excess electricity is available, it is sent to the main grid.
Smart gridA smart grid is an electrical grid which includes a variety of operation and energy measures including: Advanced metering infrastructure (of which smart meters are a generic name for any utility side device even if it is more capable e.g. a fiber optic router) Smart distribution boards and circuit breakers integrated with home control and demand response (behind the meter from a utility perspective) Load control switches and smart appliances, often financed by efficiency gains on municipal programs (e.g.
Vehicle-to-gridVehicle-to-grid (V2G), also known as Vehicle-to-home (V2H), describes a system in which plug-in electric vehicles (PEV) sell demand response services to the grid. Demand services are either delivering electricity or by reducing their charging rate. Demand services reduce pressure on the grid, which might otherwise experience disruption from load variations. Vehicle-to-load (V2L) and Vehicle-to-vehicle (V2V) are related, but the AC phase is not sychronised with the grid, so the power is only available to an "off grid" load.
Proof by contradictionIn logic, proof by contradiction is a form of proof that establishes the truth or the validity of a proposition, by showing that assuming the proposition to be false leads to a contradiction. Although it is quite freely used in mathematical proofs, not every school of mathematical thought accepts this kind of nonconstructive proof as universally valid. More broadly, proof by contradiction is any form of argument that establishes a statement by arriving at a contradiction, even when the initial assumption is not the negation of the statement to be proved.
Proof calculusIn mathematical logic, a proof calculus or a proof system is built to prove statements. A proof system includes the components: Language: The set L of formulas admitted by the system, for example, propositional logic or first-order logic. Rules of inference: List of rules that can be employed to prove theorems from axioms and theorems. Axioms: Formulas in L assumed to be valid. All theorems are derived from axioms. Usually a given proof calculus encompasses more than a single particular formal system, since many proof calculi are under-determined and can be used for radically different logics.
Structural proof theoryIn mathematical logic, structural proof theory is the subdiscipline of proof theory that studies proof calculi that support a notion of analytic proof, a kind of proof whose semantic properties are exposed. When all the theorems of a logic formalised in a structural proof theory have analytic proofs, then the proof theory can be used to demonstrate such things as consistency, provide decision procedures, and allow mathematical or computational witnesses to be extracted as counterparts to theorems, the kind of task that is more often given to model theory.
Large Hadron ColliderThe Large Hadron Collider (LHC) is the world's largest and highest-energy particle collider. It was built by the European Organization for Nuclear Research (CERN) between 1998 and 2008 in collaboration with over 10,000 scientists and hundreds of universities and laboratories, as well as more than 100 countries. It lies in a tunnel in circumference and as deep as beneath the France–Switzerland border near Geneva. The first collisions were achieved in 2010 at an energy of 3.
Multi-core processorA multi-core processor is a microprocessor on a single integrated circuit with two or more separate processing units, called cores, each of which reads and executes program instructions. The instructions are ordinary CPU instructions (such as add, move data, and branch) but the single processor can run instructions on separate cores at the same time, increasing overall speed for programs that support multithreading or other parallel computing techniques.
Constructive proofIn mathematics, a constructive proof is a method of proof that demonstrates the existence of a mathematical object by creating or providing a method for creating the object. This is in contrast to a non-constructive proof (also known as an existence proof or pure existence theorem), which proves the existence of a particular kind of object without providing an example. For avoiding confusion with the stronger concept that follows, such a constructive proof is sometimes called an effective proof.
Broadwell (microarchitecture)Broadwell is the fifth generation of the Intel Core Processor. It is Intel's codename for the 14 nanometer die shrink of its Haswell microarchitecture. It is a "tick" in Intel's tick–tock principle as the next step in semiconductor fabrication. Like some of the previous tick-tock iterations, Broadwell did not completely replace the full range of CPUs from the previous microarchitecture (Haswell), as there were no low-end desktop CPUs based on Broadwell.
Intel Core (microarchitecture)The Intel Core microarchitecture (provisionally referred to as Next Generation Micro-architecture, and developed as Merom) is a multi-core processor microarchitecture launched by Intel in mid-2006. It is a major evolution over the Yonah, the previous iteration of the P6 microarchitecture series which started in 1995 with Pentium Pro. It also replaced the NetBurst microarchitecture, which suffered from high power consumption and heat intensity due to an inefficient pipeline designed for high clock rate.
