Elements Of Stochastic Processes
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The document defines stochastic processes and their basic properties such as stationarity and ergodicity. It discusses analyzing systems using stochastic processes, including how the power spectrum represents the frequency content of a wide-sense stationary process. The power spectrum is the Fourier transform of the autocorrelation function, and the power spectrum of the output of a linear, time-invariant system is equal to the multiplication of the input power spectrum and the transfer function of the system.
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Static modeling represents the static elements of software such as classes, objects, and interfaces and their relationships. It includes class diagrams and object diagrams. Class diagrams show classes, attributes, and relationships between classes. Object diagrams show instances of classes and their properties. Dynamic modeling represents the behavior and interactions of static elements through interaction diagrams like sequence diagrams and communication diagrams, as well as activity diagrams.
Simulation Techniques
The document discusses using simulation to model queuing problems with random numbers. It describes queuing systems as having arrivals, a waiting line, service, and departure components. A single queue-single service point queuing structure is examined, with first-come, first-served queue discipline and random inter-arrival and service times. An example problem simulates 10 customer arrivals at a retail store using random numbers to estimate average waiting time and server idle time percentage. The solution shows calculating arrival and service time probabilities, simulating customer service, and finding total 4 minutes of waiting time and 12 minutes of idle time over 53 minutes.
Prob review
1) Probability is defined as a set function that satisfies three axioms: non-negativity, the probability of the sample space is 1, and countable additivity.
2) Conditional probability is the probability of an event B given that event A has occurred, defined as P(B|A)=P(A∩B)/P(A). Events A and B are independent if P(B|A)=P(B) and P(A|B)=P(A).
3) Bayes' theorem gives the probability of an event A given that event B has occurred as P(A|B)=P(A)P(B|A)/P(B).
Progress seminar
1) OFDM is used to combat channel impairments like fading and intersymbol interference that occur due to high transmission rates in wireless systems.
2) In OFDM, high rate data streams are converted to low rate parallel streams and modulated using techniques like BPSK before transmission.
3) The use of a cyclic prefix preserves orthogonality in OFDM and prevents intersymbol interference.
4) The document describes the key components of an OFDM system including the transmitter, channel model, and receiver section. It focuses on modeling the wireless channel as a Rayleigh fading channel using the Jakes model.
Feedback on Part 1 of the CSLP
The document provides feedback on Part 1 of a computer science practical. It summarizes submissions for Part 1, including operating systems used. It addresses some common problems and uncertainties students had, such as compilation errors, unfamiliar aspects of Objective-C, and error messages. It also provides clarification on issues like imports, method implementations, and pointer conversions.
Actuarial modeling of general practictioners' drug prescriptions costs
An actuarial model of drug prescriptions from a general practictioner is presented. The non life actuarial approach is applied to a health economics problem
Zhuoxin Li_School Projects
The document lists several projects completed by the individual including studies of pet insurance, automobile insurance, life insurance pricing, group legal insurance, equity analysis, pension plan pricing, and a claim experience analysis. The projects involved researching various types of insurance, analyzing industry data, developing actuarial models in Excel and SAS, calculating premiums and reserves, and presenting results.
Radio propagation
This document discusses radio propagation and propagation models. It begins with an introduction to radio and propagation mechanisms like free space propagation, refraction, diffraction, and scattering. It then discusses the objective of developing propagation models to predict signal strength at a receiver. The document outlines that propagation models are specialized based on scale, environment, and application. It covers large-scale path loss models and small-scale fading models. It discusses specific propagation mechanisms and models like free space, log-distance path loss, ground reflection, hilly terrain, indoor models, and statistical fading models.
Anatomy of an econometric modelling (1)
1. The document outlines the steps in developing an econometric model of consumption, including specifying a theory, developing a mathematical model, accounting for additional variables, obtaining data, estimating model parameters, testing hypotheses, making forecasts, and using the model for policy purposes.
2. It presents Keynes' theory that consumption increases with income but by less than the increase in income, represented mathematically as Y = β1 + β2X. Additional variables are accounted for with an error term.
3. The document estimates the parameters β1 and β2 using consumption and GDP data, finding marginal propensity to consume (MPC) of about 0.70. It then demonstrates using the model to forecast consumption and analyze
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All types of model(Simulation & Modelling) #ShareThisIfYouLike
All types of model(Simulation & Modelling) #ShareThisIfYouLike
Actuarial modeling of general practictioners' drug prescriptions costs
Actuarial modeling of general practictioners' drug prescriptions costs
Similar to Elements Of Stochastic Processes
Unit1 pg math model
This document provides an overview of mathematical modeling and analysis techniques for mechanical engineering design. It discusses what mathematical models are, how they are used for simulation, prediction, design evaluation, and control system design. It defines systems and variables, and covers dynamic and linear time-invariant systems. Modeling techniques like differential equations, transfer functions, and state-space models are presented. Identification methods like parametric and frequency-domain techniques are also summarized. Finally, neural network approaches to system identification are introduced.
L2_Dynamics Overview.pdf
The document discusses dynamic systems and modeling dynamic systems. It provides examples of dynamic systems from various domains like mechanical, electrical, biological, and economic systems. It defines dynamic systems as systems where the present output depends on both present and past inputs. The document discusses modeling dynamic systems using mathematical models and provides guidelines for formulating control-oriented models, including defining the objective, system boundaries, relevant stocks, conservation laws, and relations between flows and levels. It provides examples of modeling a room's thermal dynamics and a vehicle's motion and energy consumption.
Compit 2013 - Torsional Vibrations under Ice Impact
- The document discusses bridging the gap between steady-state and transient simulation for torsional vibrations under ice impact.
- It introduces modeling methods that allow both transient and steady-state analysis to operate on the same model base using a unified framework based on ordinary differential equations.
- It also discusses propeller modeling that incorporates established steady-state and transient methods and is being certified by classification societies for compliance with ice class simulation requirements.
Basic System Properties.ppt
The document summarizes several key properties of systems, including:
1) Memoryless systems have output that depends only on the present input, while causal systems have output that depends on present and past inputs.
2) Invertible systems have a one-to-one mapping between distinct inputs and outputs, allowing the input to be recovered from the output.
3) Time-invariant systems have parameters that do not vary over time, while time-varying systems have parameters dependent on time.
4) Impulse, unit step, and ramp signals are useful test signals that can reveal qualitative characteristics of a system's transient and steady-state response.
Machiwal, D. y Jha, MK (2012). Modelado estocástico de series de tiempo. En A...
This document provides an overview of stochastic modelling and different stochastic processes that are commonly used, including:
- Purely random (white noise) processes where data points are independent and identically distributed
- Autoregressive (AR) processes where each data point is modeled as a linear combination of previous data points plus noise
- Moving average (MA) processes where each data point is modeled as a linear combination of previous noise terms plus a constant
- Autoregressive moving average (ARMA) processes which combine AR and MA processes
- Autoregressive integrated moving average (ARIMA) processes which explicitly include differencing to make time series stationary
LeastSquaresParameterEstimation.ppt
In these two lectures, we’re looking at basic discrete time representations of linear, time invariant plants and models and seeing how their parameters can be estimated using the normal equations.
The key example is the first order, linear, stable RC electrical circuit which we met last week, and which has an exponential response.
solver (1)
- The document details a state space solver approach for analog mixed-signal simulations using SystemC. It models analog circuits as sets of linear differential equations and solves them using the Runge-Kutta method of numerical integration.
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- The state space approach allows modeling analog circuits without transistor-level details, improving simulation speed over traditional mixed-mode simulations while still capturing system-level behavior.
Lecture12me1766steadystateerror 12555290178452-phpapp03
This document discusses steady-state error in control systems. It defines steady-state error as the difference between the input and output of a system as time approaches infinity. Several types of test inputs and their effects on steady-state error are examined, including step inputs and ramp inputs. Formulas are provided for calculating steady-state error in unity feedback and non-unity feedback systems, as well as for systems with disturbances. Examples are worked through to demonstrate calculating steady-state error and sensitivity to parameter changes for various control systems and inputs.
IFAC2008art
This document discusses using an observability index to decompose the Kalman filter into two filters applied sequentially: 1) A filter estimating the transitional process caused by uncertainty in initial conditions, which treats the system as deterministic. 2) A filter estimating the steady state that treats the system as stochastic. The observability index measures observability as a signal-to-noise ratio to evaluate how long it takes to estimate states in the presence of noise. This decomposition simplifies filter implementation and reduces computational requirements by restricting estimated states and dividing the observation period into transitional and steady state estimation.
Phd Defense 2007
The document discusses modeling nonlinear digital integrated circuits (ICs) using system identification techniques. It explores using parametric models with different representations including local linear state-space models. Models are estimated from input-output port measurements and validated. Local linear state-space models provided the best results with good accuracy, a unique solution, and verified local stability, while also allowing efficient simulation. The models were successfully applied to simulate a mobile data link system.
Signals&Systems: Quick pointers to Fundamentals
It gives the flow to understand the signals and systems with their definitions, examples and properties.
Frequency Response Techniques
1. The document discusses frequency response analysis techniques, which analyze how a system responds to input signals of varying frequencies.
2. It describes two common frequency response techniques - Bode plots, which show magnitude and phase response as functions of frequency, and Nyquist plots, which plot magnitude against phase on a polar graph.
3. The techniques provide insights into system stability and dynamics and are useful for control system design, but their use requires complex derivations and they do not always directly indicate transient response characteristics.
Foundation and Synchronization of the Dynamic Output Dual Systems
In this paper, the synchronization problem of the dynamic output dual systems is firstly introduced and investigated. Based on the time domain approach, the state variables synchronization of such dual systems can be verified. Meanwhile, the guaranteed exponential convergence rate can be accurately estimated. Finally, some numerical simulations are provided to illustrate the feasibility and effectiveness of the obtained result. Yeong-Jeu Sun "Foundation and Synchronization of the Dynamic Output Dual Systems" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-6 , October 2019, URL: https://www.ijtsrd.com/papers/ijtsrd29256.pdf Paper URL: https://www.ijtsrd.com/engineering/electrical-engineering/29256/foundation-and-synchronization-of-the-dynamic-output-dual-systems/yeong-jeu-sun
df_lesson_01.ppt
1. The document summarizes a lecture on discrete-time signals and systems.
2. It defines different types of signals, including discrete-time and discrete-valued signals which are relevant for digital filter theory.
3. It also classifies systems as static vs. dynamic, time-invariant vs. time-variable, linear vs. nonlinear, causal vs. non-causal, stable vs. unstable, and recursive vs. non-recursive.
4. It describes the time-domain representation of linear, time-invariant (LTI) systems using impulse response and convolution.
Earthquake Seismic Sensor Calibration
The document provides an overview of seismic sensors and their calibration. It discusses two main types of seismic sensors - inertial seismometers which measure ground motion relative to a suspended mass, and strainmeters which measure the relative motion of two points in the ground. Inertial seismometers are generally more sensitive but strainmeters can outperform them at very low frequencies. The document focuses on describing the dynamic properties and calibration of inertial seismometers. There are four equivalent ways to characterize the response of a linear seismometer system: differential equations, transfer functions, complex frequency response, and impulse response. Calibration involves determining the system's response and expressing it using one of these representations.
Design of ternary sequence using msaa
In the classical model, the fundamental building block is represented by bits exists in two states a 0 or a 1. Computations are done by logic gates on the bits to produce other bits. By increasing the number of bits, the complexity of problem and the time of computation increases. A quantum algorithm is a sequence of operations on a register to transform it into a state which when measured yields the desired result. This paper provides introduction to quantum computation by developing qubit, quantum gate and quantum circuits.
Efficient Implementation of Self-Organizing Map for Sparse Input Data
This document describes improvements made to the self-organizing map (SOM) algorithm to make it more efficient for sparse, high-dimensional input data. The key contributions are a sparse SOM (Sparse-Som) and sparse batch SOM (Sparse-BSom) algorithm that exploit the sparseness of the data to reduce computational complexity from O(TMD) to O(TMd), where d is the number of non-zero dimensions. Sparse-Som speeds up the BMU search and weight update phases, while Sparse-BSom further allows for efficient parallelization. Experiments show Sparse-Som and Sparse-BSom train significantly faster than standard SOM on sparse datasets, with comparable or better quality
Advance control theory
1. A state variable representation uses state variables, inputs, and outputs to model dynamic systems. The state variables provide information about the internal state of the system.
2. The behavior of a system can be described by state equations that relate the time derivatives of the state variables to the inputs, state variables, and outputs.
3. Eigenvalues and eigenvectors, which are derived from state variable models, have many applications including vibration analysis, image recognition, and determining communication channel capacities.
TEST GENERATION FOR ANALOG AND MIXED-SIGNAL CIRCUITS USING HYBRID SYSTEM MODELS
In this paper we propose an approach for testing time-domain properties of analog and mixed-signal circuits. The approach is based on an adaptation of a recently developed test generation technique for hybrid systems and a new concept of coverage for such systems. The approach is illustrated by its application to some benchmark circuits.
Test Generation for Analog and Mixed-Signal Circuits Using Hybrid System Mode...
In this paper we propose an approach for testing time-domain properties of analog and mixed-signal circuits. The approach is based on an adaptation of a recently developed test generation technique for hybrid systems and a new concept of coverage for such systems. The approach is illustrated by its application to some benchmark circuits.
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Compit 2013 - Torsional Vibrations under Ice Impact
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Machiwal, D. y Jha, MK (2012). Modelado estocástico de series de tiempo. En A...
Lecture12me1766steadystateerror 12555290178452-phpapp03
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Foundation and Synchronization of the Dynamic Output Dual Systems
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Efficient Implementation of Self-Organizing Map for Sparse Input Data
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TEST GENERATION FOR ANALOG AND MIXED-SIGNAL CIRCUITS USING HYBRID SYSTEM MODELS
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Test Generation for Analog and Mixed-Signal Circuits Using Hybrid System Mode...
Test Generation for Analog and Mixed-Signal Circuits Using Hybrid System Mode...
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Discover how MongoDB Atlas and vector search technology can revolutionize your application's search capabilities. This comprehensive presentation covers:
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The introduction of DLAU and the CCB & CCX licensing model caused quite a stir in the HCL community. As a Notes and Domino customer, you may have faced challenges with unexpected user counts and license costs. You probably have questions on how this new licensing approach works and how to benefit from it. Most importantly, you likely have budget constraints and want to save money where possible. Don’t worry, we can help with all of this!
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“Building and Scaling AI Applications with the Nx AI Manager,” a Presentation...
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みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
ここ3000字までしか入らないけどタイトルの方がたくさん文字入ると思います。
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Imagine a world where machines not only perform tasks but also learn, adapt, and make decisions. This is the promise of Artificial Intelligence (AI), a technology that's not just enhancing our lives but revolutionizing entire industries.
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Unlock the Future of Search with MongoDB Atlas_ Vector Search Unleashed.pdf
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HCL Notes and Domino License Cost Reduction in the World of DLAU
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“Building and Scaling AI Applications with the Nx AI Manager,” a Presentation...
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Monitoring and Managing Anomaly Detection on OpenShift.pdf
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National Security Agency - NSA mobile device best practices
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HCL Notes und Domino Lizenzkostenreduzierung in der Welt von DLAU
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Introduction of Cybersecurity with OSS at Code Europe 2024
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Your One-Stop Shop for Python Success: Top 10 US Python Development Providers
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Programming Foundation Models with DSPy - Meetup Slides
みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
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Driving Business Innovation: Latest Generative AI Advancements & Success Story
AI 101: An Introduction to the Basics and Impact of Artificial Intelligence
AI 101: An Introduction to the Basics and Impact of Artificial Intelligence
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WeTestAthens: Postman's AI & Automation Techniques
Elements Of Stochastic Processes
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