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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
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
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)
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
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
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
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
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
Biological process of division and regeneration
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)
Multidimensional search tree for points in k dimensional space
point needs a search that accounts for the splitting dimension at each level. Unlike in an ordinary binary search tree, the point with the smallest value
K-d_tree
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
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
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
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
Reaction that splits an atomic nucleus
reaction is possible. Binary fission may produce any of the fission products, at 95±15 and 135±15 daltons. One example of a binary fission event in the
Nuclear_fission
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
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
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
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
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
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
Computer data storage architecture that manages data as objects
Gibson on Network-Attached Secure Disks first promoted the concept of splitting less common operations, like namespace manipulations, from common operations
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
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
Topics referred to by the same term
MS-DOS Process control block, an operating system data structure Precompiled Binary Bolshevik Communist Party (Spanish: Partido Comunista Bolchevique), a Mexican
PCB
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
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
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
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
Decision tree algorithm
attempt at a model based on entropy-based splitting, and the term dichotomiser is a misnomer as it implies a binary split, but the ID3 algorithm can split
ID3_algorithm
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
Computer data using only printable characters
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
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
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
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
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)
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
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
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)
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
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
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
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
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
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
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
File with the content of other files plus associated metadata
Encryption Error detection via checksums Error correction code to fix errors Splitting a large file into multiple, smaller files File patches/updates (when recording
Archive_file
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
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
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)
Thermodynamic model
1900, Jan Zawidzki proved the model via determining the composition of binary mixtures condensed at different temperatures by their refractive indices
Margules_activity_model
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
calculi of ordered binary resolution and superposition (for handling equality). The splitting rule and negative equality splitting can be simulated by
Vampire_(theorem_prover)
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
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
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
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
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
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
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
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
Computer architecture bit width
607,431,768,211,455 (2128 − 1) for representation as an (unsigned) binary number, and −170,141,183,460,469,231,731,687,303,715,884,105
128-bit_computing
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 an ellipsoidal shape
Quaoar
Programmable calculator
necessary, e.g. splitting 111000 into groups of four gives 0011 and 1000. The equivalent hexadecimal values of these two four-digit binary numbers are 3
Elektronika_MK-52
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
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
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
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
Decision support tool
scenarios. Drawn from left to right, a decision tree has only burst nodes (splitting paths) but no sink nodes (converging paths). So used manually they can
Decision_tree
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
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
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
Set of points on a line segment with certain topological properties
the Cantor set is uniquely located by a path through an infinitely deep binary tree, where the path turns left or right at each level according to which
Cantor_set
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
Romantic orientation on the aromantic spectrum
Books. pp. 26–27, 40. ISBN 978-1-63144-002-1. Mangen, Kayla (2024-05-30). Splitting Attraction: A Phenomenological Study of Coming Out With Discordant Sexual
Demiromanticism
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
various principles such as resolution, search, local search and random walk, binary decisions, and Stalmarck's algorithm. Some of these algorithms are deterministic
Boolean satisfiability algorithm heuristics
Boolean_satisfiability_algorithm_heuristics
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
Abstract data type in computer science
better bounds for some operations. Alternatively, when a self-balancing binary search tree is used, insertion and removal also take O(logn) time, although
Priority_queue
Mathematical method in graph theory
suggest to represent a given tree by keeping its Euler tour in a balanced binary search tree, keyed by the index in the tour. So for example, the unbalanced
Euler_tour_technique
Musical artist (born 2005)
Title EP details Splitting Time Released: February 18, 2022 Label: Cascine Format: Digital download, streaming
Kuru_(musician)
Hand game for two or more players
than 5 such as Chinese hand numerals, senary finger counting, and finger binary. This variation often includes rollovers. Suns: Both players start with
Chopsticks_(hand_game)
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
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
Algorithm that combines multiple sorted lists into one
conquer solution that builds on the binary merge algorithm: If k = 1, output the single input list. If k = 2, perform a binary merge. Else, recursively merge
Merge_algorithm
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
Logic puzzle forming a picture in a grid
successive sets. These puzzles are often black and white — describing a binary image — but they can also be colored. If colored, the number clues are also
Nonogram
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
Addition of several numbers or other values
(splitting a sum into its odd and even parts, for even indexes) ∑n=2s+12tf(n)=∑n=s+1tf(2n)+∑n=s+1tf(2n−1) (splitting a sum into its odd
Summation
Components used for routing signals between optical fibres on a per-wavelength basis
grating breaks the incoming light into a spectrum. A software controlled binary liquid crystal stack, individually tilts each optical channel and a second
Wavelength selective switching
Wavelength_selective_switching
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
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)
Three infinite groups introduced by R. Thompson
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
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
Greatest integer less than or equal to square root
x2>y. 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
Database stored as flat data
for relationships. A flat-file database may be stored as plain text or binary (not character encoded). When plain text, it is typically formatted as one
Flat-file_database
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BINARY SPLITTING
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BINARY SPLITTING
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