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John - Wikipedia

Look up John or john in Wiktionary, the free dictionary. John is a common English name and surname: John may also refer to: New Testament Works People John the Baptist (died c. 30  AD), regarded as a prophet and the forerunner of Jesus Christ Authorship of the Johannine works of the New Testament, sometimes identified as: John the Apostle (lived c. 30  AD), one of the twelve apostles of Jesus John the Evangelist, assigned author of the Fourth Gospel, once identified with the Apostle John of Patmos, also known as John the Divine or John the Revelator, the author of the Book of Revelation, once identified with the Apostle John the Presbyter,

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black hole | Definition, Formation, & Facts | Britannica

A black hole can be formed by the death of a massive star.

Justin Bieber - Wikipedia

The song reached number 12 on the Canadian Hot 100 during its first week of release in July 2009 and later peaked at number 17 on the Billboard Hot 100 chart in the United States.

Wikipedia - Wikipedia

The project, which is expanded and maintained by a community of volunteer editors using a wiki-based editing system, is the largest general reference work on the Internet and one of the 15 most popular websites as ranked by Alexa Internet; in 2021, it ranked as the 13th most visited.

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Without loss of generality we can assume that aaa and bbb are non-negative integers, because we can always do this: gcd⁡(a,b)=gcd⁡(∣a∣,∣b∣)\gcd(a,b)=\gcd\big(\lvert a \rvert, \lvert b \rvert\big)gcd(a,b)=gcd(∣a∣,∣b∣). Let's define the sequences {qi},{ri},{si},{ti}\{q_i\},\{r_i\},\{s_i\},\{t_i\}{qi​},{ri​},{si​},{ti​} with r0=a,r1=br_0=a,r_1=br0​=a,r1​=b. Set i←2i \gets 2i←2, and increase it at the end of every iteration. We're going to find in every iteration qi,ri,si,tiq_i, r_i, s_i, t_iqi​,ri​,si​,ti​ such that ri−2=ri−1qi+rir_{i-2}=r_{i-1}q_i+r_iri−2​=ri−1​qi​+ri​, 0≤ri<ri−10 \leq r_i < r_{i-1}0≤ri​<ri−1​ using the division algorithm. We also want to write rir_iri​ as a linear combination of aaa and bbb, i.e., ri=sia+tibr_i=s_i a+t_i bri​=si​a+ti​b. But ri=ri−2−ri−1qir_i=r_{i-2}-r_{i-1}q_iri​=ri−2​−ri−1​qi​, so ri=si−2a+ti−2b−(si−1a+ti−1b)qi=(si−2−si−1qi)a+(ti−2−ti−1qi)b.r_i=s_{i-2}a+t_{i-2}b-(s_{i-1}a+t_{i-1}b)q_i=(s_{i-2}-s_{i-1}q_i)a+(t_{i-2}-t_{i-1}q_i)b.ri​=si−2​a+ti−2​b−(si−1​a+ti−1​b)qi​=(si−2​−si−1​qi​)a+(ti−2​−ti−1​qi​)b. Hence, we obtain si=si−2−si−1qis_i=s_{i-2}-s_{i-1}q_isi​=si−2​−si−1​qi​ and ti=ti−2−ti−1qit_i=t_{i-2}-t_{i-1}q_iti​=ti−2​−ti−1​qi​. Now, we have to find the initial

Extended Euclidean Algorithm | Brilliant Math & Science Wiki

Without loss of generality we can assume that aaa and bbb are non-negative integers, because we can always do this: gcd⁡(a,b)=gcd⁡(∣a∣,∣b∣)\gcd(a,b)=\gcd\big(\lvert a \rvert, \lvert b \rvert\big)gcd(a,b)=gcd(∣a∣,∣b∣). Let's define the sequences {qi},{ri},{si},{ti}\{q_i\},\{r_i\},\{s_i\},\{t_i\}{qi​},{ri​},{si​},{ti​} with r0=a,r1=br_0=a,r_1=br0​=a,r1​=b. Set i←2i \gets 2i←2, and increase it at the end of every iteration. We're going to find in every iteration qi,ri,si,tiq_i, r_i, s_i, t_iqi​,ri​,si​,ti​ such that ri−2=ri−1qi+rir_{i-2}=r_{i-1}q_i+r_iri−2​=ri−1​qi​+ri​, 0≤ri<ri−10 \leq r_i < r_{i-1}0≤ri​<ri−1​ using the division algorithm. We also want to write rir_iri​ as a linear combination of aaa and bbb, i.e., ri=sia+tibr_i=s_i a+t_i bri​=si​a+ti​b. But ri=ri−2−ri−1qir_i=r_{i-2}-r_{i-1}q_iri​=ri−2​−ri−1​qi​, so ri=si−2a+ti−2b−(si−1a+ti−1b)qi=(si−2−si−1qi)a+(ti−2−ti−1qi)b.r_i=s_{i-2}a+t_{i-2}b-(s_{i-1}a+t_{i-1}b)q_i=(s_{i-2}-s_{i-1}q_i)a+(t_{i-2}-t_{i-1}q_i)b.ri​=si−2​a+ti−2​b−(si−1​a+ti−1​b)qi​=(si−2​−si−1​qi​)a+(ti−2​−ti−1​qi​)b. Hence, we obtain si=si−2−si−1qis_i=s_{i-2}-s_{i-1}q_isi​=si−2​−si−1​qi​ and ti=ti−2−ti−1qit_i=t_{i-2}-t_{i-1}q_iti​=ti−2​−ti−1​qi​. Now, we have to find the initial

Canada - Wikipedia

Canada seeks to expand its ties to Pacific Rim economies through membership in the Asia-Pacific Economic Cooperation forum (APEC).

Electroencephalography - Wikipedia

Electroencephalography (EEG) is an electrophysiological monitoring method to record electrical activity of the brain.

3D reconstruction - Wikipedia

3D reconstruction through monocular cues is simple and quick, and only one appropriate digital image is needed thus only one camera is adequate.

Evolution - Wikipedia

An example of such a speciation event is when the plant species Arabidopsis thaliana and Arabidopsis arenosa crossbred to give the new species Arabidopsis suecica.

Brain-computer interface - Wikipedia

The EPOC is the first commercial BCI to use dry sensor technology, which can be dampened with a saline solution for a better connection.

Uncertainty principle - Wikipedia

Also, it must be stressed that the Heisenberg formulation is not taking into account the intrinsic statistical errors There is increasing experimental evidence that the total quantum uncertainty cannot be described by the Heisenberg term alone, but requires the presence of all the three terms of the Ozawa inequality.

Quantum mechanics - Wikipedia

The Mach-Zehnder interferometer (MZI) illustrates the concepts of superposition and interference with linear algebra in dimension 2, rather than differential equations.

World War II - Wikipedia

By late May 1944, the Soviets had liberated Crimea, largely expelled Axis forces from Ukraine, and made incursions into Romania, which were repulsed by the Axis troops.

Algorithm - Wikipedia

An algorithm in the form of a differential equation that operates continuously on the data, running on an analog computer.

Computer vision - Wikipedia

More advanced systems for missile guidance send the missile to an area rather than a specific target, and target selection is made when the missile reaches the area based on locally acquired image data.

Pragmatics - Wikipedia

As mentioned, these meanings are brought about through the relationship between the signified and the signifier.

Feature learning - Wikipedia

These p singular vectors are the feature vectors learned from the input data, and they represent directions along which the data has the largest variations.

Unsupervised learning - Wikipedia

Clustering methods include: hierarchical clustering, k-means, mixture models, DBSCAN, and OPTICS algorithm Anomaly detection methods include: Local Outlier Factor, and Isolation Forest

Supervised learning - Wikipedia

There are several algorithms that identify noisy training examples and removing the suspected noisy training examples prior to training has decreased generalization error with statistical significance.

Machine translation - Wikipedia

Although there have been concerns about machine translation's accuracy, Dr. Ana Nino of the University of Manchester has researched some of the advantages in utilizing machine translation in the classroom.

Machine learning - Wikipedia

Machine learning (ML) is the study of computer algorithms that improve automatically through experience.

Semi-supervised learning - Wikipedia

Some methods for semi-supervised learning are not intrinsically geared to learning from both unlabeled and labeled data, but instead make use of unlabeled data within a supervised learning framework.

Linguistics - Wikipedia

As constructed popularly through the Sapir-Whorf hypothesis, relativists believe that the structure of a particular language is capable of influencing the cognitive patterns through which a person shapes his or her world view.

Information engineering (field) - Wikipedia

Information engineering is the engineering discipline that deals with the generation, distribution, analysis, and use of information, data, and knowledge in systems.

Self-driving car - Wikipedia

The British law interprets the meaning of "automated vehicle" based on the interpretation section related to a vehicle "driving itself" and an insured vehicle.

Computer science - Wikipedia

This branch of computer science aims to manage networks between computers worldwide.

Natural language processing - Wikipedia

Though natural language processing tasks are closely intertwined, they can be subdivided into categories for convenience.

Artificial intelligence - Wikipedia

Their work revived the non-symbolic point of view of the early cybernetics researchers of the 1950s and reintroduced the use of control theory in AI.

Last universal common ancestor - Wikipedia

These were assembled from free amino acids by translation of a messenger RNA via a mechanism of ribosomes, transfer RNAs, and a group of related proteins.

Event horizon - Wikipedia

If the rope is lowered quickly (perhaps even in freefall), then indeed the observer at the bottom of the rope can touch and even cross the event horizon.

General relativity - Wikipedia

The cosmic censorship hypothesis states that all realistic future singularities (no perfect symmetries, matter with realistic properties) are safely hidden away behind a horizon, and thus invisible to all distant observers.

Star - Wikipedia

Astronomers label all elements heavier than helium "metals", and call the chemical concentration of these elements in a star, its metallicity.

Gravity - Wikipedia

The force of gravity on Earth is the resultant (vector sum) of two forces: (a) The gravitational attraction in accordance with Newton's universal law of gravitation, and (b) the centrifugal force, which results from the choice of an earthbound, rotating frame of reference.

Black hole - Wikipedia

In this way, astronomers have identified numerous stellar black hole candidates in binary systems, and established that the radio source known as Sagittarius A*, at the core of the Milky Way galaxy, contains a supermassive black hole of about 4.3 million solar masses.

DNA - Wikipedia

This ancient RNA world where nucleic acid would have been used for both catalysis and genetics may have influenced the evolution of the current genetic code based on four nucleotide bases.

RNA - Wikipedia

RNA is transcribed with only four bases (adenine, cytosine, guanine and uracil), but these bases and attached sugars can be modified in numerous ways as the RNAs mature.

Protein - Wikipedia

Shortly after or even during synthesis, the residues in a protein are often chemically modified by post-translational modification, which alters the physical and chemical properties, folding, stability, activity, and ultimately, the function of the proteins.

Gene - Wikipedia

However, more recent analyses suggest that, although protein-coding DNA makes up barely 2% of the human genome, about 80% of the bases in the genome may be expressed, so the term "junk DNA" may be a misnomer.