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P versus NP problem

P versus NP problem
Diagram of complexity classes provided that P≠NP. The existence of problems within NP but outside both P and NP-complete, under that assumption, was established by Ladner's theorem.[1] The P versus NP problem is a major unsolved problem in computer science. Informally, it asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer. It was essentially first mentioned in a 1956 letter written by Kurt Gödel to John von Neumann. Gödel asked whether a certain NP complete problem could be solved in quadratic or linear time.[2] The precise statement of the P=NP problem was introduced in 1971 by Stephen Cook in his seminal paper "The complexity of theorem proving procedures"[3] and is considered by many to be the most important open problem in the field.[4] It is one of the seven Millennium Prize Problems selected by the Clay Mathematics Institute to carry a US$1,000,000 prize for the first correct solution. Context[edit] Related:  ComputationalAIMachine learning/nlp/AI

Dilawar (torture victim) Dilawar (born c. 1979 – December 10, 2002), also known as Dilawar of Yakubi, was an Afghan taxi driver who was tortured to death by US army soldiers at the Bagram Collection Point, a US military detention center in Afghanistan. He arrived at the prison on December 5, 2002, and was declared dead 5 days later. His death was declared a homicide and investigated and prosecuted in the Bagram torture and prisoner abuse trials. The award winning documentary Taxi to the Dark Side focuses on the murder of Dilawar.[1] The New York Times reported on May 20, 2005 that:[2] A sketch by Thomas V. The various accounts of torture [3] have been detailed as follows: A black hood pulled over his head limiting his ability to breatheKnee strikes to the abdomenOver 100 peroneal strikes (a nerve behind the kneecap)Shoved against a wallPulled by his beardHis bare feet stepped onKicks to the groinChained to the ceiling for extended hours, depriving him of sleepSlammed his chest into a table front Alicia A. Duane M.

Computational complexity theory Computational complexity theory is a branch of the theory of computation in theoretical computer science and mathematics that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other. A computational problem is understood to be a task that is in principle amenable to being solved by a computer, which is equivalent to stating that the problem may be solved by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used. The theory formalizes this intuition, by introducing mathematical models of computation to study these problems and quantifying the amount of resources needed to solve them, such as time and storage. Closely related fields in theoretical computer science are analysis of algorithms and computability theory. Computational problems[edit] Problem instances[edit] Turing machine[edit]

Non-Human Consciousness Exists Say Experts. Now What? Non-Human Consciousness Exists Say Experts. Now What? Phillip Low at Singularity University Have you ever considered the consciousness, or unconsciousness, of your dog? Earlier this month, some of the leading scientists from around the world congregated at the Hotel Du Vin in Cambridge to discuss the evidence that has amassed over the years. the declaration of consciousness Organized by Philip Low, CEO of NeuroVigil and inventor of the iBrain, the group consisted of 25 of the planet’s top minds on the mind, including honorary guest Stephen Hawking. This announcement arises in a manner similar to the Pluto files in 2006, when the world's leading astronomer's demoted Pluto from planet to "dwarf planet". As mankind continues to explore the universe, many more discoveries will prompt an official announcement such as the one Phillip Low delivered this week at Singularity University. For more on the conference and the Cambridge declaration, check out

NP - Wikipedia From Wikipedia, the free encyclopedia NP may refer to: Arts and entertainment[edit] Organizations[edit] Places[edit] NP postcode area, Newport, Wales, United KingdomNepal (ISO 3166-1 alpha-2 country code NP) .np, the country code top level domain (ccTLD) for NepalNichols Point, Australia Science, technology and mathematics[edit] Biology and medicine[edit] Mathematics and computer science[edit] Physics and chemistry[edit] NP junction or PN junction, the simplest electronic device, used to make diodes and transistorsNeper (Np), a dimensionless logarithmic unit for ratios of measurements of physical field and power quantitiesNeptunium, a chemical element with symbol NpPower number (Np), a dimensionless number relating the resistance force to the inertia force Other uses in science and technology[edit] Other uses[edit]

Rotfrontkämpferbund RFB leaders Thälmann and Leow in Berlin, June 1927 The Roter Frontkämpfer-Bund RFB (English: Alliance of Red Front-Fighters) was officially a non-party and legally registered association (German: Eingetragener Verein e.V.) but in practice a paramilitary organization under the leadership of the Communist Party of Germany during the Weimar Republic. The first local groups of the RFB were established in July 1924 and Ernst Thälmann was elected the first leader of the federal committee during the first nationwide meeting in February 1925 in Berlin. After the takeover of the political power in Germany by the Nazis in 1933, former RFB-members were among the first arrested and incarcerated in the concentration camps of the Sturmabteilung (SA). After the end of World War II former RFB-members such as Erich Honecker and Erich Mielke were actively involved in the creation of the first police and military units of the German Democratic Republic (GDR). Formation[edit] RFB meeting in Berlin, May 1928 Title: The Mystery of the Binary Author: Viznut Originally published in the [ALT] magazine issue 0x0000 The subcultures of computing are very young. There are no legends nor values that come from the distant past. No ancient mysticism, no generations-old symbols that have deep emotional effects. Even the old and classical things tend to be quite recent. Stone-age binary counting We are so completely surrounded by decimal numbers that most people believe humans were "built" to count in base ten: "we have ten fingers, you know." Divine binary protocols The human mind has a strange relationship with randomness. The Two Symbols There's a great deal of similarity between the African and Chinese notations for binary combinations: both use vertical piles where a single bit is designated by one or two "somethings", such as sticks, stones or seeds. The Eight Trigrams This figure shows the eight trigrams (the three-bit numbers) in the millennia-old Chinese Xiantian arrangement. The Sixteen Tetragrams

Automated Grading Software In Development To Score Essays As Accurately As Humans Roboreaders that can score essays in standardized tests could also help teachers grade and students becomes better writers. April 30 marks the deadline for a contest challenging software developers to create an automated scorer of student essays, otherwise known as a roboreader, that performs as good as a human expert grader. In January, the Hewlett Foundation of Hewlett-Packard fame introduced the Automated Student Assessment Prize (ASAP…get it?) offering up $100,000 in awards to “data scientists and machine learning specialists” to develop the application. The contest is only the first of three, with the others aimed at developing automated graders for short answers and charts and graphs. Developers of reliable roboreaders will not just rake in massive loads of cash thrown at them by standardized testing companies, educational publishers, and school districts, but they’ll potentially change the way writing is taught forever. [Media: Eduify] [Sources: Citypages, Kaggle, PBS, Reuters]

NP-hardness - Wikipedia Definition[edit] A decision problem H is NP-hard when for every problem L in NP, there is a polynomial-time reduction from L to H[1]:80 An equivalent definition is to require that every problem L in NP can be solved in polynomial time by an oracle machine with an oracle for H.[7] Informally, we can think of an algorithm that can call such an oracle machine as a subroutine for solving H, and solves L in polynomial time, if the subroutine call takes only one step to compute. Another definition is to require that there is a polynomial-time reduction from an NP-complete problem G to H.[1]:91 As any problem L in NP reduces in polynomial time to G, L reduces in turn to H in polynomial time so this new definition implies the previous one. Awkwardly, it does not restrict the class NP-hard to decision problems, for instance it also includes search problems, or optimization problems. Consequences[edit] If P ≠ NP, then NP-hard problems cannot be solved in polynomial time. Examples[edit] NP-hard NP-easy

Fractal antenna An example of a fractal antenna: a space-filling curve called a Minkowski Island (ref 1). Such fractal antennas are also referred to as multilevel and space filling curves, but the key aspect lies in their repetition of a motif over two or more scale sizes,[1] or "iterations". For this reason, fractal antennas are very compact, multiband or wideband, and have useful applications in cellular telephone and microwave communications. A good example of a fractal antenna as a spacefilling curve is in the form of a shrunken fractal helix.[2] Here, each line of copper is just a small fraction of a wavelength. A fractal antenna's response differs markedly from traditional antenna designs, in that it is capable of operating with good-to-excellent performance at many different frequencies simultaneously. This makes the fractal antenna an excellent design for wideband and multiband applications. Log periodic antennas and fractals[edit] Fractal element antennas and performance[edit] Other uses[edit] 1.