What is Models: Definition and 400 Discussions

A model is an informative representation of an object, person or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin modulus, a measure.
Representational models can be broadly divided into the concrete (e.g. physical form) and the abstract (e.g. behavioural patterns, especially as expressed in mathematical form). Of particular importance in the modern context, conceptual models are central to philosophy of science, as almost every scientific theory effectively embeds some kind of model of the physical or human sphere.
In commerce, a model might instead reference a specific version or configuration of a product offering, rather than functioning as a representation of something else.
In taxonomic settings (e.g. biology, architecture, art) a model is sometimes a particular instance of a set of related entities (species, built structures, artistic compositions) chosen as a convenient reference point around which to build discourse; such a model is almost always chosen to typify some central tendency of the group, exemplify the group's defining characteristic, or reify the group's historical lineage.
Kinds of models include:

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  1. U

    Bianchi Models and Kantowski-Sachs

    What are main differencies between Bianchi models and Kantowski-Sachs models. Can anyone give mathematical definition clearly and possibly simple form?
  2. B

    What are the implications of spatial homogeneity in cosmological models?

    In a spatially homogeneous model, spacetime is filled with a one-parameter set of invariant hypersurfaces H(t). Spatial homogeneity means that the metric on each H(t) is described in terms of constants. Meaning that the metric becomes a function of time only. I guess that this means that...
  3. B

    Exploring Bianchi IX Models for Metric Invariance

    In a Bianchi IX universe the metric must be invariant under the SO(3) group acting on the 3-sphere. Hence, the metric must be translation invariant in the spatial parts, where t=constant. This implies that the metric must take the form such that: ds^2 = dt^2 - g_ij(t)(x^i)(x^j), where g is a...
  4. S

    Three Models of Light: Definition & Use

    Hello experts! I was taking class of optical fiber and communication. My teacher was teaching the class via projector and slides (transparencies). He taught us light models and he just changed his slide after reading the few lines. I was not able to note down the main points of the slides...
  5. carllacan

    Older nuclear structure models.

    Hi people. I just read this somewhere and I can't get my head around it. How is the Uncertainty Relation uncompatible with the idea of a proton-electron nucleus? And can you explain why this model predicted those values for the nuclear spin? Thank you.
  6. M

    MHB How Can I Combine PCA Models for Enhanced Face Recognition?

    Hello, I am working with face recognition. I have two models from two separate datasets with the same number of dimensions. I wish to implement this method to combine PCA models. http://www.cs.cf.ac.uk/Dave/Papers/Pami-EIgenspace.pdf My linear algebra isn't great. So i am lost after step 1...
  7. S

    Difference between large signal and small signal models

    Please can someone explain the clear concept between large signal model and small signal models in BJT. Please explain what to assume in large signal and small signals problem solving wise and also the concept. Amongst vBE, VBE, vbe which is large signal?, small signal? and what we assume in...
  8. E

    F test for R^2 when comparing two models

    Hi all I am comparing the performance of two models and have calculated the coefficient of determination R squared for each. I would like however to test the significance of this value. The F test however requires that the number of degrees of freedom for each model. The trouble is one...
  9. Sudharaka

    MHB Gaussian Mixture Models and Geodesics

    Hi everyone, :) This is a question that one of my friends sent me. It is kind of open ended and I don't have any clue about the particular area of research he is undertaking. Therefore I am posting the question here with the hope that anybody knowledgeable in this area would be able to help...
  10. Dilatino

    Massive particles in D-brane models ?

    How does a zero separation of parallel D-branes give mass to the particles that correspond to strings stretched between them? Is there a scalar field corresponding to the separation of the D-branes which takes the role of a higgs field, or how does it work?
  11. T

    Logistic Growth Models (interpreting r value)

    I originally posted this on the Biology message boards. But I have not received any responses. In models of exponential growth, we have an intrinsic growth rate (r) that is calculated as the difference of birth rates to death rates. With the logistic growth model, we also have an intrinsic...
  12. T

    Logistic models and the intrinsic growth rate

    In models of exponential growth, we have an intrinsic growth rate (r) that is calculated as the difference of birth rates to death rates. With the logistic growth model, we also have an intrinsic growth rate (r). How then do birth rates and death rates relate to the intrinsic growth rate in...
  13. U

    Biological neuron models and simulated data

    I have some very simple questions. 1. What are the real life applications of the biological neuron models (for example Hodgkin-Huxely model)? 2. Is their any online database from where I can get the original recordings data of a neuron? 3. or is there any way that I can...
  14. M

    How to fit distribution models for a frequency analysis?

    I have a rainfall (mm) vs. year plot of a catch basin (see Excel file below) and I would like to get it's frequency curve. But before that, I need to fit certain distribution models (i.e. log-Pearson Type III and Gumbel Distributions) to my plot to be able to know the fittest model that I can...
  15. S

    Design a 15 dB π Attenuator with 600Ω Impedance

    Homework Statement Design a π section symmetrical attenuator to provide a voltage attenuation of 15 dB and a characteristic impedance of 600 Ω. Zc=600Ω,\alpha=15dB (attenuation) Z1,Z3=? Homework EquationsThe Attempt at a Solution \alpha[dB]=20log(Vin/Vout)=15 \alpha=5.623...
  16. W

    Probabilities on Non-Standard Models.

    Hi, I think I read here; maybe not, that , within a non-standard model of the Reals, it is possible to have probabilities , say over an interval, so that each point has non-zero probability. AFAIK, the transfer principle ( a.k.a elementary equivalence of models) does not disallow having a...
  17. A

    Two-port network models (V in & V out)

    Homework Statement Construct and test the ∏ section symmetrical attenuator. Measure and record the Input & Output Voltages of the attenuator and determine the attenuation in dB. Homework Equations Vout = Vin * [ R2 / (R1 + R2) ] Decibel Attenuation (dB) = 20LOG10(Vout / vin)...
  18. A

    Design a 15 dB Symmetrical Attenuator with 600Ω Characteristic Impedance

    [/SUB]Homework Statement Design a ∏ section symmetrical attenuator to provide a voltage attenuation of 15 dB and a characteristic impedance of 600 Ω. Homework Equations ZS = ZL = Z R1 = R3 = Z (K + 1 / K -1) R2 = Z (K2 - 1 / 2 K) The Attempt at a Solution Z = 600Ω K =...
  19. D

    Hidden Markov Model Homework: State Space S={1,2,3}, Alphabet A={a,b,c}

    Homework Statement Define a Hidden Markov Model with the following parameters: State space S={1,2,3}, alphabet A = {a,b,c,}, P = 0 .5 .5 1 0 0 0 1 0 initial probability vector, ∏ = 1 0 0...
  20. L

    Newton's Law of Cooling and other Models

    Hello, In my Differential Equations class we are learning about modelling with first order differential equations. We learned that Newton's Law of Cooling breaks down when the temperature of the object is approaching the temperature of the room its in. You eventually get to a point where you...
  21. U

    Writing expressions, Markov Models

    Homework Statement Through donations the food bank tries to feed as many people as possible. Assume there are no backorders - any unsatisfied demand is lost. The food bank also has limited facilities to store donations, 200,000lbs maximum can be held in storage. Assume donations are processed...
  22. J

    Maximal Entropy Random Walk - quantum corrections to stochastic models

    Imagine there is a complex system and we are interested in its basic statistical properties, like the stationary probability distribution. For example for a single electron wandering in defected lattice of semiconductor. Physics offers two basic ways of answering such question: - from one side...
  23. J

    What are Soliton Particle Models?

    I see there are mainly discussed here very abstract approaches like string theory. I would like to suggest a general discussion about much less abstract models: to get not exactly beyond, but rather behind the standard model - ask about the internal structure of particles (behind abstract...
  24. Drakkith

    Evaluating an exponential function that models a real-world situation

    Homework Statement Suppose that the velocity v(t) (in m/s) of a sky diver falling near the Earth's surface is given by the following exponential function, where time is measured in seconds. v(t) = 55 (1-e-0.18(t)) Find the initial velocity of the sky diver and the velocity after 6...
  25. N

    MHB Quadratic and logarithmic models (new post)

    Here is my previous post! please look at pages 3 - 4 to see what I am talking about. http://mathhelpboards.com/pre-algebra-algebra-2/mathematical-modeling-6006-4.html I figured out how to input the quadratic and logarithmic equations into wolfram, this is what i got. Let me know if its correct...
  26. shounakbhatta

    Symmetry and models of Symmetry

    Hello, I am quiet new to this subject. I am reading over grand unified theory and found that there are quiet a number of Symmetries, like U(1) and SU(2)..... Can anybody help me in finding all the types of symmetries and how it evolved and what are they basically are? Thanks
  27. A

    Inflation Deflated ? the dead of inlation models ?

    according inflation, the universe should to be uniform in all directions at large scale, but observations from the Planck spacecraft found fluctuations in the cosmic microwave background that undermines the model. http://www.kavlifoundation.org/science-spotlights/kicc-planck-universe
  28. Physics Monkey

    Dynamics in non-commutative geometry models

    I was reminded of this point by a recent discussion in the "Classification of manifolds ..." thread. The question is this: As I understand it, the NCG framework requires a Riemannian manifold. Given this, at best one could hope to obtain a Euclidean theory, right? So is it fair to say...
  29. C

    Usefulness of SUSY models when it cant exist at non-zero temperatures

    Unlike other symmetries (like electroweak symmetry), SUSY is spontaneously broken at any non-zero temperature due to some variation of the fact that the boundary conditions on bosons and fermions in thermal QFT are different. If this is the case, what is the rationale for considering SUSY...
  30. J

    Accurate equations vs. accurate models in QM

    In QED, Feynman says: "The situation today is, we haven't got a good model to explain partial reflection by two surfaces; we just calculate..." I've been frustrated in that I'm still not clear if this is the case (is there still no model to explain the behavior). A similar dynamic seems to...
  31. E

    Electric field and gauss law for different models of sphere

    Hello all! I actually have a few doubts regarding "gauss law" when applied "for different models of sphere" First, If we place a charge 'Q' inside a spherical shell at the center (somehow) then it should come out to its surface that means in no way can we do it. True or False? Next...
  32. nomadreid

    Model Theory: relation between two theories with the same models?

    This is a question out of model theory. (This preamble is due to the fact that "model" and "theory" are used in different ways in different fields.) Is there any specific relationship between two theories which have the same models? A knee-jerk reaction would be to say that they are isomorphic...
  33. tom.stoer

    Current status of canonical LQG and SF models

    From time to time I try to get an overview regarding the current status of LQG. Unfortunately there seem to be a lot of interesting ideas and new proposals, but I am missing a summary paper which addresses and summarizes both main achievements and main open issues. What about status of...
  34. L

    Finding practice problems on linear models grad level

    Hi, I am a first year stats grad student and I am taking a class on linear models. The book and lectures focus on the format of definition, proof, lemma, definition, proof, lemma etc. However, I cannot seem to find anywhere some practice problems where I could use these definitions before I...
  35. A

    Dimensions Models and String Theory

    Right, Hello, I am new to this, and do not have much understanding, but can someone here help explain the Dimension Models and String theory to me?
  36. B

    Differential Equations Problem, logistic models

    Homework Statement Given that a population, P, after t months, can be modeled by the logistic model dP/dt = .3 P (3.5 - P/40). P(0) = 30 a) Solve the diff eq b) Find the population after 2.5 months c) Find lim P(t) as t -> infinity Homework Equations P(t) = P0 P1 /(P0 + (P1...
  37. A

    MHB Graph that models one but not both

    Here is an exercise from Shawn Hedman's course of logic, like all others I have posted. I would say that only the empty graph is the correct solution, because if a structure is not empty then I can derive $\exists xR(x,x)$ from each of the given sentences.
  38. L

    Viscoelastic Models: Analyzing Relaxation & Creep Data

    Hi everyone, So I have a set of relaxation data and creep data for a solid polymer that I want to analyse. In the relaxation I use the Prony series derived from the generalized maxwell equation (incl a spring) and get a very nice fit. My question is if I should use the same to model the...
  39. C

    Exploring Quantum Graphity Models: Bridging Locality, Geometry, and Relativity

    Hello all After reading different things about Bell inequalities, EPR like experiments and the tension with relativity I have discovered the quantum graphity models (http://arxiv.org/abs/hep-th/0611197) where locality and geometry are not fundamental in the Universe and appear only after a...
  40. F

    Zombie epidemiologist models bieber fever

    This is the same mathematician who did that paper on the zombie apocalypse a couple years ago: pdf here http://mysite.science.uottawa.ca/rsmith43/bieber.htm
  41. R

    Two Species Population Models

    The academics and the technicians of a university faculty are planning a paintball battle and the mathematicians are trying to predict their chances of winning with a continuous model. They are representing the numbers in the two teams at any time t as and respectively and have decided that the...
  42. H

    Autoregression and ARCH GARCH models

    Hello guys, I need to understand the ARCH and GARCH models and so I need some advice on where I should begin my study. In order to understand ARCH models, am I right to begin with studying autoregression? If so can you guys provide me with a link or book I should look into... By the way, I...
  43. S

    Hidden Markov Models - Likelihood of

    Hi, I try to teach myself Hidden Markov Models. I am using this text "www.cs.sjsu.edu/~stamp/RUA/HMM.pdf" as Material. The Introduction with the example was reasonable but now I have trouble in unterstanding some of the derivation. I can follow the math and use the formulas to get...
  44. X

    Cannot stand the eternity in cyclic models

    I have had this question for a long time and thought this forum might be the best place to answer.. If there is an infinite number of bangs happened before the big bang, our universe's bang should never have happened because it would require an endless number of bangs that -by definition- would...
  45. W

    Question on relationships between nuclear models

    So far in my physics education I've developed a basic understanding of two nuclear models, the liquid-drop model and the shell model. I read something a while ago (don't have the text on hand to quote the exact phrasing, unfortunately) that seemed to imply, in a couple of places, at least...
  46. L

    Are static models totally static?

    Hi, I appreciate the basics if static models, but I'm wondering just how static they are. I understand there is no expansion, but is there any element of evolution? (For example, colliding galaxies, collapsing dust clouds, etc.) Regards, Noel.
  47. D

    Hill and BBC Yield Criterion, Hardening Models

    Sorry - I didn't post according to the template as even though this is a homework/coursework question; it's not as black and white as a question and answer! I am doing a piece of coursework, or research if you like, for university. The purpose of it is to investigate how the results of FEA...
  48. C

    Statistical models and likelihood functions

    Homework Statement I have a couple of notation interpretation questions: 1) What does f_X(x|θ) represent in this case? The realization function of of our random vector X for some value x and a parameter θ (so that if our random vector has n random variables, its realization vector will be a...
  49. harrylin

    Are flowing space models compatible with GR?

    Are "flowing space" models compatible with GR? Recently papers have been published with new "flowing space" models for GR. In particular a "flowing river" model by Hamilton: http://ajp.aapt.org/resource/1/ajpias/v76/i6/p519_s1? http://arxiv.org/abs/gr-qc/0411060 "In this model, space flows...
  50. M

    Thermodynamic potential and energy density in cosmic models

    I'm reading this paper http://arxiv.org/abs/0911.1728 It's about the authors' consideration of the Mass Varying Neutrino model with a new approach that try to explain the cosmic acceleration then. I often encounter the thermodynamic potential during reading and re-calculating the...
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