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Mathematical model for state estimation
In the theory of stochastic processes, filtering describes the problem of determining the state of a system from an incomplete and potentially noisy set
Filtering problem (stochastic processes)
Filtering_problem_(stochastic_processes)
Topics referred to by the same term
theoretic) filter with respect to set inclusion Filters in topology, the use of collections of subsets to describe convergence. Filtering problem (stochastic processes)
Filter
processing) Kalman filter, a well-known filtering algorithm related to both the filtering problem and the smoothing problem Generalized filtering Smoothing 1942
Smoothing problem (stochastic processes)
Smoothing_problem_(stochastic_processes)
Collection of random variables
where the index of the family often has the interpretation of time. Stochastic processes are widely used as mathematical models of systems and phenomena that
Stochastic_process
Difference of forecasted and actual values
information available till (including) time t. Kalman filter Filtering problem (stochastic processes) Errors and residuals in statistics Innovation butterfly
Innovation (signal processing)
Innovation_(signal_processing)
Algorithm that estimates unknowns from a series of measurements over time
beta filter Covariance intersection Data assimilation Ensemble Kalman filter Extended Kalman filter Fast Kalman filter Filtering problem (stochastic processes)
Kalman_filter
Optimization process
Kalman filter Invariant extended Kalman filter Fast Kalman filter Filtering problem (stochastic processes) Kernel adaptive filter Non-linear filter Particle
Moving_horizon_estimation
Randomly determined process
Markov process, and stochastic calculus, which involves differential equations and integrals based on stochastic processes such as the Wiener process, also
Stochastic
Russian mathematician (1930–1997)
Prize, 1988 State Prize of the Russian Federation, 1996 Filtering problem (stochastic processes) with Pyotr Kuznetsov: The propagation of electromagnetic
Ruslan_Stratonovich
Differential equations involving stochastic processes
random behaviour are possible, such as jump processes like Lévy processes or semimartingales with jumps. Stochastic differential equations are in general neither
Stochastic differential equation
Stochastic_differential_equation
Type of Monte Carlo algorithms for signal processing and statistical inference
filters, also known as sequential Monte Carlo methods, are a set of Monte Carlo algorithms used to find approximate solutions for filtering problems for
Particle_filter
Probabilistic optimal control
Stochastic control or stochastic optimal control is a sub field of control theory that deals with the existence of uncertainty either in observations or
Stochastic_control
Filter for nonlinear state estimation
Unscented Kalman filter Nonlinear filtering problem Projection filters Julier, S.J.; Uhlmann, J.K. (2004). "Unscented filtering and nonlinear estimation" (PDF)
Extended_Kalman_filter
Representation of a type of random process
dependent linearly on their own previous values on a stochastic basis. The model is in the form of a stochastic difference equation (or recurrence relation) which
Autoregressive_model
Statistical model
In probability theory and statistics, a Gaussian process is a stochastic process (a collection of random variables indexed by time or space), such that
Gaussian_process
Signal filter whose output is not a linear function of its input
such filters is known as the filtering problem for a stochastic process in estimation theory and control theory. Examples of nonlinear filters include:
Nonlinear_filter
Resource problem in machine learning
Gentile (SIGIR 2016), where the classical collaborative filtering, and content-based filtering methods try to learn a static recommendation model given
Multi-armed_bandit
Homomorphic filtering is a generalized technique for signal and image processing, involving a nonlinear mapping to a different domain in which linear filter techniques
Homomorphic_filtering
Signal processing algorithm
as filtering, and α < 0 {\displaystyle \alpha <0} is known as smoothing (see Wiener filtering chapter of for more details). The Wiener filter problem has
Wiener_filter
Statistical algorithm
between the desired and the actual signal). It is a stochastic gradient descent method in that the filter is only adapted based on the error at the current
Least_mean_squares_filter
Probabilistic problem-solving algorithm
Markov process whose transition probabilities depend on the distributions of the current random states (see McKean–Vlasov processes, nonlinear filtering equation)
Monte_Carlo_method
Generalized filtering is a generic Bayesian filtering scheme for nonlinear state-space models. It is based on a variational principle of least action
Generalized_filtering
Model in probability theory
In probability theory, a martingale is a stochastic process in which the expected value of the next observation, given all prior observations, is equal
Martingale (probability theory)
Martingale_(probability_theory)
In filtering theory the Zakai equation is a linear stochastic partial differential equation for the un-normalized density of a hidden state. In contrast
Zakai_equation
Random process independent of past history
most important and central stochastic processes in the theory of stochastic processes. These two processes are Markov processes in continuous time, while
Markov_chain
Filters used in signal processing that are optimal in some sense
matched filter is the optimal linear filter for maximizing the signal-to-noise ratio (SNR) in the presence of additive stochastic noise. Matched filters are
Matched_filter
Optimization algorithm
Stochastic gradient descent (often abbreviated SGD) is an iterative method for optimizing an objective function with suitable smoothness properties (e
Stochastic_gradient_descent
inference Field experiment Fieller's theorem File drawer problem Filtering problem (stochastic processes) Financial econometrics Financial models with long-tailed
List_of_statistics_articles
stochastic analysis (the extension of calculus to stochastic processes) and of differential geometry. The connection between analysis and stochastic processes
Stochastic analysis on manifolds
Stochastic_analysis_on_manifolds
Theoretical problem in quantum physics
and he notes that these processes are irreversible. He considered a consistent account of this issue to be an unsolved problem. Hugh Everett's many-worlds
Measurement_problem
Partial differential equations with random force terms and coefficients
1090/bull/1670. Bain, A.; Crisan, D. (2009). Fundamentals of Stochastic Filtering. Stochastic Modelling and Applied Probability. Vol. 60. New York: Springer
Stochastic partial differential equation
Stochastic_partial_differential_equation
Adaptive filter algorithm for digital signal processing
Vinter, Stochastic Modelling and Control, Springer, 1985, ISBN 0-412-16200-8 Weifeng Liu, Jose Principe and Simon Haykin, Kernel Adaptive Filtering: A Comprehensive
Recursive least squares filter
Recursive_least_squares_filter
Dutch mathematician
J.H. van Schuppen, On the weak finite stochastic realization problem, Filtering and Control of Random Processes, Proceedings of the ENST-CNET Colloquium
Jan_H._van_Schuppen
Russian-Israeli mathematician (1936–2019)
theory and applications of stochastic processes, in particular to martingales, stochastic control and nonlinear filtering. Liptser was born in Kirovograd
Robert_Liptser
Geometric algorithms for signal processing
used to find approximate solutions for filtering problems for nonlinear state-space systems. The filtering problem consists of estimating the unobserved
Projection_filters
Concept in probability and statistics
theory and statistics, given a stochastic process, the autocovariance is a function that gives the covariance of the process with itself at pairs of time
Autocovariance
realization, stochastic modeling, estimation and control, and moment problems in systems and control. He is known for the discovery of the fast filtering algorithms
Anders_Lindquist
Computational model used in machine learning
Generative AI Data visualization Machine translation Social network filtering E-mail spam filtering Medical diagnosis Disaster response NNs have been used to diagnose
Neural network (machine learning)
Neural_network_(machine_learning)
In filtering theory the Kushner equation (after Harold Kushner) is an equation for the conditional probability density of the state of a stochastic non-linear
Kushner_equation
principle is one of the fundamental principles of stochastic control theory, which states that the problems of optimal control and state estimation can be
Separation principle in stochastic control
Separation_principle_in_stochastic_control
Mathematician
a mathematician known for research in mathematical finance, filtering theory, stochastic analysis with differential geometry, probability theory and statistics
Damiano_Brigo
Time at which a random variable stops exhibiting a behavior of interest
In probability theory, in particular in the study of stochastic processes, a stopping time (also Markov time, Markov moment, optional stopping time or
Stopping_time
Statistical Markov model
stochastic processes. The pair ( X t , Y t ) {\displaystyle (X_{t},Y_{t})} is a hidden Markov model if X t {\displaystyle X_{t}} is a Markov process whose
Hidden_Markov_model
Czech-American mathematician (born 1930)
nonanticipating solutions to stochastic DEs: implications for functional DEs, filtering, and control. Stochastic Processes Applied 5:3, 243–263., 1977
Václav_E._Beneš
Process in microfabrication
physical vapor deposition, plating, or ion implantation processes. Photolithography processes can be classified according to the type of light used, including
Photolithography
Israeli scientist (born 1926–2015)
the study of the theory of stochastic processes and its application to information and control problems; namely, problems of noise in communication radar
Moshe_Zakai
Class of mathematical problems
optimal time to exercise. Halting problem Markov decision process Optional stopping theorem Prophet inequality Stochastic control Sequential analysis Chow
Optimal_stopping
Study of mathematical algorithms for optimization problems
Dynamic programming is the approach to solve the stochastic optimization problem with stochastic, randomness, and unknown model parameters. It studies
Mathematical_optimization
Israeli mathematician
professor at the University of Minnesota. His research deals with stochastic processes and filtering theory with applications to control theory (electrical engineering)
Ofer_Zeitouni
Sequence of data points over time
have many forms and represent different stochastic processes. When modeling variations in the level of a process, three broad classes of practical importance
Time_series
{\textstyle {\dot {D}}=rD+G(t)-T(t)} Stochastic differential equation Geometric Brownian motion Ornstein–Uhlenbeck process Cox–Ingersoll–Ross model Vidale–Wolfe
List of named differential equations
List_of_named_differential_equations
Probabilistic numerical ODE solver
distribution, for the ODE solution, in the form of a stochastic processes, more specifically, as Gauss–Markov processes. Discretization results in nonlinear Gaussian
ODE_filter
Overview of and topical guide to machine learning
Collaborative filtering Content-based filtering Hybrid recommender systems Search engine Search engine optimization Social engineering Graphics processing unit
Outline_of_machine_learning
Stieltjes moment problem / mnt (1:R) Stochastic matrix / Mar Stochastic processes and boundary value problems / scl Trigonometric moment problem / mnt (1:R)
Catalog of articles in probability theory
Catalog_of_articles_in_probability_theory
Statistical filter
of the KZ filter and its extensions in different areas. KZ filter can be used to smooth the periodogram. For a class of stochastic processes, Zurbenko
Kolmogorov–Zurbenko_filter
Algorithms to complete a sudoku
second using an exhaustive search routine and faster processors.p:25 Sudoku can be solved using stochastic (random-based) algorithms. An example of this method
Sudoku_solving_algorithms
Winds that vary randomly in space and time
Continuous gusts or stochastic gusts are winds that vary randomly in space and time. Models of continuous gusts are used to represent atmospheric turbulence
Continuous_gusts
Process of calculating the causal factors that produced a set of observations
An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating
Inverse_problem
Mathematical model of continuous gusts
power spectral densities, so exact filters can be designed that take white noise inputs and output stochastic processes with the Dryden gusts' power spectral
Dryden_Wind_Turbulence_Model
Intelligence of machines
(2021, sect. 16.6) Markov decision processes and dynamic decision networks: Russell & Norvig (2021, chpt. 17) Stochastic temporal models: Russell & Norvig
Artificial_intelligence
states that under some assumptions the problem of designing an optimal feedback controller for a stochastic system can be solved by designing an optimal
Separation_principle
Intellectual isolation through internet algorithms
the impact of filter bubble and algorithmic filtering on social media polarization. They used a mathematical model called the "stochastic block model"
Filter_bubble
Israeli-American mathematician
Quantitative Science there. His research deals with probability theory and stochastic processes, the theory of large deviations, the spectral theory of random matrices
Amir_Dembo
Linear optimal control technique
system parameters may be assumed stochastic instead of deterministic. The associated more difficult control problem leads to a similar optimal controller
Linear–quadratic–Gaussian control
Linear–quadratic–Gaussian_control
Type of feedforward neural network
network that learns features via filter (or kernel) optimization. This type of deep learning network has been applied to process and make predictions from many
Convolutional_neural_network
Lithography using 13.5 nm UV light
Patterns and Stochastic Printing Failures in a 5 nm Logic Process with EUV Lithography," CSTIC 2020. Frederick Chen (2025-03-21). 7nm EUV Stochastics from Electron
Extreme ultraviolet lithography
Extreme_ultraviolet_lithography
Study of uncertainty in the output of a mathematical model or system
the sensitivity measures can be hard to interpret. Stochastic code: A code is said to be stochastic when, for several evaluations of the code with the
Sensitivity_analysis
Signal with equal energy per octave
indicate amplification and coupling of processes in the climate system. Many time-dependent stochastic processes are known to exhibit 1/fα noises with
Pink_noise
Printing process
method of creating screens, frequency modulation, is used in a process also known as stochastic screening. Both modulation methods are named by analogy with
Halftone
Parameter-free superresolution algorithm
inverse problem in spectral estimation, direction-of-arrival (DOA) estimation and tomographic reconstruction with applications in signal processing, medical
SAMV_(algorithm)
Area of research in signal processing
the array processing problem, two main methods have been considered depending on the signal data model assumption. According to the Stochastic ML, the signals
Array_processing
Term used in the United States and Canada to describe a type of water pollution control
Urban Runoff Program (NURP) - EPA research program on stormwater BMPs Stochastic Empirical Loading and Dilution Model for modeling the performance of BMPs
Best management practice for water pollution
Best_management_practice_for_water_pollution
Soviet mathematician (1903–1987)
bombers during the Battle of Moscow. In his study of stochastic processes, especially Markov processes, Kolmogorov and the British mathematician Sydney Chapman
Andrey_Kolmogorov
American mathematician and philosopher (1894–1964)
prodigy, Wiener later became an early researcher in stochastic and mathematical noise processes, contributing work relevant to electronic engineering
Norbert_Wiener
Method of machine learning
optimization, shortest path prediction (with stochastic weights, e.g. traffic on roads for a maps application), spam filtering, real-time fraud detection, dynamic
Online_machine_learning
Branch of engineering and mathematics
modeling errors. Stochastic control deals with control design with uncertainty in the model. In typical stochastic control problems, it is assumed that
Control_theory
Competitive algorithm for searching a problem space
the objective function in the optimization problem being solved. The more fit individuals are stochastically selected from the current population, and
Genetic_algorithm
Type of differential equation
differential algebraic equation Recurrence relation Stochastic processes and boundary value problems "Regularity and singularities in elliptic PDE's: beyond
Partial_differential_equation
Filter that rejects signals outside a certain range
the kind of data (stochastic rather than deterministic) arising in macroeconomics. In this paper entitled "General Model-Based Filters for Extracting Trends
Band-pass_filter
map Skill chaining Sparse PCA Stochastic gradient descent Structured kNN Support vector machine T-distributed stochastic neighbor embedding Weighted majority
List of artificial intelligence algorithms
List_of_artificial_intelligence_algorithms
Theory of stochastic processes
In the theory of stochastic processes, the Karhunen–Loève theorem (named after Kari Karhunen and Michel Loève), also known as the Kosambi–Karhunen–Loève
Kosambi–Karhunen–Loève theorem
Kosambi–Karhunen–Loève_theorem
Iterative simulation method
optimizes a problem by iteratively trying to improve a population of candidate solutions with regard to a given measure of quality. It solves a problem through
Particle_swarm_optimization
Equation that describes density changes of a material that is diffusing in a medium
diffusion, Horwood Ikeda, N., Watanabe, S. (1981). Stochastic Differential Equations and Diffusion Processes, Elsevier, Academic Press Philibert, J., Laskar
Diffusion_equation
American-born computer scientist
signals from motor cortex. The team was the first to use Kalman filtering and particle filtering to decode motor cortical ensemble activity. With these Bayesian
Michael_J._Black
Identification of nonlinear systems
the signals are modeled using stochastic processes. The process x t {\displaystyle x_{t}} is known as the state process, w t {\displaystyle w_{t}} and
Nonlinear system identification
Nonlinear_system_identification
Optimization algorithm
used in the following decades. A simple extension of gradient descent, stochastic gradient descent, serves as the most basic algorithm used for training
Gradient_descent
Time series models
process) can be thought of as digital filtering and "unfiltering" operations. As such, it is useful to study the frequency response of such filters to
Autoregressive fractionally integrated moving average
Autoregressive_fractionally_integrated_moving_average
Soviet and Russian mathematician (born 1934)
Bulinsky: Theory of Stochastic Processes. A course of lectures. Moscow 2003 (in Russian) From "Disorder" to Nonlinear Filtering and Martingale Theory
Albert_Shiryaev
Mathematical modeling of psychological theories and phenomena
the developments in signal processing, information theory, linear systems and filter theory, game theory, stochastic processes and mathematical logic gained
Mathematical_psychology
Statistical estimation method
ISBN 978-94-011-0854-6, retrieved 2023-07-06 Jazwinski A.H., Stochastic Processes and Filtering Theory, Academic Press, New York, 1970. Nielsen, Jan Nygaard;
Innovation_method
Type of machine learning model
may include filtering out such content. LLM-generated content can pose a problem if the content is similar to human text (making filtering difficult) but
Large_language_model
Indian mathematician
obtained his doctoral degree in 1951 in the then developing field of stochastic processes. In the start of his career he held the position of lecturer at the
Gopinath_Kallianpur
Area of applied mathematics
modeled as continuous-time Markov jump processes governed by the chemical master equation. Beyond describing stochastic fluctuations, several studies have
Chemical reaction network theory
Chemical_reaction_network_theory
Statistical analysis
times when the probability distribution of a stochastic process or time series changes. In general the problem concerns both detecting whether or not a change
Change_detection
Paradigm in machine learning that uses no classification labels
such as massive text corpus obtained by web crawling, with only minor filtering (such as Common Crawl). This compares favorably to supervised learning
Unsupervised_learning
simpler way to solve a specific problem or a broad set of problems. Simply speaking, algorithms define different processes, sets of rules and regulations
List_of_algorithms
Change of species in a region over time
of microbial succession evaluated the balances between stochastic and deterministic processes in the bacterial colonization of a salt marsh chronosequence
Ecological_succession
Indian mathematician
Finitely additive probability measures, stochastic calculus, martingale problems and Markov processes, Filtering theory, option pricing theory, psephology
Rajeeva_Laxman_Karandikar
Computer system simulating intelligence
environment or in the process itself, or the processes are simply stochastic in nature. Thus, CI techniques are properly aimed at processes that are ill-defined
Computational_intelligence
Simulation software developed by Ventana Systems
like logit. It supports discrete delays, queues and a variety of stochastic processes. There are multiple paths for cross sectional and time-series data
Vensim
FILTERING PROBLEM-STOCHASTIC-PROCESSES
FILTERING PROBLEM-STOCHASTIC-PROCESSES
Boy/Male
Hindu
Altering form at will
Boy/Male
Hindu
Born during the rainy season, Money
Girl/Female
Indian, Telugu
Destroyer of Problems
Boy/Male
Indian, Tamil
People with this Name are Preferably Intelligent and Very Generous; Highly Knowledgeable in Problem Solving Skills
Surname or Lastname
English
English : variant of Preble.
Surname or Lastname
English
English : unexplained. It may be a variant of a medieval name, Preville, a habitational name from a Norman place named with the elements pré ‘meadow’ + ville ‘settlement’. However, this theory is not supported by evidence of early forms.
Boy/Male
Tamil
Born during the rainy season, Money
Boy/Male
Hindu, Indian
Problem
Boy/Male
Tamil
Kamaroopine | காமாஂரூபீநே
Altering form at will
Kamaroopine | காமாஂரூபீநே
Surname or Lastname
English
English : occupational name for a winder of wool, from an agent derivative of Middle English winde(n) ‘to wind’ (Old English windan ‘to go’, ‘to proceed’). The verb was also used in the Middle Ages of various weaving and plaiting processes, so that in some cases the name may have referred to a basket or hurdle maker.English : habitational name from any of the various minor places in northern England so called, from Old English vindr ‘wind’ + erg ‘hut’, ‘shelter’, i.e. a shelter against the wind.English : John Winder is recorded in Somerset Co., MD, in 1665. William Henry Winder, born in the county in 1775, was blamed for the military defeat that led to the British burning of Washington, DC, in 1814; his son John Henry Winder (b. 1800) was a confederate general who was commander of southern military prisons.
Surname or Lastname
English
English : variant of Preble.
Boy/Male
Arabic, Indian, Muslim
Problem Solver
Girl/Female
Bengali, Indian
Eternity; Problem Solver
Girl/Female
Muslim/Islamic
Away from all Problems
Boy/Male
Hindu, Indian
Glitering Like Diamond
Surname or Lastname
English
English : occupational name for a maker of wheels (for vehicles or for use in spinning or various other manufacturing processes), from an agent derivative of Middle English whele ‘wheel’. The name is particularly common on the Isle of Wight; on the mainland it is concentrated in the neighboring region of central southern England.A founder of Salisbury, NH, in 1634 was John Wheeler.
Boy/Male
Muslim
Problem solver
Male
Hebrew
(ישִׂימִ×ֵל) Hebrew name YESIYMAEL means "whom God makes" according to Gesenius. But hasn't he omitted the first element (Ye-)? It looks to actually be composed of 'el "god" and suwm "to create, to make" or "to place, to set" and yÄ• "to age, to grow old," from yashen "to blanch, to fester, to grow weary;" hence "whom God makes grow old," especially from a festering sickness called leprosy (Hebrew tsara'ath "leprosy" from tsara "struck down, smitten" by God). Gesenius states that "leprosy" (צָרַע) may be the same as (גָרַע) "scabby," so that it means to be struck by a scabby disease. In the bible, this is the name of a Simeonite chief of the family of Shimei. Jesimiel is the Anglicized form.
Surname or Lastname
English
English : from an agent derivative of Middle English wasch(en) ‘to wash’ (Old English wæscan), hence an occupational name for a laundryman, or for someone who washed raw wool before spinning. Various other occupations, too, involved washing processes and the name may relate to any of these. For example, it may have denoted a man who washed sheep; some tenants on the manor of Burpham, near Worthing, in Sussex (where the surname is found from an early date), had as part of their feudal service to wash the flocks of their master.Americanized spelling of the German cognate Wascher.
Boy/Male
African, Australian, Hindu, Indian
Flowers
FILTERING PROBLEM-STOCHASTIC-PROCESSES
FILTERING PROBLEM-STOCHASTIC-PROCESSES
Girl/Female
Tamil
Ratnajyouti | ரதà¯à®¨à®¾à®œà¯à®¯à¯Œà®¤à¯€
Light from a jewel, Lustrous jewel
Surname or Lastname
English and Scottish
English and Scottish : variant of Marshall, derived from an Anglo-Norman French form of Old French maresc(h)al ‘marshal’.
Surname or Lastname
English
English : habitational name from a place in Shropshire named Chetwynd, from the Old English personal name Ceatta + Old English (ge)wind ‘winding ascent’.
Girl/Female
Indian, Telugu
Lightning
Boy/Male
Hindu, Indian
Shiva is Only One
Girl/Female
Tamil
Niramayi | நிராமயீ
Pure, Clean, Spotless, Without blemish
Boy/Male
Australian, Biblical, French, German, Latin
Who Loves the Forest; Wood Dweller; From the Woods
Girl/Female
Tamil
A holy river
Boy/Male
Tamil
Lake, Lake of the fairies
Female
French
Variant spelling of Old French Giselle, GISÈLE means "pledge, hostage, noble offspring."
FILTERING PROBLEM-STOCHASTIC-PROCESSES
FILTERING PROBLEM-STOCHASTIC-PROCESSES
FILTERING PROBLEM-STOCHASTIC-PROCESSES
FILTERING PROBLEM-STOCHASTIC-PROCESSES
FILTERING PROBLEM-STOCHASTIC-PROCESSES
n.
One of the fleshy legs found on the abdominal segments of the larvae of Lepidoptera, sawflies, and some other insects. Those of Lepidoptera have a circle of hooks. Called also proped, propleg, and falseleg.
a.
Altering; gradually changing.
n.
The act or process of straining or filtering.
n.
A stammering; a faltering in speech.
imp. & p. p.
of Probe
n.
A filtering machine operated by air pressure.
superl.
Bland; mild; smoothing; fattering.
n.
A faltering in speech; stammering.
a.
Conjectural; able to conjecture.
p. pr. & vb. n.
of Filter
v. t.
To clarify by filtering through clay, as sugar.
n.
The art or process of covering metals, wood, paper, glass, etc., with a thin film of metallic silver, or a substance resembling silver; also, the firm do laid on; as, the silvering of a glass speculum.
n.
Same as Proleg.
n.
A festering.
n.
Anything which is required to be done; as, in geometry, to bisect a line, to draw a perpendicular; or, in algebra, to find an unknown quantity.
v. t.
To propose problems.
v. t.
To examine, as a wound, an ulcer, or some cavity of the body, with a probe.
n.
A question proposed for solution; a matter stated for examination or proof; hence, a matter difficult of solution or settlement; a doubtful case; a question involving doubt.
n.
Prowler; thief.
n.
One who proposes problems.