Pmpslp ppsub 2011
A simulation is an imitation of some real thing, state of affairs, or process.
The act of simulating something generally entails representing certain key
characteristics or behaviours of a selected physical or abstract system.
Historically, the word had negative connotations:
…for Distinction Sake, a Deceiving by Words, is commonly called a Lye, and
a Deceiving by Actions, Gestures, or Behavior, is called Simulation… Robert
South (1643–1716)
However, the connection between simulation and dissembling later faded
out and is now only of linguistic interest.
Simulation is used in many contexts, including the modeling of natural
systems or human systems in order to gain insight into their functioning.
Other contexts include simulation of technology for performance
optimization, safety engineering, testing, training and education.
Simulation can be used to show the eventual real effects of alternative
conditions and courses of action.
Key issues in simulation include acquisition of valid source information
about the referent, selection of key characteristics and behaviours, the
use of simplifying approximations and assumptions within the
simulation, and fidelity and validity of the simulation outcomes.
Historically, simulations used in different fields developed largely
independently, but 20th century studies of Systems theory and
Cybernetics combined with spreading use of computers across all those
fields have led to some unification and a more systematic view of the
Physical simulation refers to simulation in which physical objects are
substituted for the real thing. These physical objects are often chosen
because they are smaller or cheaper than the actual object or system.
Interactive simulation is a special kind of physical simulation, often
referred to as a human in the loop simulation, in which physical
simulations include human operators, such as in a flight simulator or a6
driving simulator.
A computer simulation is an attempt to model a real-life or
hypothetical situation on a computer so that it can be studied to
see how the system works.
By changing variables, predictions may be made about the
behaviour of the system.
An interesting application of computer simulation is to simulate
computers using computers.
The related software is called computer architecture simulators,
which can be further divided into instruction set simulators or
full system simulators.
Computer simulation has become a useful part of modeling
many natural systems in physics, chemistry and biology, and
human systems in economics and social science (the
computational sociology) as well as in engineering to gain
insight into the operation of those systems.
A good example of the usefulness of using computers to
simulate can be found in the field of network traffic simulation.
In such simulations the model behaviour will change each
simulation according to the set of initial parameters assumed
for the environment.
Computer simulations are often considered to be human out of
the loop simulations.
Traditionally, the formal modeling of
systems has been via a mathematical
model, which attempts to find
analytical solutions enabling the
prediction of the behaviour of the
system from a set of parameters and
initial conditions.
Computer simulation is often used as
an adjunct to, or substitution for,
modeling systems for which simple
closed form analytic solutions are
not possible.
There are many different types of
computer simulation, the common
feature they all share is the attempt
to generate a sample of
representative scenarios for a model
in which a complete enumeration of
all possible states would be
prohibitive or impossible.
Various industries use discrete
event simulation to model
systems of interest in
commerce, health, defence,
manufacturing, logistics etc., for
example the value-adding
business processes.
Imagine a business, where each
person could do 30 tasks, where
thousands of products or
services involved dozens of
tasks in a sequence, where
customer demand varied
seasonally and forecasting was
inaccurate — this is the domain
where such simulation helps
with business decisions across
all functions.
Related topics include Theory of Constraints, bottlenecks,
and management consulting.
Several software packages exist for running computerbased simulation modeling (e.g. Monte Carlo simulation and
stochastic modeling) that makes the modeling almost
It is increasingly common to hear simulations of many kinds
referred to as "synthetic environments".
This label has been adopted to broaden the definition of
"simulation" to encompass virtually any computer-based
In computer science, simulation has an even more specialized meaning: Alan
Turing uses the term "simulation" to refer to what happens when a digital
computer runs a state transition table (runs a program) that describes the state
transitions, inputs and outputs of a subject discrete-state machine. The computer
simulates the subject machine.
In computer architecture, a simulator is often used to execute a program
that has to run on some inconvenient type of computer, or in a tightly
controlled testing environment (see Computer architecture simulator).
For example, simulators are usually used to debug a microprogram or
sometimes commercial application programs.
Since the operation of the computer is simulated, all of the information about the
computer's operation is directly available to the programmer, and the speed and
execution of the simulation can be varied at will.
Simulators may also be used to interpret fault trees, or test
VLSI logic designs before they are constructed.
Symbolic simulation that uses variables to stand for unknown
In theoretical computer science the term simulation represents
a relation between state transition systems.
This is useful in the study of operational semantics.
In the field of optimization, simulations of physical processes
are often used in conjunction with evolutionary computation to
optimize control strategies.
Simulation is often used in the training of civilian and military
This usually occurs when it is prohibitively expensive or simply too
dangerous to allow trainees to use the real equipment in the real
world. In such situations they will spend time learning valuable
lessons in a "safe" virtual environment.
Often the convenience is to permit mistakes during training for a
safety-critical system.
Model SIMULASI unit
Pengolahan Air minum
Training simulations typically come in one of three categories:
"live" simulation (where real people use simulated (or
"dummy") equipment in the real world);
"virtual" simulation (where real people use simulated
equipment in a simulated world (or "virtual environment")), or
"constructive" simulation (where simulated people use
simulated equipment in a simulated environment).
Constructive simulation is often referred to as "wargaming"
since it bears some resemblance to table-top war games in
which players command armies of soldiers and equipment that
move around a board.
Truck Simulator
A truck simulator provides an opportunity to reproduce the
characteristics of real vehicles in a virtual environment. It
replicates the external factors and conditions with which a
vehicle interacts enabling a driver to feel as if they are sitting in
the cab of their own vehicle.
Scenarios and events are replicated with sufficient reality to
ensure that drivers become fully immersed in the experience
rather than simply viewing it as an educational programme.
Closed-Loop Transportation Simulation in Multi-Robot System
the state flow that describes the robot's
The robot is located at the middle of the
lane before started, the present value
from the three light sensors are stored as
the set values. Then during the robot is
moving, the NXT Brick reads values from
the light sensors continually, as actual
values. The controller attempts to
minimize the error by adjusting the
process control inputs, here which means
the output of the controller is added to the
inputs to the motors, converting to PWM
signal finally. The left motor and the right
motor are given different inputs therefore
they generate torques to drive the robot,
adjusting the direction. As a result, the
actual values from the sensors change
and form a close-loop control with
Healthcare (Clinical) Simulators
Medical simulators are increasingly being developed and deployed to
teach therapeutic and diagnostic procedures as well as medical concepts
and decision making to personnel in the health professions.
Simulators have been developed for training procedures ranging from
the basics such as blood draw, to laparoscopic surgery and trauma care.
They are also important to help on prototyping new devices for
biomedical engineering problems.
Currently, simulators are applied to research and development of tools
for new therapies, treatments and early diagnosis in medicine.
Many medical simulators involve a
computer connected to a plastic
simulation of the relevant anatomy.
Sophisticated simulators of this
type employ a life size mannequin
that responds to injected drugs
and can be programmed to create
simulations of life-threatening
In others simulations, visual
components of the procedure are
reproduced by computer graphics
techniques, while touch-based
components are reproduced by
haptic feedback devices combined
with physical simulation routines
computed in response to the user's
Medical simulations of this sort will
often use 3D CT or MRI scans of
patient data to enhance realism.
Some medical simulations are
developed to be widely distributed
(such as web-enabled simulations
that can be viewed via standard web
browsers) and can be interacted with
using standard computer interfaces,
such as the keyboard and mouse.
Another important medical
application of a simulator —
although, perhaps, denoting a
slightly different meaning of
simulator — is the use of a placebo
drug, a formulation that simulates
the active drug in trials of drug
History of Simulation in Healthcare
The first medical simulators were simple models of human
Since antiquity, these representations in clay and stone were
used to demonstrate clinical features of disease states and their
effects on humans.
Models have been found from many cultures and continents.
These models have been used in some cultures (e.g., Chinese
culture) as a "diagnostic" instrument, allowing women to
consult male physicians while maintaining social laws of
Models are used today to help students learn the anatomy of the
musculoskeletal system and organ systems.
Active models that attempt to reproduce living anatomy or physiology are
recent developments.
The famous “Harvey” mannikin was developed at the University of Miami
and is able to recreate many of the physical findings of the cardiology
examination, including palpation, auscultation, and electrocardiography.
More recently, interactive models have been developed that respond to
actions taken by a student or physician. Until recently, these simulations
were two dimensional computer programs that acted more like a textbook
than a patient. Computer simulations have the advantage of allowing a
student to make judgements, and also to make errors. The process of
iterative learning through assessment, evaluation, decision making, and
error correction creates a much stronger learning environment than
passive instruction.
Simulators have been proposed as an ideal tool for assessment of students
for clinical skills.
Programmed patients and simulated clinical situations, including mock
disaster drills, have been used extensively for education and evaluation.
These “lifelike” simulations are expensive, and lack reproducibility.
A fully functional "3Pi" simulator would be the most specific tool available
for teaching and measurement of clinical skills.
Such a simulator meets the goals of an objective and standardized
examination for clinical competence.
This system is superior to examinations that use "standard patients"
because it permits the quantitative measurement of competence, as well as
reproducing the same objective findings.
The "classroom of the future"
The "classroom of the future" will probably contain several kinds of simulators, in
addition to textual and visual learning tools. This will allow students to enter the
clinical years better prepared, and with a higher skill level. The advanced student
or postgraduate will have a more concise and comprehensive method of retraining
— or of incorporating new clinical procedures into their skill set — and regulatory
bodies and medical institutions will find it easier to assess the proficiency and
competency of individuals.
The classroom of the future will also form the basis of a clinical skills unit for
continuing education of medical personnel; and in the same way that the use of
periodic flight training assists airline pilots, this technology will assist practitioners
throughout their career.
The simulator will be more than a "living" textbook, it will become an integral a
part of the practice of medicine. The simulator environment will also provide a
standard platform for curriculum development in institutions of medical
In finance, computer simulations are often used for scenario
planning. Risk-adjusted net present value, for example, is computed
from well-defined but not always known (or fixed) inputs. By
imitating the performance of the project under evaluation,
simulation can provide a distribution of NPV over a range of
discount rates and other inputs.
The Net Present Value (NPV) of an
investment (project) is the difference
between the sum of the discounted
cash flows which are expected from
the investment, and the amount
which is initially invested. It is a
traditional valuation method (often for
a project) used in the Discounted
Cash Flow measurement
Sophisticated Irrigation Technology And Biotechnology Adoption: Impacts On Ground Water
Talah S. Arabiyat, Eduardo Segarra, and David B. Willis
Texas Tech University
Net present value of returns and
ground water use levels associated
with the BASELINE simulation and
scenarios A to D.
The optimal levels of NPVR and
ground water use for scenarios A, B,
and C are as follows. Scenario A
achieves a NPVR $2,891.50 per acre
and water use of 26.04 feet/acre;
scenario B achieves a NPVR
$2,953.35 per acre and water use of
17.87 feet/per acre; and scenario C
achieves a NPVR $3,624.46 per acre
and water use of 17.87 feet/acre.
Home-built Flight Simulators
Some people who use simulator software, especially flight simulator
software, build their own simulator at home.
Some people in order to further the realism of their homemade simulator,
buy used cards and racks that still run the exact same software they did
before they were disassembled from the actual machine itself.
Though this brings along the problem of matching hardware and
software, and the fact that hundreds of cards plug into many different
racks, still, many find that is it well worth it.
Some are very serious in building their simulator by buying real aircraft
parts like complete nose sectionals of written off aircraft at aircraft
boneyards. This permits people who are unable to perform their hobby in
real life to simulate it.
Engineering (Technology) simulation or Process
Simulation is an important feature in engineering systems or
any system that involves many processes.
For example in electrical engineering, delay lines may be used
to simulate propagation delay and phase shift caused by an
actual transmission line.
Similarly, dummy loads may be used to simulate impedance
without simulating propagation, and is used in situations
where propagation is unwanted.
A simulator may imitate only a few of the operations and
functions of the unit it simulates.
Most engineering simulations entail mathematical modeling
and computer assisted investigation.
There are many cases, however, where mathematical
modeling is not reliable.
Simulation of fluid dynamics problems often require both
mathematical and physical simulations.
In these cases the physical models require dynamic
Physical and chemical simulations have also direct realistic
uses, rather than research uses;
in chemical engineering, for example, process simulations are
used to give the process parameters immediately used for
operating chemical plants, such as oil refineries.
Model Sistem Pengelolaan Air Minum
Simulation and games
Strategy games — both traditional and modern — may be viewed as
simulations of abstracted decision-making for the purpose of training
military and political leaders.
In a narrower sense, many video games are also simulators, implemented
These are sometimes called "sim games". Such games can simulate
various aspects of reality, from economics to piloting vehicles, such as
flight simulators (described above).
Another type of simulation is a government simulation, which can be used
to help the player understand certain aspects of political science —
specifically cause and effect.
Model Simulasi
Sistem Pengelolaan
Sumberdaya Air
Simulation in education
Simulations in education are somewhat like training simulations.
They focus on specific tasks. In the past, video has been used for
teachers and education students to observe, problem solve and role
play; however, a more recent use of simulations in education include
animated narrative vignettes (ANV).
ANVs are cartoon-like video narratives of hypothetical and realitybased stories involving classroom teaching and learning.
ANVs have been used to assess knowledge, problem solving skills and
dispositions of children, and pre-service and in-service teachers.
Here is a simplified systems dynamic model of what I think is going on in the world. The circles
are, roughly speaking, processes identified by their predominant feature(s).
The arrows show the flow of cause
or influence. The 'plus' signs indicate
positive influence or pressure to
increase the effects. The 'minus'
signs show a pressure to diminish negative feedback. So, for example,
the positive arrow from human
nature to population, labeled 'br',
causes an increase in population
(sub-served by the supply of energy
and technology). Eventually,
however, at large enough population
sizes and densities the effects of
toxins and resource depletion
feedback negatively reducing the
population through disease,
starvation, etc.
Sustainability and resilience: toward a systems approach
Structure and feedback loops in
Threshold 21 system dynamics
The Millennium Institute has applied
system dynamics to develop the
Threshold 21 (T21) model, which
combines proven economic-sector
models into an integrated framework
(Sterman, 2000). The approach uses
differential equations to represent
changes in stocks and flows, and
considers nonlinearity, feedback, and
delays. Customized T21 models
have been created at a national
scale for the United States and Italy,
for less-developed countries
(Bangladesh, Malawi), and at a
regional level in Africa and
Integrated Approaches to Systems Modeling and Management
Modeling of coupled parameters in a lake
A multidisciplinary research team at The
Ohio State University (OSU) is investigating
the complex interactions among biological,
physical, and human components of large
lake ecosystems (OSU, 2004).
Figure illustrates some of these interactions.
While a large lake provides amenities, or
ecological services, that support economic
growth, such growth can degrade these
This team of biologists, ecologists,
physicists, economists, geographers, and
others is attempting to model the patterns of
socio-economic activity, and the potential
impacts of policies to protect natural
amenities, in the Lake Erie region. Beginning
with simple equilibrium models, the project is
investigating increasingly sophisticated
techniques, including agent-based
Analytic Hierarchy Process: AHP
The Analytic Hierarchy Process (AHP) is a
decision making technique developed by Thomas
He claimed AHP allows for the rational
evaluation of pros. and cons. concerning
different alternative solutions to a multi-goal
AHP is based on a series pairwise comparions and
then those comparisons are checked for internal
The Analytic Hierarchy Process (AHP) was developed by Thomas L. Saaty in the 1970s. It
is basically a decision support system, derived from the decision making theory.
The goal of an AHP is to find the appropriate alternative out of a range of given
alternatives in order to solve a decision problem. Furthermore, an AHP can show the
importance of the defined criteria regarding their impact on the solution of the problem.
The process of analytic decision
Modeling a hierarchy is the most
important task when using the
decision part of questfox. There are
several levels of modeling to be
1. Hierarchy itself
2. Meta Hierarchy: the master plan
of routing the hierarchies
3. Semantics of the hierarchy:
question texts
4. Design issues
5. Hierarchy routing
6. Adaptive hierarchy design
The procedure can be
summarized as:
Decision makers are asked their
preferences of attributes of
For example, if the alternatives
are comparing potential realestate purchases, the investors
might say they prefer location over
price and price over timing.
Then they would be asked if the
location of alternative "A" is
preferred to that of "B", which
has the preferred timing, and so
AHP has had many challenges to
its theoretical and practical
shortcomings from those who
have a more thurough grounding
in all the decision sciences.
Some have maintained that AHP
assigns arbitrary or ordinal
measures to the pairwise
The limitation of the AHP is the
simulation of market shares and pricing
These are only possible in combination
with other methods. questfox offers the
opportunity of the Price-Sensitivity
Meter integrated for live calculations.
Proponents maintain that while
this is true of the 'verbal' mode of
AHP, it has been demonstrated
that in situations where there is
adequate variety and redundancy,
accurate ratio scale priorities can
be derived from such judgments.
In relation to aquaculture development,
each step of the process is however
rarely encountered, as it depends
largely on the advancement of the
sector in a given country. Countries
wishing to develop their yet marginal
aquaculture sector may only possess a
framework, whilst those at a more
advanced stage will have formulated
strategies and plans to guide and
manage aquaculture development at the
national level. The country documents
obtained ranged from frameworks to
plans, with production targets and
corresponding activities. Their close
examination however revealed a great
deal of confusion over appropriate use
of planning terms and development
AHP, like many systems based on pairwise comparisons, can produce
"rank reversal" outcomes.
That is a situation where the order of preference is, for example, A, B, C
then D. But if C is eliminated for other reasons, the order of A and B
could be reversed so that the resulting priority is then B, A, then D.
It has been proven that any pairwise comparison system will still have
rank-reversal solutions even when the pair preferences are consistent .
Proponents argue that rank reversal may still be desirable but this is
also controversial.
Given the example, this would be the position that if C were elliminated,
the preference of A over B should be switched.
Another strong theoretical problem
of AHP was found by Perez, et. al.
This has to do with what they
identify as an "indiferent criterion"
Indiferent criterion requires that
once A, B, C and D are ranked
according to criteria, say, W, X, Y,
adding another criterion for which
A, B, C, and D are equal, should
have no bearing on the ranks.
Yet, Perez et al prove that such an
outcome is possible.
Note that this flaw, too, is a
shortcoming of any pairwise
comparison process, not just AHP.
But AHP's consistency-checking
methods offer no guarantee such
flaws cannot occur, since there are
solution sets with these flaws even
when preferences are consistent.
Many alternatives to AHP are
economically viable, especially for
larger, riskier decision.
Methods from decision theory and
various economic modeling methods
can be applied.
A scoring method that has a superior
track record of improving decisions
was developed by Egon Brunswik in
the 1950's.
Other methods such as Applied
Information Economics quantify
risk, cost and value in economically
meaningful terms even where AHP
considers them to be
Comparison of racing
Experimentation in silico
Futures studies
Mathematical model
Merger simulation
Mining Simulation
Monte Carlo simulation
Network Simulator
Placebo (origins of
technical term)
Similitude (model)
Simulated reality
Simulation language
Scientific modeling
Identifying improvement areas when implementing green initiatives using a
multitier AHP approach
A mathematical model is a description of a system using
mathematical concepts and language. The process of
developing a mathematical model is termed mathematical
Mathematical models are used not only in the natural
sciences (such as physics, biology, earth science,
meteorology) and engineering disciplines (e.g. computer
science, artificial intelligence), but also in the social sciences
(such as economics, psychology, sociology and political
science); physicists, engineers, statisticians, operations
research analysts and economists use mathematical models
most extensively.
Mathematical models can take many forms, including but not
limited to dynamical systems, statistical models, differential
equations, or game theoretic models. These and other types
of models can overlap, with a given model involving a variety
of abstract structures. In general, mathematical models may
include logical models, as far as logic is taken as a part of
In many cases, the quality of a scientific field depends on how
well the mathematical models developed on the theoretical
side agree with results of repeatable experiments. Lack of
agreement between theoretical mathematical models and
experimental measurements often leads to important
advances as better theories are developed.
Population Growth. A simple (though approximate) model of population
growth is the Malthusian growth model. A slightly more realistic and
largely used population growth model is the logistic function, and its
Model of a particle in a potential-field. In this model we consider a particle
as being a point of mass which describes a trajectory in space which is
modeled by a function giving its coordinates in space as a function of
time. The potential field is given by a function V : R3 → R and the trajectory
is a solution of the differential equation
Note this model assumes the particle is a point mass, which is certainly
known to be false in many cases in which we use this model; for example,
as a model of planetary motion.
The sigmoid graph showing the population growth of a species has three phases which
are; the exponential phase, the transitional phase and the plateau phase. At the start of
the sigmoid curve we can see the exponential phase.
This is where there is a rapid increase in population growth as natality rate exceeds
mortality rate. The reason for this is because there are abundant resources available
such as food for all members of the population and diseases as well as predators are
rare. As time passes, the population reaches the transitional phase. This is where the
natality rate starts to fall and/or the mortality rate starts to rise. It is the result of a
decrease in the abundance of resources, and an increase in the number of predators
and diseases. However, even though population growth has decreased compared to
the exponential phase, it is still increasing as natality rate still exceeds mortality rate.
Finally, the population reaches the plateau phase. Here, the population size is constant so
no more growth is occurring. This is the result of natality rate being equal to mortality
rate and is caused by resources becoming scarce as well as an increase in predators,
diseases and parasites. These are the limiting factors to the population growth. If
natality rate starts to drop then mortality rate will drop too as more resources become
As natality rate starts to increase again so does mortality rate as resources become
scarce. This keeps the population number relatively stable. If a population is limited by
a shortage of resources then we say that it has reached the carrying capacity of the
Today in Biology we looked at population growth,
graphing populations of bacteria
(hypothetical), bees in a hive, deer and the
human population. The rate of population
growth is dependent on four factors – births
and immigration (increase) and deaths and
emigration (decrease). In the hypothetical
situation of bacterial growth with no limits,
we saw that the population increased
exponentially. Bees showed a gradual
increase and then reached their equilibrium
around the ‘carrying capacity’ of the hive.
The ‘carrying capacity’ is dependent on
environmental pressures such as space
and nutrient availablity. Other environmental
factors that will affect population growth
include predation, disease (parasites and
pathogens), catastrophic weather events
(drought, flood, fire, storms) and habitat
destruction. The deer population showed a
more gradual increase, a peak and then a
sharp decline..
Model of rational behavior for a consumer. In this model we assume a consumer faces
a choice of n commodities labeled 1,2,...,n each with a market price p1, p2,..., pn.
The consumer is assumed to have a cardinal utility function U (cardinal in the sense
that it assigns numerical values to utilities), depending on the amounts of
commodities x1, x2,..., xn consumed.
The model further assumes that the consumer has a budget M which is used to
purchase a vector x1, x2,..., xn in such a way as to maximize U(x1, x2,..., xn).
The problem of rational behavior in this model then becomes an optimization problem,
that is:
subject to:
This model has been used in general equilibrium theory, particularly to show existence
and Pareto efficiency of economic equilibria. However, the fact that this particular
formulation assigns numerical values to levels of satisfaction is the source of criticism
(and even ridicule). However, it is not an essential ingredient of the theory and again
this is an idealization.
Neighbour-sensing model explains the mushroom
formation from the initially chaotic fungal network.
Computer Science: models in Computer Networks,
data models, surface model,...
Mechanics: movement of rocket model,...
A computer simulation, a computer model, or a computational
model is a computer program, or network of computers,
that attempts to simulate an abstract model of a particular
system. Computer simulations have become a useful part
of mathematical modeling of many natural systems in
physics (computational physics), astrophysics, chemistry
and biology, human systems in economics, psychology,
social science, and engineering.
Simulations can be used to explore and gain new insights
into new technology, and to estimate the performance of
systems too complex for analytical solutions.
Traditionally, building large models of systems has been via a
statistical model, which attempts to find analytical solutions to
problems and thereby enable the prediction of the behavior of the
system from a set of parameters and initial conditions.
The term computer simulation is broader than computer modeling; the
latter implies that all aspects are being modeled in the computer
representation. However, computer simulation also includes
generating inputs from simulated users in order to run actual
computer software or equipment, with only part of the system being
An example would be a flight simulator that can run machines as well
as actual flight software.
Computer simulations are used in many fields, including science,
technology, entertainment, health care, and business planning and
In the most general sense, a model is anything used in any way to
represent anything else. Some models are physical objects, for
instance, a toy model which may be assembled, and may even be made
to work like the object it represents. They are used to help us know and
understand the subject matter they represent.
The term conceptual model may be used to refer to models which are
represented by concepts or related concepts which are formed after a
conceptualization process in the mind.
Conceptual models represent human intentions or semantics.
Conceptualization from observation of physical existence and
conceptual modeling are the necessary means human employ to think
and solve problems. Concepts are used to convey semantics during
various natural languages based communication. Since that a concept
might map to multiple semantics by itself, an explicit formalization is
usually required for identifying and locating the intended semantic
from several candidates to avoid misunderstandings and confusions in
conceptual models.
A scientific model is a simplified abstract view of the
complex reality. A scientific model represents
empirical objects, phenomena, and physical
processes in a logical way.
Attempts to formalize the principles of the empirical sciences,
use an interpretation to model reality, in the same way
logicians axiomatize the principles of logic.
The aim of these attempts is to construct a formal system for
which reality is the only interpretation. The world is an
interpretation (or model) of these sciences, only insofar as
these sciences are true
A statistical model is a probability distribution function proposed as
generating data. In a parametric model, the probability distribution
function has variable parameters, such as the mean and variance in a
normal distribution, or the coefficients for the various exponents of the
independent variable in linear regression.
A nonparametric model has a distribution function without parameters,
such as in bootstrapping, and is only loosely confined by assumptions.
Model selection is a statistical method for selecting a distribution function
within a class of them, e.g., in linear regression where the dependent
variable is a polynomial of the independent variable with parametric
coefficients, model selection is selecting the highest exponent, and may
be done with nonparametric means, such as with cross validation.
Mathematical models can take many forms, including but not limited to
dynamical systems, statistical models, differential equations, or game
theoretic models. These and other types of models can overlap, with a
given model involving a variety of abstract structures.
A more comprehensive type of mathematical model[5] uses a linguistic
version of category theory to model a given situation. Akin to entityrelationship models, custom categories or sketches can be directly
translated into database schemas.
The difference is that logic is replaced by category theory, which brings
powerful theorems to bear on the subject of modeling, especially useful
for translating between disparate models (as functors between
In economics, a model is a theoretical construct that
represents economic processes by a set of variables and a
set of logical and/or quantitative relationships between them.
The economic model is a simplified framework designed to
illustrate complex processes, often but not always using
mathematical techniques.
Frequently, economic models use structural parameters.
Structural parameters are underlying parameters in a model
or class of models. A model may have various parameters
and those parameters may change to create various
A scientific theory is a set of principles that explain and predict
phenomena. Scientists create scientific theories with the scientific
method, when they are originally proposed as hypotheses and
tested for accuracy through observations and experiments. Once a
hypothesis is verified, it becomes a theory.
The term "theory" is a polyseme, even among scientists. While
most scientists reserve the term for verifiable principles, others
use it to refer to hypothetical frameworks. Colloquially, it is often
used to refer to a guess.
In the humanities, the concept is called a philosophical theory and
is intended to explain noumena. Philosophical theories can refer to
a set of principles or a set of propositions.
The previously dominant position in philosophy of science -- the received view of
theories -- which was prevalent in logical empiricism has in the course of the second
half of the 20th century been replaced by the semantic view of theories which
identifies scientific theories with models rather than propositions.
A model of the solar system, for example, might consist of abstract objects that
represent the sun and the planets. These objects have associated properties, e.g.,
positions, velocities, and masses.
Functions defined on this set of objects, e.g., Newton's Law of Gravitation,
determine how the positions and velocities change with time.
This model can be tested; astronomers can verify that the positions of the model's
objects over time match the actual positions of the planets. For most planets, they
do match; for Mercury, if the model is based on Newton's Law of Gravitation, they
In this approach, the theory is the model. More precisely, a theory is a collection of
similar models. One can use language to describe a model; however, the theory is
the model, not the description of the model.
The word "semantic" refers to the way that a model represents the real world.74

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