Download - Data Structure Presentation
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Introduction to Simulation:
OVERVIEW:
This implies that:
1. All data must be stored symbolically. All operations such as
bitwise operations, arithmetic operations, comparisons and
assignments must also be performed symbolically.2. For all statements, which split the control-flow, e.g., if-then-
else statements or loops, all possible execution paths must be
simulated.
DEFINITION:
Simulation is a formal verification technique, which combines
the flexibility of conventional simulation with powerful
symbolic methods.
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The Simulation Algorithm:
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Simulation Techniques :
1. Algorithm Visualization
2. Algorithm Animation
3. Algorithm Simulation
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1. Algorithm Visualization
Visualization of a sorting algorithm
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2. Algorithm Animation
Bubble sort Animation
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The challenge is to construct a simulation toolbased on this theoretical framework.
A user could then use this simulation tool for examine of states of behavior of
algorithms and data structures.
The goal ofAlgorithm Simulation is to further the understanding of algorithms and data
structures.
Another possible views of Simulation:1. In the context of a vehicle:
2. The researcher's point of view:
3. An experimental technique: comprising such aspects as model calibration and data
collection as well as experimental design and output analysis.
4. Representation : Representation will always be needed for simulation, since it is by
definition an experimental technique where data generatedby each experiment must
be collected, summarizedandreportedin a meaningful way.
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1. Deterministic Algorithms
Deterministic algorithms deal with the aggregated quantity of
concentration and rate of change of concentration.The methods are:
Euler Forward method Euler Backward method Trapezoidal method Explicit 4th order Runge-Kutta method Rosenbrock method (Generalized fourth order Runge-Kutta method) Advanced ODE Solver (Adams-Bashforth)
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The Trapezoidal method:-
The trapezoidal method is a used to approximate the area
under a curve. This is done by inscribing or
circumscribing n number of trapezoids under a curve. The
areas of the trapezoids are then summed.
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First start with the area of one trapezoid:
The trapezoids are circumscribed under the curve,
lengths a and bbecome dependant on:
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Animation Algorithms for Trapezoidal Method
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2. Stochastic Algorithms
Stochastic algorithms can be used for modeling such stochastic or
random events.The methods are:
3. Hybrid Algorithms
StochODE method
Gillespie's Direct method
Gibson Next Reaction methodExplicit Tau-Leap method
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Monte Carlo method:
INTRODUCTION :
Monte Carlo methods are a class of computational algorithms that rely
on repeated random sampling to compute their results. Monte Carlo
methods are often used when simulating physical and mathematicalsystems.
The term Monte Carlo Method was coined by S. Ulam and Nicholas Metropolis
in reference to games of chance, a popular attraction in Monte Carlo.
DEFINITION:
A Monte Carlo method is a technique that involves using random
numbers and probability to solve problems.
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Monte Carlo simulation methods are used in studying systemswith a large number of coupled degrees of tools like :
1. Fluids,
2. Disordered materials,
3. Strongly coupled solids, and
4. Cellular structures
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The steps in Monte Carlo simulation corresponding to theuncertainty propagation shown in Previous figure.
For that we need to do is follow the five simple steps listed below:
Step 1: Create a parametric model, y = f(x1, x2, ..., xq).Step 2: Generate a set of random inputs, xi1, xi2, ..., xiq.
Step 3: Evaluate the model and store the results as yi.Step 4: Repeat steps 2 and 3 for i = 1 to n.Step 5: Analyze the results using histograms, summary statistics,confidence intervals, etc.
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Scheduling algorithms are used in:
Computer networks
Operating systems
Real time applications
Real life Applications :
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Network simulator
A network simulator is a software program that imitates the working of a
computer network. In simulators, the computer network is typically modelled
with devices, traffic etc and the performance is analysed. Typically, users can
then customize the simulator to fulfil their specific analysis needs. Simulators
typically come with support for the most popular protocols in use today, such
as IPv4, IPv6, UDP, and TCP.
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Scheduling in RTOS
More information about the tasks are known
1. No of tasks
2. Resource Requirements
3. Release Time
4. Execution time
5. Deadlines
Being a more deterministic system better scheduling
algorithms can be devised.
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Real-Time Operating Systems
Real-time operating systems are an integral part of real-time
systems. Not surprisingly,four main functional areas that they support are process
management and synchroniza-
tion, memory management, interprocess communication, and
I/O.
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Definition : Simulation is a formal verification technique, which combines theflexibility of conventional simulation with powerful symbolic methods.
Summary
Use of simulation tool for user is Examine of states ofbehavior of
algorithms and data structures.
The goal of Algorithm Simulation is to further the understanding of
algorithms and data structures.
Types of Simulation Algorithms :
1. Deterministic Algorithms2. Stochastic Algorithms3. Hybrid Algorithms
Real life Applications :
Simulation Techniques :
1. Algorithm Visualization
2. Algorithm Animation
3. Algorithm Simulation
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Thank You