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In mathematics, the master stability function is a tool used to analyze the stability of the synchronous state in a dynamical system consisting of many
Master_stability_function
Network of coupled dynamical systems
The local stability of complete synchronization in networks of identical dynamical systems can be analyzed using the master stability function, which relates
Synchronization_network
Exactly solvable model of coupled oscillators
based on the Kuramoto model and phase oscillator. Circle map Master stability function Oscillatory neural network Phase-locked loop Swarmalators Kuramoto
Kuramoto_model
Russian mathematician (1857–1918)
Lyapunov by Chebyshev as a topic for his masters thesis which he submitted in 1884 with the title On the stability of ellipsoidal forms of rotating fluids
Aleksandr_Lyapunov
Spanish physicist
interactions are encoded as a network; and the generalization of the Master Stability Function to the case of interactions encoded as multiplex networks. In
Jesús_Gómez-Gardeñes
Function of the electronic stability control on production motor vehicles
system (TCS), is typically (but not necessarily) a secondary function of the electronic stability control (ESC) on production motor vehicles, designed to prevent
Traction_control_system
Model-free reinforcement learning algorithm
definition, the advantage function is an estimate of the relative value for a selected action. If the output of this function is positive, it means that
Proximal_policy_optimization
2025–26 fraud scandal in Brazil
Banco Master scandal is an ongoing political scandal in Brazil, involving investigations into alleged financial fraud in private bank Banco Master and the
Banco_Master_scandal
Electro-hydraulic braking system
each wheel, enabling the use of stability control methods such as Anti-lock Braking System (ABS) and Electronic Stability Program (ESP). On some vehicles
Sensotronic_Brake_Control
Sociological theory of society
a complex system whose parts work together to promote solidarity and stability". This approach looks at society through a macro-level orientation, which
Structural_functionalism
Control loop feedback mechanism
change of the error, which helps to mitigate overshoot and enhance system stability, particularly when the system undergoes rapid changes. The PID output
PID_controller
Type of differential equation
in which the derivative of the unknown function at a certain time is given in terms of the values of the function at previous times. DDEs are also called
Delay_differential_equation
Upper house of the US Congress
the "senatorial trust" called for a "greater extent of information and stability of character": A senator must be thirty years of age at least; as a representative
United_States_Senate
Person in a company or organization responsible for finances
new opportunities—can significantly affect a company’s direction and stability, especially given the CFO’s growing role as a strategic partner to the
Chief_financial_officer
Type of feedforward neural network
function as its nonlinear activation function. However, the backpropagation algorithm requires that modern MLPs use continuous activation functions such
Multilayer_perceptron
Stages in development and support of computer software
features implemented but is not yet final due to bugs, performance or stability issues. This occurs at the end of alpha testing in development. Usually
Software_release_life_cycle
(feedback) systems and stability analysis of these systems. Signal flow graphs and their use in determining transfer functions of systems; transient and
Education and training of electrical and electronics engineers
Education_and_training_of_electrical_and_electronics_engineers
Checking software against expectations
rare workloads. Stability testing (often referred to as load or endurance testing) checks to see if the software can continuously function well in or above
Software_testing
Scientific study of politics and social science
governance and specific policies by examining many factors, including stability, justice, material wealth, peace, and public health. Some political scientists
Political_science
President of the United States from 2001 to 2009
While Bush admitted there were strategic mistakes made in regard to the stability of Iraq, he maintained he would not change the overall Iraq strategy.
George_W._Bush
American politician (born 1978)
in New York. He graduated from Johns Hopkins University and received a master's degree from Wolfson College, Oxford, as a Rhodes Scholar. After several
Wes_Moore
Japanese manga series
studies, the Mongols invade Tus. Sitara is captured by Tolui's army and her master is killed while protecting her. After being taken to Mongolia, she takes
A_Witch's_Life_in_Mongol
Branch of mathematics
how functions, sequences, and operators behave under limiting processes and perturbations: convergence and continuity, regularity and stability, quantitative
Mathematical_analysis
Safety anti-skid braking system used on aerospace and land vehicles
distribution, traction control system, emergency brake assist, or electronic stability control (ESC). The concept for ABS predates the modern systems that were
Anti-lock_braking_system
American politician (born 1984)
Trump's words had encouraged "unconstitutional theories that risk the stability of our nation", he had voted against the second impeachment because he
Dan_Crenshaw
Member of a monastic religious order
ask for anything. The monks live in monasteries, and have an important function in traditional Asian society. Young boys can be ordained as samaneras.
Monk
American psychologist (born 1942)
marital stability through relationship analyses. Gottman's work is centered on the field of relationship counseling: enhanced relationship functioning and
John_Gottman
President of Paraguay from 2023 to 2026
dictatorship of Alfredo Stroessner had resulted in "more than 50 years of stability in Paraguay". He further asserted that Stroessner, who came to power as
Santiago_Peña
Chinese philosopher (1130–1200)
trace of frivolity and abruptness. Indeed, his calligraphy possesses stability and elegance in construction with a continuous flow of energy. Without
Zhu_Xi
General-purpose programming language
point function main. The run-time environment calls this function to begin program execution. The type specifier int indicates that the function returns
C_(programming_language)
American cell biologist
leading figure in RNA biology. Her PhD research investigated how mRNA stability was regulated during different stages of early development using Xenopus
Gia_Voeltz
Instrument for measuring, keeping or indicating time
inside as well as multiple prominent sundials outside, allowing it to function as a kind of early clocktower. The Greek and Roman civilizations advanced
Clock
Mid-size crossover SUV
assist and electronic brakeforce distribution were standard, Vehicle Stability Control w/traction control optional on 2001–03 models became standard
Toyota_Highlander
Swiss mathematician (1707–1783)
mathematical terminology and notation, including the notion of a mathematical function. He is known for his work in mechanics, fluid dynamics, optics, astronomy
Leonhard_Euler
Disc-shaped analog sound storage medium
both record and reproduce sound, via two separate needles, one for each function. The first commercially sold disc records were created by Emile Berliner
Phonograph_record
Pathogenic type of misfolded protein
major prion protein (PrP), a naturally occurring protein with an uncertain function. They are the hypothesized cause of various diseases, including scrapie
Prion
Great Lakes freighter sunk in Lake Superior
throughout the final day, finally resulting in a fatal loss of buoyancy and stability. As a result, Edmund Fitzgerald plummeted to the bottom without warning
SS_Edmund_Fitzgerald
Chinese automobile manufacturer
amphibious maneuvers, and a 1,758-meter paved race track. Handling and stability systems are tested on a low-friction circular track and a kick-plate designed
BYD_Auto
Tabletop role-playing game
Health and Stability are general abilities, they function differently. While other abilities are exhausted once they reach 0, Health and Stability can reach
Gumshoe_System
Tail section of an aircraft containing stabilisers
simplest configuration that performs all three aspects of the function of a tail: trim, stability, and control. Around 60% of current aircraft designs — and
Empennage
Central bank of the United Kingdom
the bank's new mandate on financial stability. The Financial Services Act 2012 gave the bank additional functions and bodies, including an independent
Bank_of_England
Formula for solving a quadratic equation
the roots represent the x values at which the graph of the quadratic function y=ax2+bx+c, a parabola, crosses the x-axis: the graph's x-intercepts
Quadratic_formula
Country in West Asia
economic capabilities, rich mineral and energy resources, and internal stability, added to its far greater geostrategic importance." In Hooman Peimani
Iran
Country in West Africa
president who is head of state and head of government. For political stability in Africa, it ranked seventh in the 2022 Ibrahim Index of African Governance
Ghana
timeline. An "anchor being" is an individual whose existence is vital to the stability of their universe. Once this individual is killed or removed, their reality
Features of the Marvel Cinematic Universe
Features_of_the_Marvel_Cinematic_Universe
equation in phase separation Chemical reaction model Brusselator Oregonator Master equation Rate equation Streeter–Phelps equation in water quality modeling
List of named differential equations
List_of_named_differential_equations
Diode that emits light from an organic compound
materials solved the problems previously encountered with the long-term stability of the organic films and enabled high-quality films to be easily made
OLED
Country primarily in North America
In Baaklini, Abdo I.; Desfosses, Helen (eds.). Designs for Democratic Stability: Studies in Viable Constitutionalism. Routledge. pp. 53–72. ISBN 978-0-7656-0052-3
United_States
Divergent series
it can be assigned a finite value. In particular, the methods of zeta function regularization and Ramanujan summation assign the series a value of −+1/12
1_+_2_+_3_+_4_+_⋯
Group of muscles
Arend, C.F. (2013). "01.1 Rotator Cuff: Anatomy and Function". Ultrasound of the Shoulder. Master Medical Books. Archived from the original on 14 October
Rotator_cuff
Country ranking by public sector corruption
These nations also generally have well-functioning judicial systems, a strong rule of law, and political stability – all factors that contribute to perceptions
Corruption_Perceptions_Index
Privately pooled investment fund using diverse strategies to seek high returns
trades and portfolios to regulators including the newly created Financial Stability Oversight Council. In this regard, most hedge funds and other private
Hedge_fund
Intelligence in machines
September 2024. Retrieved 5 October 2024. Edwards, Benj (22 February 2024). "Stability announces Stable Diffusion 3, a next-gen AI image generator". Ars Technica
Artificial_intelligence
2019 video game
science-fiction setting because it has "this sense of power, weight, strength and stability to it". The clean, utilitarian design of the Oldest House provides juxtaposition
Control_(video_game)
Shared boundary between elements of a computing system
have major ramifications—sometimes disastrous ones—for functionality and stability.[citation needed] Interfaces between software components can provide constants
Interface_(computing)
Device or computer program used for writing and editing documents
features. Early word processors were stand-alone devices dedicated to the function, but current word processors are primarily word processor programs running
Word_processor
1968 science fiction novel by Philip K. Dick
as seen in the mirror. The androids, Benesch argues, perform a doubling function similar to the mirror image of the self, but they do this on a social,
Do Androids Dream of Electric Sheep?
Do_Androids_Dream_of_Electric_Sheep?
but the Emperor by unwritten constitutional convention fulfills the functions and duties of this role. The Governor-General of New Zealand also serves
List of current heads of state and government
List_of_current_heads_of_state_and_government
Virtual marketplace in the darknet
website on the dark web that operates via darknets such as Tor and I2P. They function primarily as black markets, selling or brokering transactions involving
Darknet_market
Tenth generation of Toyota Corolla
without Electronic Stability Control, which can reduce the chances of a fatal accident by up to 55 percent. Electronic Stability Control has been available
Toyota_Corolla_(E140)
Catalan architect (1852–1926)
style created by the compasses, a formulaic industrial repetition. Its stability depends on constant propping up by the buttresses: it is a defective body
Antoni_Gaudí
Figure in the mythology of the Nation of Islam
an enclave on Moroccan soil, thereby posing a potential threat to the stability of the Moorish empire". Yusuf Nuruddin says that a more direct source
Yakub_(Nation_of_Islam)
Physics problem related to laws of motion and gravity
solved to give explicit formulas for the positions of the bodies as a function of time. For most initial conditions, the dynamical system for three orbiting
Three-body_problem
Inquirer. Retrieved 15 August 2022 – via johnnery.wordpress.com. "Glory In Stability And Moderation". Forbes. Retrieved 21 June 2013. Quintus Horatius Flaccus
List_of_Latin_phrases_(full)
American mathematician and Nobel Laureate (1928–2015)
of polynomials. Nash's proof introduced the concepts now known as Nash function and Nash manifold, which have since been widely studied in real algebraic
John_Forbes_Nash_Jr.
Anglo-Norman soldier and statesman (1146/7–1219)
although by his time much of the function was delegated to more specialised representatives (as happened with other functions in the king's household). Because
William Marshal, 1st Earl of Pembroke
William_Marshal,_1st_Earl_of_Pembroke
U.S. presidential administration since 2025
the United States and of the state of Qatar and to restore peace and stability." Knickmeyer, Ellen; et al. (December 7, 2024). "Trump says US should
Second presidency of Donald Trump
Second_presidency_of_Donald_Trump
Symbols for constants, special functions
where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities
Greek letters used in mathematics, science, and engineering
Greek_letters_used_in_mathematics,_science,_and_engineering
Electronic control system
filter) generally has two distinct functions. The primary function is to determine loop dynamics, also called stability. This is how the loop responds to
Phase-locked_loop
Fifth generation of BMW 5 Series
head-up display and active steering. Safety-related items include Dynamic Stability Control (DSC), adaptive headlights and night vision. In 2009, the iDrive
BMW_5_Series_(E60)
Capital and largest city of Latvia
League. The Hansa was instrumental in giving Riga economic and political stability, thus providing the city with a strong foundation which endured the political
Riga
Open-source word processor
software Italo Vignoli (29 October 2026). "LibreOffice 26.8.2 improves stability, multimedia and compatibility". Retrieved 29 October 2026. Italo Vignoli
LibreOffice_Writer
2025 Chinese television drama series
his actions are driven by a pursuit of social mobility and financial stability. His character represents the impact of class disparity on interpersonal
Shine_on_Me
Motor vehicle
Differential Lock" (EDL). EDL is an integrated additional function of the Bosch Electronic Stability Programme (ESP) system, and works by monitoring and comparing
Audi_RS_6
1741 sacred oratorio by Handel
by the soprano in B♭, in what Burrows terms a rare instance of tonal stability. The aria "He shall feed his flock" underwent several transformations
Messiah_(Handel)
increasingly concerned, and large numbers of people have long doubted his stability. But it's not clear that swing voters are overly concerned, and Trump's
False or misleading statements by Donald Trump
False_or_misleading_statements_by_Donald_Trump
Economic system based on social ownership of the means of production in a market economy
mixed economy. While social democracy aims to achieve greater economic stability and equality through policy measures such as taxes, subsidies, and social
Market_socialism
Spreadsheet component of LibreOffice
software Italo Vignoli (29 October 2026). "LibreOffice 26.8.2 improves stability, multimedia and compatibility". Retrieved 29 October 2026. Italo Vignoli
LibreOffice_Calc
1999 Microsoft operating system version
is the client version of Windows 2000. It offers greater security and stability than many of the previous Windows desktop operating systems. It supports
Windows_2000
Academic discipline studying businesses and investments
value and minimize volatility. Financial analysis assesses the viability, stability, and profitability of an action or entity. Some fields are multidisciplinary
Finance
Drug mixture used mainly to treat ADHD and narcolepsy
decreases abnormalities in brain structure and function found in subjects with ADHD, and improves function in several parts of the brain, such as the right
Adderall
Prime Minister of Senegal since 2026
"consistently champion[ing] the stability of this currency, asserting that it fulfills all the essential functions of money and maintains a robust external
Ahmadou_Al_Aminou_Lo
New Zealand politician (born 1945)
relations, other key issues include climate change, development policies and stability. On 12 May, Peters met with Solomon Islands Prime Minister Jeremiah Manele
Winston_Peters
journeyman eventually to widely recognized master and grandmaster began to emerge. In order to become a master, a journeyman would often go on a two or
Guilds_in_medieval_Europe
Process of calculating the causal factors that produced a set of observations
language processing, machine learning, nondestructive testing, slope stability analysis and many other fields.[citation needed] Starting with the effects
Inverse_problem
Sports car manufactured by Mercedes-AMG
lift, and more downforce, resulting in faster acceleration and better stability at high speeds. It also had more power compared to the standard GT 63
Mercedes-AMG_GT
American private military contractor
from very small scale up major operations to "facilitate large scale stability operations requiring large numbers of people to assist in securing a region"
Blackwater_(company)
Engineering, property and infrastructure company based in Malaysia
Corporation Berhad. Completed in year 2007, this 9.7 km SMART tunnel primary function is to divert excess floodwater from Sungai Klang and Sungai Ampang to be
Gamuda
Statistical law in machine learning
law function of NE,ND, where NE,ND are encoder and decoder parameter count. It is not simply a function of total parameter count N=NE+ND. The function has
Neural_scaling_law
Accumulation of data corruption on a storage device over time
Matija (9 September 2011). "Dose–response functions for historic paper" (PDF). Polymer Degradation and Stability. 96 (12): 2029–2039. doi:10.1016/j.polymdegradstab
Data_degradation
Extremity at the end of an arm or forelimb
provides cushioning, and palmar fascia contributes to the palm's shape and stability. There are five digits attached to the hand, notably with a flat nail
Hand
Indian combat aircraft
1990 as a small tailless compound delta wing design with relaxed static stability. To provide enhanced manoeuvrability, it was planned to be a control configured
HAL_Tejas
American ocean liner (1951–2026)
earlier, it was discovered her tall funnels compromised the vessel's stability. To avoid this issue on United States, Gibbs decided the funnels and the
SS_United_States
Free and open-source VPN protocol
Excluding such complex features from the minimal core codebase improves its stability and security. For ensuring security, WireGuard restricts the options for
WireGuard
Branch of civil engineering dealing with man-made structures
structures. Structural engineers also must understand and calculate the stability, strength, rigidity and earthquake-susceptibility of built structures
Structural_engineering
Moroccan sultanate (1666–1912)
different sultans. A long period of stability returned under Sidi Mohammed ibn Abdallah (r. 1757–1790). Regional stability was disrupted by the French conquest
Alawi_Sultanate
Financial Stability Oversight Council released a report in October 2021 that identified climate change as an emerging and increasing threat to the stability of
Economy_of_the_United_States
Species of rodent
means of propulsion and the unique tail mainly important in directional stability. Muskrats spend most of their time in the water and can swim underwater
Muskrat
Political institution in ancient Rome
Stability and Crisis of a City, 900–1150. Oxford University Press. pp. 23, 448. ISBN 9780199684960. Wickham, Chris (2014). Medieval Rome: Stability and
Roman_Senate
Oscillator whose frequency can be tuned over some range
advantages include smaller designs, lack of moving parts, the higher stability of set frequency reference oscillators, and the ease with which preset
Variable-frequency_oscillator
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MASTER STABILITY-FUNCTION
MASTER STABILITY-FUNCTION
MASTER STABILITY-FUNCTION
MASTER STABILITY-FUNCTION
MASTER STABILITY-FUNCTION
MASTER STABILITY-FUNCTION
MASTER STABILITY-FUNCTION
MASTER STABILITY-FUNCTION
MASTER STABILITY-FUNCTION
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