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Waiting time property of certain probability distributions
In continuous situations, memorylessness models random phenomena, like the time between two earthquakes. The memorylessness property asserts that the
Memorylessness
Probability distribution
definitions of the geometric distribution, there are also two definitions of memorylessness for discrete random variables. Expressed in terms of conditional probability
Geometric_distribution
Probability distribution
analogue of the geometric distribution, and it has the key property of being memoryless. In addition to being used for the analysis of Poisson point processes
Exponential_distribution
Limit on data transfer rate
{W}}\neq W\right\}.} Theorem (Shannon, 1948): 1. For every discrete memoryless channel, the channel capacity, defined in terms of the mutual information
Noisy-channel_coding_theorem
Theory about lossy data compression
famous Shannon lower bound (SLB), which in the case of squared error and memoryless sources, states that for arbitrary sources with finite differential entropy
Rate–distortion_theory
Type of random mathematical object
/ λ {\textstyle 1/\lambda } ). This implies that the points have the memoryless property: the existence of one point existing in a finite interval does
Poisson_point_process
Memoryless property of a stochastic process
In probability theory and statistics, the Markov property is the memoryless property of a stochastic process, which means that its future evolution is
Markov_property
Physical or logical connection used for transmission of information
of channel inputs. In information theory, it is common to start with memoryless channels in which the output probability distribution only depends on
Communication_channel
The Kanon anime, which encompasses two television series produced by different studios and an original video animation (OVA), is based on the visual novel
List_of_Kanon_episodes
Measure of inequality of a statistical distribution
Retrieved 30 November 2022. "Exponential Distribution | Definition | Memoryless Random Variable". www.probabilitycourse.com. Retrieved 30 November 2022
Gini_coefficient
Message encoded with more bits than needed
rate of a source of information is the average entropy per symbol. For memoryless sources, this is merely the entropy of each symbol, while, in the most
Redundancy (information theory)
Redundancy_(information_theory)
| x 1 , x 2 ) {\displaystyle p(y_{1},y_{2}|x_{1},x_{2})} is the noisy memoryless channel, which is modeled by a conditional probability distribution. The
Interference_channel
Theorized increase of longevity with age
Law and Zipf’s Law are in effect synonymous laws." Doomsday argument Memorylessness Longevity escape velocity Planning fallacy Preferential attachment Survivorship
Lindy_effect
Random process independent of past history
process that satisfies the Markov property (sometimes characterized as "memorylessness"). In simpler terms, it is a process for which predictions can be made
Markov_chain
Foundational object in quantum communication theory
systems considered, classical or quantum, are finite-dimensional. The memoryless in the section title carries the same meaning as in classical information
Quantum_channel
surgery characterization as a work-process (repetitive, semi-repetitive or memoryless) and its effect on SD distributional shape. A most straightforward SD
Predictive methods for surgery duration
Predictive_methods_for_surgery_duration
Branch of probability theory
distribution is the unique continuous random variable with the property of memorylessness. Let W 1 , W 2 , … {\displaystyle W_{1},W_{2},\ldots } be a sequence
Renewal_theory
Scientific study of digital information
role such as capacity of channel with feedback, capacity of discrete memoryless networks with feedback, gambling with causal side information, compression
Information_theory
Type of error correcting code
provably achieve the channel capacity for symmetric binary-input, discrete, memoryless channels (B-DMC) with polynomial dependence on the gap to capacity. Polar
Polar_code_(coding_theory)
Topics referred to by the same term
model describing a sequence of possible events The Markov property, the memoryless property of a stochastic process The Markovians, an extinct god-like species
Markovian
measure) between events has an exponential distribution, representing a memoryless process. In probability theory it is common to say a distribution, D,
Super-Poissonian_distribution
Family of error-correcting codes that encode data in blocks
( n , k ) {\displaystyle (n,k)} . Consequently, the block coder is a memoryless device. Under this definition codes such as turbo codes, terminated convolutional
Block_code
Type of physical or mathematical property
excitation waveform being played at the initial source. T-symmetry Memorylessness Markov property Reversible computing David Albert on Time and Chance
Time_reversibility
Mistakenly drawing statistical inference from independent events
Law of averages Martingale (betting system) Mean reversion (finance) Memorylessness Oscar's grind Regression toward the mean Statistical regularity Problem
Gambler's_fallacy
Concept in computing
bounds, such as random-coding exponents, and converse bounds. For discrete memoryless channels, Suguru Arimoto gave a converse bound showing exponential decay
Error_exponent
Reliable digital data delivery methods on unreliable channels
characteristics of the communication channel. Common channel models include memoryless models where errors occur randomly and with a certain probability, and
Error detection and correction
Error_detection_and_correction
Quantum mechanical system that interacts with a quantum-mechanical environment
For example, a common approximation is that the bath is Markovian, or memoryless. Taking this assumption results in a set of quantum master equations that
Open_quantum_system
Loop that increases an initial effect
Archived (PDF) from the original on 2015-04-13. * Non-Hysteretic Switches, Memoryless Switches: These systems have no memory, that is, once the input signal
Positive_feedback
Transfer of information within a process
Programming Languages and Analysis for Security, ACM, 2009. J. S. Fenton. Memoryless Subsystems, Comput. J. 17(2): 143-147 (1974) S. Zdancewic. Challenges
Information flow (information theory)
Information_flow_(information_theory)
Inequality in information theory
Körner, János (2011). Information Theory: Coding Theorems for Discrete Memoryless Systems. Cambridge University Press. p. 44. ISBN 9781139499989. Raymond
Pinsker's_inequality
Scheme for controlling errors in data over noisy communication channels
of forward error correcting codes. Many communication channels are not memoryless: errors typically occur in bursts rather than independently. If the number
Error_correction_code
Systems that do not produce or consume energy
active (e.g., certain types of nonlinear capacitors). Formally, for a memoryless two-terminal element, this means that the current–voltage characteristic
Passivity_(engineering)
Probability concept
only on its current state and not on its past behavior, due to the memorylessness of the exponential distribution and of discrete-time Markov chains.
Continuous-time_Markov_chain
Interpretation of quantum mechanics
models listed so far, the noise responsible for the collapse is Markovian (memoryless): either a Poisson process in the discrete GRW model, or a white noise
Objective-collapse_theory
Mathematical study of waiting lines, or queues
queueing model in 1920. In Kendall's notation: M stands for Markov or memoryless, and means arrivals occur according to a Poisson process D stands for
Queueing_theory
Model of electrical conduction
average time between subsequent collisions of such an electron is τ, with a memoryless Poisson distribution. The nature of the collision partner of the electron
Drude_model
Type of electronic audio manipulation
(excluding filters) and particularly to the introduction of new frequencies by memoryless nonlinearities. In music, the different forms of linear distortion have
Distortion_(music)
Probability of survival beyond any specified time
no matter the age of the individual or device. This fact leads to the "memoryless" property of the exponential survival distribution: the age of a subject
Survival_function
Sender of a communication
exactly as possible elsewhere in space or time. A source may be modelled as memoryless, ergodic, stationary, or stochastic, in order of increasing generality
Communication_source
Memoryless continuous-time stochastic process that shows two distinct values
In probability theory, the telegraph process is a memoryless continuous-time stochastic process that shows two distinct values. It models burst noise (also
Telegraph_process
Japanese anime television series
World. Both works share a common setting of a walled town inhabited by memoryless residents, and some individual elements were also borrowed, such as birds
Haibane_Renmei
Error-correcting codes used in wireless communication
have been shown to asymptotically achieve Shannon capacity on symmetric memoryless channels. Reed–Muller codes generalize the Reed–Solomon codes and the
Reed–Muller_code
Khmaladze, Estate V.; Brownrigg, Ray; Haywood, John (December 2010). "Memoryless Reigns of the "Sons of Heaven"". International Statistical Review. 78
List_of_Chinese_monarchs
System where the output depends only on past and current inputs
systems with an input x {\displaystyle x} and output y {\displaystyle y} . Memoryless system y ( t ) = x ( t ) cos ( ω t ) {\displaystyle
Causal_system
Concept in physics
additional assumptions, including spatial homogeneity, isotropy, and memorylessness. Hermann Minkowski also implicitly used both postulates when he introduced
Postulates of special relativity
Postulates_of_special_relativity
{\displaystyle 1.908<v<2.329} . These bounds are obtained by studying so-called memoryless strategies, that is strategies in which the decision to stop on X k {\displaystyle
Robbins'_problem
Collection of efficiently-computable functions which emulate a random oracle
the adversary can not force collisions. Constructing deterministic, memoryless authentication schemes (message authentication code based) which are provably
Pseudorandom_function_family
Process of mapping a continuous set to a countable set
J. (1984). "Optimum quantizer performance for a class of non-Gaussian memoryless sources". IEEE Transactions on Information Theory. 30 (3): 485–497. Bibcode:1984ITIT
Quantization (signal processing)
Quantization_(signal_processing)
Concept in quantum mechanics
dynamics. This approximation assumes that the environment, or bath, is memoryless. Approximate Markovian quantum master equations include the Redfield equation
Quantum_master_equation
Topics referred to by the same term
devices) tasked with finding content on digital media servers Discrete memoryless channel Dynamic Markov Compression algorithm Dynamic Mesh Communication
DMC
Channel used to relay signals
a receiver aided by one or more intermediate relay nodes. A discrete memoryless single-relay channel can be modelled as four finite sets, X 1 , X 2 ,
Relay_channel
shift-invariant although they are often approximated as shift-invariant (memoryless). Although MDDPD enables the use of DPD in multi source systems, there
Multidimensional digital pre-distortion
Multidimensional_digital_pre-distortion
Information-theoretical limit on transmission rate in a communication channel
bounds, have been proposed in the literature. The capacity of a discrete memoryless channel can be computed using the Blahut-Arimoto algorithm. Deep learning
Channel_capacity
Series whose partial sums eventually only have a fixed number of terms after cancellation
at random times, the waiting time until the next occurrence having a memoryless exponential distribution, and the number of "occurrences" in any time
Telescoping_series
Examples of the probabilistic construct
by the knowledge of earlier tosses showcases the Markov property, the memoryless property of a stochastic process. This example came from Markov himself
Examples_of_Markov_chains
Determining all voltages and currents within an electrical network
current values for static networks, which are circuits consisting of memoryless components only but have difficulties with complex dynamic networks. In
Network analysis (electrical circuits)
Network_analysis_(electrical_circuits)
High-performance forward error correction codes
{\displaystyle \textstyle y_{2k}} inputs with padding bits (zeros). Consider a memoryless AWGN channel, and assume that at k-th iteration, the decoder receives
Turbo_code
Limiting density of discrete points / (1:DC) Mean difference / (1:DCR) Memorylessness / (1:DCR) Probability vector / (1:D) Probability-generating function /
Catalog of articles in probability theory
Catalog_of_articles_in_probability_theory
Branch of thermodynamics
deeply than for time-dependent local equilibrium thermodynamics with memoryless materials, but fluxes are not independent variables of state. Extended
Non-equilibrium thermodynamics
Non-equilibrium_thermodynamics
Term in mathematics
probability distributions on the interval from 0 to ∞ on the real line, memorylessness characterizes the exponential distributions." This statement means that
Characterization (mathematics)
Characterization_(mathematics)
Concept in game theory
the following criteria: The strategies have the Markov property of memorylessness, meaning that each player's mixed strategy can be conditioned only on
Markov_perfect_equilibrium
polish Median test Mediation (statistics) Medical statistics Medoid Memorylessness Mendelian randomization Meta-analysis Meta-regression Metalog distribution
List_of_statistics_articles
System for describing queueing models
Symbol Name Description Examples M Markovian or memoryless Poisson process (or random) arrival process (i.e., exponential inter-arrival times). M/M/1 queue
Kendall's_notation
Class of algorithms in information theory
version of Blahut–Arimoto algorithm for directed information. A discrete memoryless channel (DMC) can be specified using two random variables X , Y {\displaystyle
Blahut–Arimoto_algorithm
such as the capacity of channels with feedback, capacity of discrete memoryless networks, capacity of networks with in-block memory, gambling with causal
Directed_information
that the two quantities are equal when the service time distribution is memoryless. Quantum capacity: The capacity of a quantum channel is in general not
List of unsolved problems in information theory
List_of_unsolved_problems_in_information_theory
Field of electrical engineering
time in the past (or in the future!). Memoryless systems do not depend on any past input. In common usage memoryless systems are also independent of future
System_analysis
Two-port non-reciprocal network element
similar to an ideal transformer in being a linear, lossless, passive, memoryless two-port device. However, whereas a transformer couples the voltage on
Gyrator
timing out in Jibril's game, and leaving Jibril vacantly happy yet mostly memoryless for a time.LN 8.2 Since her game with them became Blank's first true loss
List of No Game No Life characters
List_of_No_Game_No_Life_characters
Algorithms to decode messages
{\displaystyle x} . Note that if the probability of error on a discrete memoryless channel p {\displaystyle p} is strictly less than one half, then minimum
Decoding_methods
Theorem of probability theory
Körner, János (2011). Information Theory: Coding Theorems for Discrete Memoryless Systems. Cambridge University Press. p. 14. ISBN 9781139499989. Thomas
Stein's_lemma
Data compression algorithms
different source coding algorithms for an efficient description of a discrete memoryless source. Unfortunately, in spite of being different, both schemes became
Shannon–Fano_coding
Random process of binary (boolean) random variables
Bernoulli trials. Independence of the trials implies that the process is memoryless, in which past event frequencies have no influence on about future event
Bernoulli_process
exponential, it is an M/M/1 queue. However, the Poisson traffic model is memoryless, which means that it does not reflect the bursty nature of packet data
Traffic_generation_model
Similarity of two probability distributions
for constructing capacity-achieving codes for symmetric binary-input memoryless channels". IEEE Transactions on Information Theory. 55 (7): 3051–3073
Bhattacharyya_distance
Audio process
such as tube amplifiers, waveshaping is used to introduce a static, or memoryless, nonlinearity to approximate the transfer characteristic of a vacuum tube
Waveshaper
Topic in mathematics
independent output symbols) and noisy-channel coding theorem for non-stationary memoryless channels. T {\textstyle T} is a measure-preserving map on the probability
Asymptotic equipartition property
Asymptotic_equipartition_property
Type of bacterial motion
self-propelled motion in a dissipative environment Telegraph process – Memoryless continuous-time stochastic process that shows two distinct values Berg
Run-and-tumble_motion
American mathematician (1925–2011)
and Markov chains, in "Management Science", Vol. 9(1), 1962. A note on memoryless rules for controlling sequential control processes with R.E. Strauch in
Cyrus_Derman
Czech linguist (1932–2010)
Jelinek, Frederick (1968). Probabilistic Information Theory: Discrete and memoryless models. McGraw-Hill series in systems science. New York: McGraw-Hill.
Frederick_Jelinek
Non-parametric statistic on information transfer
S2CID 13178. Kramer, G. (January 2003). "Capacity results for the discrete memoryless network". IEEE Transactions on Information Theory. 49 (1): 4–21. doi:10
Transfer_entropy
Function in actuarial science
corresponds to an exponential distribution for X {\displaystyle X} and gives a memoryless survival pattern. In actuarial work, the Gompertz–Makeham law of mortality
Force_of_mortality
Term in quantum information theory
strong-converse property without assuming stationarity or memorylessness. For stationary memoryless channels, their formulation recovers the usual Holevo-capacity
Classical_capacity
2009 non-fiction book discussing mathematics
distribution associated with the previous state. In that sense, it is "memoryless": each random choice depends only on the current state, and not on the
Markov Chains and Mixing Times
Markov_Chains_and_Mixing_Times
strategy with errors. In 1956, Claude Shannon introduced the discrete memoryless channel with noiseless feedback. In 1961, Alfréd Rényi introduced the
Error-correcting codes with feedback
Error-correcting_codes_with_feedback
Before the heavy-tail distribution is introduced mathematically, the memoryless Poisson distribution, used to model traditional telephony networks, is
Long-tail_traffic
still in active use today. It is the most simplified model. In this "memoryless" model, every I/O reference represents an i.i.d multinomial random variable
Independent_Reference_Model
{\displaystyle X_{k}} are independent exponential random variables, then the memoryless property implies (if s is exceeded) the distributional symmetry of the
BRS-inequality
Canadian engineer
digital predistortion for power amplifiers with real time modeling of memoryless complex gains". "A latest innovation from Prof. Mohamad Sawan's team:
Mohamad_Sawan
Denoising scheme in information theory
sequences over a finite alphabet, which have been corrupted by a discrete memoryless channel. The DUDE was proposed in 2005 by Tsachy Weissman, Erik Ordentlich
Discrete_Universal_Denoiser
true name, Beloved, which Seimei told Ritsuka just before he died. 2 "Memoryless" Yumi Nakayama Yuji Kawahara April 13, 2005 (2005-04-13) Ritsuka uses
List_of_Loveless_episodes
Vehicle monitoring system
equipment failures could not be predicted (e.g. equipment failures exhibited memoryless behavior). Rockwell International GPS Systems Engineering Manager ordered
Integrated vehicle health management
Integrated_vehicle_health_management
Type of set in information theory
Strong typicality is often easier to work with in proving theorems for memoryless channels. However, as is apparent from the definition, this form of typicality
Typical_set
Hungarian mathematician (1941–2019)
theory she used a combinatorics approach to characterize error in discrete memoryless sources under distortion. She was particularly well known for her two-page
Katalin_Marton
parity game on a finite graph G. Using the above positional (also called memoryless) determinacy, this can be simulated by a finite game that ends when we
S2S_(mathematics)
is a known characteristic of the exponential distribution, i.e., its memoryless property. Intuitively, this means that it does not matter how long it
Residual_time
Hungarian mathematician
(1989) With János Körner: Information Theory: Coding Theorems for Discrete Memoryless Systems. Academic Press, 1981; 2nd edition, Cambridge University Press
Imre_Csiszár
Problem in information theory and communication
given distortion D {\displaystyle D} . It was found that for Gaussian memoryless sources and mean-squared error distortion, the lower bound for the bit
Distributed_source_coding
Abelaziz; Benzaouia, Abdellah; Rami, Mustapha Ait; Tadeo, Fernando (2008). "Memoryless Control to Drive States of Delayed Continuous-time Systems within the
Positive_systems
Method for determining the origin of a packet on the Internet
Edmonds, and Matoušek. For a single attack path, they proved that any memoryless PPM scheme requires at least Ω ( 2 b ⋅ 2 2 n / ( 2 b − 1 ) ) {\displaystyle
IP_traceback
MEMORYLESSNESS
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Boy/Male
Australian, French, Italian
Manly
Girl/Female
Indian, Tamil
Sure
Girl/Female
Indian
Hope, Aspiration, Expectation
Girl/Female
Hindu, Indian, Traditional
Bird
Girl/Female
Arabic, Farsi, Iranian, Muslim, Parsi
Heaven; Paradise
Boy/Male
Hindu, Indian
A Hindu Month
Girl/Female
Hindu
Dedicated to truth, Personified
Boy/Male
Gaelic
Moorish.
Girl/Female
Tamil
Victorious, Victory
Female
Greek
(á¼Î²Î·) Greek name derived from the word hebos, HÊBÊ means "young." In mythology, this is the name of a goddess of youth.
MEMORYLESSNESS
MEMORYLESSNESS
MEMORYLESSNESS
MEMORYLESSNESS
MEMORYLESSNESS