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Algorithmic technique
In mathematics, binary splitting is a technique for speeding up numerical evaluation of many types of series with rational terms. In particular, it can
Binary_splitting
Algorithmic runtime requirements for common math procedures
Crandall, R.; Pomerance, C. (2005). "Algorithm 9.4.7 (Stehlé-Zimmerman binary-recursive-gcd)". Prime Numbers – A Computational Perspective (2nd ed.).
Computational complexity of mathematical operations
Computational_complexity_of_mathematical_operations
Failure to think in nuances
Splitting, also called binary thinking, dichotomous thinking, black-and-white thinking, all-or-nothing thinking, or thinking in extremes, is the failure
Splitting_(psychology)
Statistical procedure of testing by group
introduction of the generalised binary-splitting algorithm. The generalised binary-splitting algorithm works by performing a binary search on groups that test
Group_testing
Data compression algorithms
-\log _{2}p_{i}\rceil } . One common way of choosing the codewords uses the binary expansion of the cumulative probabilities. This method was proposed in Shannon's
Shannon–Fano_coding
2.71828...; base of natural logarithms
produces the nth partial sum of the series above. This method uses binary splitting to compute e with fewer single-digit arithmetic operations and thus
E_(mathematical_constant)
Fast method for calculating the digits of π
optimization technique used for the world record computations is called binary splitting. Mathematics portal Bailey–Borwein–Plouffe formula Borwein's algorithm
Chudnovsky_algorithm
Topics referred to by the same term
asteroids orbiting each other Binary fission, the splitting of a single-celled organism into two daughter cells Binary phase, a chemical compound containing
Binary
Election result affecting losing candidate
Academy of Sciences. Other systems exhibit an exit incentive. The vote splitting effect in plurality voting demonstrates this method's strong exit incentive:
Spoiler_effect
Encoding for a sequence of byte values using 64 printable characters
and 110 which in 8-bit binary representation are 01001101, 01100001, and 01101110. Joining these representations and splitting into 6-bit groups gives:
Base64
Biological process
populations, or species split into discrete parts. The fission may be binary fission, in which a single organism produces two parts, or multiple fission
Fission_(biology)
squares Methods of computing square roots nth root algorithm Summation: Binary splitting: a divide and conquer technique which speeds up the numerical evaluation
List_of_algorithms
Free library for arbitrary precision arithmetic
implements advanced algorithms like Schönhage–Strassen multiplication, binary splitting for computing certain mathematical constants and others. All CLN objects
Class_Library_for_Numbers
Ordering of binary values, used for positioning and error correction
The reflected binary code (RBC), also known as reflected binary (RB) or Gray code after Frank Gray, is an ordering of the binary numeral system such that
Gray_code
Formulas for pi
{i} )\cdot \Re (z)~.\end{aligned}}} For large computations of π, the binary splitting algorithm can be used to compute the arctangents much, much more quickly
Machin-like_formula
Binary tree derived from a sequence of numbers
to analyze the average-case complexity of concatenation and splitting operations on binary search trees. The name is derived from the Cartesian coordinate
Cartesian_tree
Varying methods used to calculate pi
7 trillion decimal digits of π. Calculations were performed in base 2 (binary), then the result was converted to base 10 (decimal). The calculation, conversion
Approximations_of_pi
Gender identity differing from sex assigned at birth
The definition given above includes binary trans men and trans women and may also include people who are non-binary or genderqueer. Being transgender is
Transgender
Reaction that splits an atomic nucleus
arose in a discussion with physicist William A. Arnold, who suggested "binary fission". In their second publication on nuclear fission in February 1939
Nuclear_fission
Apple multi-architecture binary files
The universal binary format is a format for executable files that run natively either on both PowerPC-based and x86-based Macs or on both Intel 64-based
Universal_binary
Variant of heap data structure
binary heap is a heap data structure that takes the form of a binary tree. Binary heaps are a common way of implementing priority queues. The binary heap
Binary_heap
Pairwise summation — slightly worse than Kahan summation but cheaper Binary splitting 2Sum Multiplication: Multiplication algorithm — general discussion
List of numerical analysis topics
List_of_numerical_analysis_topics
Multidimensional search tree for points in k dimensional space
point clouds. k-d trees are a special case of binary space partitioning trees. The k-d tree is a binary tree in which every node is a k-dimensional point
K-d_tree
Binary tree selected at random
likely, distributions on a given number of nodes obtained by repeated splitting, binary tries and radix trees for random data, and trees of variable size
Random_binary_tree
American actor
biological father's identity has not been made public. In 2014, after splitting from Bernard, Jodie married photographer and filmmaker Alexandra Hedison
Charlie_B._Foster
Graphics structure
spent at each node. In practice, binary trees (degree = 2) are by far the most common. One of the main reasons is that binary trees are easier to build. There
Bounding_volume_hierarchy
Term for computer data consisting only of unformatted characters of readable material
sections, and the like are identified; and from binary files in which some portions must be interpreted as binary objects (encoded integers, real numbers, images
Plain_text
Tree-based computer data structure
the binary search tree, allowing nodes to have more than two children. By allowing more children under one node than a regular self-balancing binary search
B-tree
Computer data storage architecture that manages data as objects
for Rdb/VMS. Blob is often humorously explained to be an abbreviation for binary large object. According to Starkey, this backronym arose when Terry McKiever
Object_storage
Disk encryption software
versions. The LUKS2 header has a binary area and a JSON area, a second binary and JSON area, and a keyslots area. The binary and JSON areas are repeated two
Linux_Unified_Key_Setup
Self-adjusting binary search tree
tree is a binary search tree with the additional property that recently accessed elements are quick to access again. Like self-balancing binary search trees
Splay_tree
Process for the dissociation of water into hydrogen and oxygen
Photocatalytic water splitting is a process that uses photocatalysis for the dissociation of water (H2O) into hydrogen (H 2) and oxygen (O 2). The inputs
Photocatalytic water splitting
Photocatalytic_water_splitting
Fractal shape formed from a line segment
canopy is created by splitting a line segment into two smaller segments at the end (symmetric binary tree), and then splitting the two smaller segments
Fractal_canopy
Self-balancing binary search tree data structure
In computer science, a red–black tree is a self-balancing binary search tree data structure noted for fast storage and retrieval of ordered information
Red–black_tree
Repeated application of an operation to a sequence
In mathematics, an iterated binary operation is an extension of a binary operation on a set S to a function on finite sequences of elements of S through
Iterated_binary_operation
Method for dividing a secret among multiple parties
Secret sharing (also called secret splitting) refers to methods for distributing a secret among a group, in such a way that no individual holds any intelligible
Secret_sharing
Mapping function that preserves data point locality
interleaving the binary representations of its coordinate values. However, when querying a multidimensional search range in these data, using binary search is
Z-order_curve
Index of chemical compounds with the same name
and hexafluoronickelate(IV), NiF2−6. Seventeen elements are known to form binary hexafluorides. Nine of these elements are transition metals, three are actinides
Hexafluoride
Soviet ternary computer
numeral system and three-valued ternary logic instead of the two-valued binary logic prevalent in other computers. The computer was built to fulfill the
Setun
Splitting a file into parts of a specific size
Splitting a file into parts of a specific size
File_spanning
Decision tree algorithm
attempt at a model based on entropy-based splitting, and the term dichotimser is a misnomer as it implies a binary split, but the ID3 algorithm can split
ID3_algorithm
Data structure in computer science
Inserting k into a balanced binary search tree that contains O(log M) elements also takes O(log log M) time. Splitting a binary search tree that contains
Y-fast_trie
1988 video game
Amstrad CPC, and Atari ST in 1989. The computer ports were developed by Binary Design, the same studio that handled the computer ports of the first game
Double_Dragon_II:_The_Revenge
Measure of similarity and diversity between sets
variables, one could replicate the behaviour of the SMC by splitting the dummies into two binary attributes (in this case, male and female), thus transforming
Jaccard_index
Mathematical function, inverse of an exponential function
widespread in mathematics and physics because of its very simple derivative. The binary logarithm uses base 2 and is widely used in computer science, information
Logarithm
Partition into two separate parts
the other. Treating continuous variables or multicategorical variables as binary variables is called dichotomization. The discretization error inherent in
Dichotomy
Type of fair division
Consensus splitting, also called exact division, is a partition of a continuous resource ("cake") into some k pieces, such that each of n people with
Consensus_splitting
Castable objects with two distinct faces for generating random outcomes
A binary lot is an object that, when cast, comes to rest with one of two distinct faces uppermost. These can range from precisely machined objects like
Binary_lot
Data structure
that node is the radix r of the radix trie. When r is 2, the radix trie is binary (i.e., compare that node's 1-bit portion of the key), which minimizes sparseness
Radix_tree
Informal fallacy involving falsely limited alternatives
A false dilemma, also referred to as false dichotomy or false binary, is an informal fallacy based on a premise that erroneously limits what options are
False_dilemma
Elementwise product of two matrices
known as the element-wise product, entrywise product or Schur product) is a binary operation that takes in two matrices of the same dimensions and returns
Hadamard_product_(matrices)
Structure formed by diffuse material in orbital motion around a massive central body
as compared to around 0.7 percent for nuclear fusion processes. In close binary systems the more massive primary component evolves faster and has already
Accretion_disk
Symbol "#!", used in computing
ELF binary any kind of file for which an interpreter was registered via the binfmt_misc mechanism (such as for executing Microsoft .exe binaries using
Shebang_(Unix)
decimal arithmetic, in the binary numeral system used in computer programming, and in other even-numbered bases. In binary arithmetic, division by two
Division_by_two
Tree node with two other nodes as descendants
the tree is a complete binary tree, the nodes may be indexed in such a way that lowest common ancestors reduce to simple binary operations on the indices
Lowest_common_ancestor
Form of problem solving, often applied to repair failed products or processes
is simply the application of a binary search across the range of dependencies and is often referred to as "half-splitting". It is similar to the game of
Troubleshooting
Ringed dwarf planet in the Kuiper belt
Quaoar (minor-planet number 50000) is a ringed dwarf planet in the Kuiper belt, a band of icy planetesimals beyond Neptune. It has a slightly ellipsoidal
Quaoar
Large self-illuminated object in space
Edward Pickering discovered the first spectroscopic binary in 1899 when he observed the periodic splitting of the spectral lines of the star Mizar in a 104-day
Star
Secure communication method
such functions, which takes as its input a binary string of length equal to the key and outputs a binary string of a chosen shorter length. The amount
Quantum_key_distribution
Type of error correcting code
Polar Codes, Polarization of Binary Erasure Channels, Mathematical Modelling of Polar Codes, Channel Combining and Splitting and Polarization Rate and Performance
Polar_code_(coding_theory)
Procedures for constructing new graphs in graph theory
produce new graphs from initial ones. They include both unary (one input) and binary (two input) operations. Unary operations create a new graph from a single
Graph_operations
Three groups
group F also has realizations in terms of operations on ordered rooted binary trees, and as a subgroup of the piecewise linear homeomorphisms of the unit
Thompson_groups
Tree data structure that partitions a 2D area
array as an implicit data structure similar to the way a binary heap can store a complete binary tree compactly in an array. Quadtrees may be classified
Quadtree
"Little Sapiens" March 14, 2024 (2024-03-14) 8 "Fluid: Life Beyond the Binary" March 28, 2024 (2024-03-28) 9 "Secrets of the Jurassic Dinosaurs" April 4
List of The Nature of Things episodes
List_of_The_Nature_of_Things_episodes
Non-comparative lexicographical sorting algorithm
change the resulting counts. Binary MSD radix sort, also called binary quicksort, can be implemented in-place by splitting the input array into two bins
Radix_sort
Shell command for reporting and running with modified environment variables
found in both versions include -u, for unsetting variables, and -S, for splitting arguments (mainly in shebang). The following command line prints the current
Env
file B6T – BlindWrite 6 image file BWT – BlindWrite 4 image file BIN – Raw binary format, often paired with CUE CDI – DiscJuggler image file CUE – CDRWrite
List_of_file_formats
Tool for analyzing divide-and-conquer algorithms
{\displaystyle T(n)=\Theta \left(n^{c_{\operatorname {crit} }}\right)} (The splitting term does not appear; the recursive tree structure dominates.) If b =
Master theorem (analysis of algorithms)
Master_theorem_(analysis_of_algorithms)
orientations are not given explicitly but implicitly by some recursive splitting-function defined on the hyperrectangles belonging to the tree's nodes
Implicit_k-d_tree
Type of mathematical proof
numbering Enumeration Large cardinal inaccessible Aleph number Operation binary Theories Zermelo–Fraenkel axiom of choice continuum hypothesis General Kripke–Platek
Proof_by_exhaustion
Algorithms which recursively solve subproblems
algorithms that reduce each problem to only one sub-problem, such as the binary search algorithm for finding a record in a sorted list (or its analogue
Divide-and-conquer_algorithm
A B-heap is a binary heap implemented to keep subtrees in a single page. This reduces the number of pages accessed by up to a factor of ten for big heaps
B-heap
Topics referred to by the same term
Communist Party of Belgium (French: Parti Communiste de Belgique), until splitting in 1989 Communist Party of Belgium (1989)(French: Parti Communiste de
PCB
Star system in the Centaurus constellation
are Sun-like stars (class G and K, respectively) that together form the binary star system α Centauri AB. To the naked eye, these two main components appear
Alpha_Centauri
Machine learning algorithm
built by splitting the source set, constituting the root node of the tree, into subsets—which constitute the successor children. The splitting is based
Decision_tree_learning
Similarity measure
variables, one could replicate the behaviour of the SMC by splitting the dummies into two binary attributes (in this case, male and female), thus transforming
Simple_matching_coefficient
Quantum mechanics thought experiment
Tegmark suggested that the flaw in that reasoning is that dying is not a binary event as in the thought experiment; it is a progressive process, with a
Quantum suicide and immortality
Quantum_suicide_and_immortality
Musical artist (born 2005)
Title EP details Splitting Time Released: February 18, 2022 Label: Cascine Format: Digital download, streaming
Kuru_(musician)
calculi of ordered binary resolution and superposition (for handling equality). The splitting rule and negative equality splitting can be simulated by
Vampire_(theorem_prover)
Mathematical result
2003). "Database-friendly random projections: Johnson-Lindenstrauss with binary coins". Journal of Computer and System Sciences. 66 (4): 671–687. doi:10
Johnson–Lindenstrauss_lemma
Astronomical phenomenon due to the gravitational lens effect
detect exoplanets, study limb darkening in distant stars, constrain the binary star population, and constrain the structure of the Milky Way's disk. Microlensing
Gravitational_microlensing
US political parties other than the two major parties
parties can potentially be regarded as splitting votes away from the most similar major party. Third party vote splitting exceeded a president's margin of victory
Third_party_(U.S._politics)
Approximate distinct counting algorithm
variance. In the HyperLogLog algorithm, the variance is minimised by splitting the multiset into numerous subsets, calculating the maximum number of
HyperLogLog
Greatest integer less than or equal to square root
. A speed-up is achieved by using binary search instead. def isqrt(y: int) -> int: """ Integer square root (binary search) """ L = 0 # lower bound of
Integer_square_root
Hypothetical types of stars
observations interpreted as originating in a black hole binary could really originate in a boson star binary. The invisible companion to a Sun-like star identified
Exotic_star
Digital image having no color information
are images with only two colors: black and white (also called bilevel or binary images). Grayscale images have many shades of gray in between. Grayscale
Grayscale
artist One Be Lo (a.k.a. OneManArmy). It also includes work with his groups Binary Star (with Senim Silla), Security (with Magestik Legend), and work from
One_Be_Lo_discography
Sitter showed that Ritz's theory would have predicted that the orbits of binary stars would appear more eccentric than consistent with experiment and with
De Sitter double star experiment
De_Sitter_double_star_experiment
American mathematician and computer scientist
input be a 10x15 binary image. It is equivalent to a single string with 150 binary letters. Now, randomly partition the 150 binary pixels into 75 pairs
Woody_Bledsoe
Method by which voters make a choice between options
in Italy. Primary elections limit the possible adverse effect of vote splitting by ensuring that a party puts forward only one party candidate. In Argentina
Electoral_system
Chemical compound
with the chemical formula P2H4. This colourless liquid is one of several binary phosphorus hydrides. It is the impurity that typically causes samples of
Diphosphane
Type of search algorithm
check is done assuming the opposite truth value. This is known as the splitting rule, as it splits the problem into two simpler sub-problems. The simplification
DPLL_algorithm
Hydrogen spectral series
examined at very high resolution, they were closely spaced doublets. This splitting is called fine structure. It was also found that excited electrons from
Balmer_series
Computer algorithm
satisfy a memory request as suitably as possible. This system makes use of splitting memory into halves to try to give a best fit. According to Donald Knuth
Buddy_memory_allocation
Application layer protocol
speeds than HTTP/1.1 communications. HTTP/2 adds support for: a compressed binary representation of metadata (HTTP headers) instead of a textual one, so that
HTTP
Data structure
storage context—in particular, filesystems. This is primarily because unlike binary search trees, B+ trees have very high fanout (number of pointers to child
B+_tree
Series of free software licenses
the freedoms that define free software. The first method is publishing binary files that are only executable, but not readable or modifiable by humans
GNU_General_Public_License
Human-readable data serialization language
timestamps, and hexadecimal. Here is an example of base64-encoded binary data. --- picture: !!binary | R0lGODdhDQAIAIAAAAAAANn Z2SwAAAAADQAIAAACF4SDGQ ar3xxbJ9p0qa7R0YxwzaFME
YAML
Field (mathematics) generated by the square root of an integer
fields have been studied in great depth, initially as part of the theory of binary quadratic forms. There remain some unsolved problems. The class number problem
Quadratic_field
Deliberate creation of difficult-to-understand code
chooses a secret key and applies the XOR bitwise operation to the malware binary. This transforms the executable into what looks like random data. Function
Obfuscation_(software)
BINARY SPLITTING
BINARY SPLITTING
Boy/Male
Latin
Happy; Cheerful.
Girl/Female
English
Originally a diminutive used for names ending in -bina, like Albina, Columbina, and Robina, now...
Girl/Female
Hindu
Shore, Musical instrument, Goddess of wealth
Male
Hindi/Indian
Variant spelling of Hindi Vijay, BIJAY means "victory."
Female
English
English pet form of German Belinda, possibly BINDY means "bright serpent" or "bright linden tree."
Surname or Lastname
English
English : variant spelling of Vickery.
Girl/Female
Indian
Modesty
Boy/Male
Irish
An ancient Irish name whos meaning is lost in antiquety.
Surname or Lastname
English (chiefly South Yorkshire)
English (chiefly South Yorkshire) : topographic name for someone who lived on land enclosed by a bend in a river, from Old English binnan ēa ‘within the river’, or a habitational name from places in Kent called Binney and Binny, which have this origin.Scottish : habitational name from Binney or Binniehill near Falkirk, named in Gaelic as Beinnach, from beinn ‘hill’ + the locative suffix -ach.
Female
Hebrew
Variant spelling of Hebrew Bina, BINAH means "intelligence, wisdom."Â
Girl/Female
Indian
(the wife of Sage Kashyap)
Female
Turkish
Turkish name PINAR means "spring."
Boy/Male
Indian, Punjabi, Sikh
Blessing
Female
Hebrew
(×‘Ö¼Ö´×™× Ö¸×”) Hebrew name BINA means "intelligence, wisdom."Â
Boy/Male
American, Australian, French, German, Greek, Latin, Polish, Swedish
Cheerful; Happy; Joyful; Similar to Hilary
Male
Scandinavian
Scandinavian form of Old Norse Einarr, EINAR means "lone warrior."
Male
English
English unisex form of Latin Hilarius and Hilaria, HILARY means "joyful; happy."Â Originally, this was strictly a masculine name.
Girl/Female
Hindu
Shore, Musical instrument, Goddess of wealth
Boy/Male
Indian
An intimate particle of the God of heaven
Male
Hindi/Indian
(विनय) Hindi name VINAY means "leading asunder."
BINARY SPLITTING
BINARY SPLITTING
Boy/Male
Hindu, Indian, Malayalam, Marathi, Sanskrit
Like the Blue Lotus
Boy/Male
Arabic, Muslim
Servant of the Supervising; The Guardian; The Protector
Boy/Male
Hindu
Female
Italian
Feminine form of Italian Pasqualino, PASQUALINA means "Passover; Easter."
Boy/Male
Hebrew
My parents are alive.
Girl/Female
Australian, British, English, Portuguese
Form of Marilyn; Bitter; Wished for Child; Bitter Rebellious
Surname or Lastname
English
English : probably a variant of the Anglo-Norman French personal name Mory, a short form of Amaury (see Emery, Morey).Roger Mowry (c. 1612–66) emigrated from England to MA before 1634, when he married Mary Johnson in Roxbury, Suffolk Co., MA.
Boy/Male
Arabic, Muslim, Sindhi
Name of a Reciter of the Holy Quran
Surname or Lastname
English
English : variant spelling of Ince.
Girl/Female
Indian, Punjabi, Sikh
Gods Lover
BINARY SPLITTING
BINARY SPLITTING
BINARY SPLITTING
BINARY SPLITTING
BINARY SPLITTING
n.
A pale yellow color, like that of a canary bird.
n.
That which is constituted of two figures, things, or parts; two; duality.
n.
A binary compound of zinc.
a.
Containing ten; tenfold; proceeding by tens; as, the denary, or decimal, scale.
n.
A binary compound of selenium, or a compound regarded as binary; as, ethyl selenide.
a.
Of or pertaining to the Canary Islands; as, canary wine; canary birds.
n.
See Finery.
a.
Compounded or consisting of two things or parts; characterized by two (things).
n.
A binary compound of silicon, or one regarded as binary.
n.
Wine made in the Canary Islands; sack.
a.
Of or pertaining to the urine; as, the urinary bladder; urinary excretions.
n.
A binary compound of phosphorus.
n.
A register of daily events or transactions; a daily record; a journal; a blank book dated for the record of daily memoranda; as, a diary of the weather; a physician's diary.
a.
lasting for one day; as, a diary fever.
v. i.
To perform the canary dance; to move nimbly; to caper.
a.
Relating or belonging to bile; conveying bile; as, biliary acids; biliary ducts.
n.
A canary bird.
n.
A binary compound of iodine, or one which may be regarded as binary; as, potassium iodide.
n.
A binary compound of hydrogen; a hydride.
a.
Of a pale yellowish color; as, Canary stone.