Mathematical Modelling

Mathematical Modelling

  • Amin Oroji added an answer:
    In Target Theory, is there any estimation for the number of targets of human cells?
    In Target Theory, it is supposed that each human body cell contains some radio sensitive sites named targets. The question is whether there is any estimation for the number of these targets?
    Amin Oroji · Putra University, Malaysia
    Thank you so much for your response.
  • Hossein Hassanpoor asked a question:
    How can implicate two set of differential equations with different time scaling simultaneously (second and millisecond) in Matlab R2013a simulink?
    We have to sets of differential equations for neuron dynamics and astrocyte Ca2+ oscillations but with different time scale (Di Garbo 2009). Is it correct that for simulation these sets simultaneously, using integrators with 1000 coefficient for rescaling one set?
  • Martin Stepnicka added an answer:
    Time series of epidemiological data
    As someone who has much more background in medicine than in mathematics, econometrics etc., I have become interested in the application of time series analysis in the medical field, particularly in epidemiology. I have gathered a huge amount of data on some infectious diseases, from 1994-2008, and I am interested in making a forecast model. 1. Can someone suggest what would be the best approach to systematically learn about time series analysis? What would be the prerequisites (eg. calculus?) 2. Can you suggest the best way that I can perform with the data attached and the best model that I can use? Visualizing the data, seasonality becomes visible, showing that the highest incidence appears to be in the winter time. 3. What is the main difference between classical mathematical modeling of infectious diseases using differential equations and time series analysis? What way provides better results?
    Martin Stepnicka · University of Ostrava
    Hi Matej. We have made simple predictions by ARIMA, Exponential smoothing and Theta methods form the R package which is for free. Depending if the results were rounded (to avoid prediction such as 8,76 patients :-) ) or not, the results slightly changed however, theyr were taking RMSE values from ca 2.9 to 3.3 with ES as the best followed by ARIMA and THETA. The differences were not big as you may see. We tried also are ensemble that combines all three methods also with random walk. Without roundening, our approach was between ES and ARIMA, with roundening, it was the best, but again, with a small difference to the others. However, all methods failed in the prediction of seasonal effects. All predictions were too flat. That is the influence of the fact that the season is not alwasy in the same months, one year, the epidemy is in 10-12 month, another year, it is 12-03 etc. Therefore, also the ensemble of flat predictions was flat. The positive influence of the ensemble could be seen on more time series were each methods sometimes wins and sometimes loses, which is warning for you: do not rely on a single method. Unless it is a specific one developed for your problem, but do not rely on a single general method for any time series. For the analysis of some aspects of such time series, some data-mining technique would be desirable. I would prefer associations mining. Nice weekend Marrtin
  • How can we model the random motion of natural particles in an air medium?
    How can I model the random motion of natural targets (for example trees)?
    Abdallah Daddi Moussa Ider · Aix-Marseille Université
    Naveem. The random motion can be modeled as a Gaussian White Noise (GWN), delta correlated in time and the diffusion is known to be standard since the mean squared traveled distance of your particle varies linearly with respect to time. If you want to model that numerically, I suggest to you the following: Consider a computational domain (a squared box in 2D) and then define a random velocity field using the standard function that generate noises. If you want to satisfy the incompressibility, you may instead define a stream function in the form of a Gaussian White Noise and then obtain your velocity field using the definition. In a second hand, put one particle (in the center of your box for example) and then see how does it behave as it is advected by this random field by integrating the Lagrangian velocity equation if you consider of course a tracer particle. There will be not any preferential direction and you get a real Brownian motion. You could find the second order moment of the particle displacement in order to see whether you have a standard diffusion. If you want to go further, consider a set of many particles. You may look to the relative separation between a pair of particles to check the Richardson law in 2D, and you could also see the evolution of high order correlations: triangles or tetrahedral and so on. Hope this could help you a bit! best
  • Anjani Dhrangadhariya added an answer:
    What is the mathematical difference between supervised and unsupervised learning?
    I require some detailed but simple explanation to distinguish between these topics.
    Anjani Dhrangadhariya · Fraunhofer Institute for Algorithms and Scientific Computing SCAI
    Thank you everyone for making the explanation so easy for me. Im novice to Machine Learning thing and trying to grasp things in a way I my brain indices can hold.
  • Farah Najdawi added an answer:
    Can anyone help me build a mathematical model for a desiccant cooling wheel in a cooling solar system?
    I've come to a standstill trying to build a mathematical model for a desiccant wheel in a solar cooling system which is connected to a flat plate in order to serve as an air conditioning system.
    Farah Najdawi · California State University, Fresno
    oooooh thank you Mr.Mohamed Hamdy and if you have more information about that ,your help would be highly appreciated
  • Qefsere Doko Gjonbalaj added an answer:
    Can someone recommend a research area in mathematics?
    Which area to choose as a research area that has a lot of applications in everyday life.
    Qefsere Doko Gjonbalaj · University of Prishtina
    “To the scientific mind, all knowledge is an answer to a question. Without questions there cannot be any scientific knowledge. Nothing is obvious. Nothing is given. Everything is constructed.” Gaston Bachelard, 1938
  • Harish Garg asked a question:
    How can data envelopment analysis (DEA) theory be modeled in nonlinear instead of linear one?
    Is it possible to develop a model of DEA in nonlinear functions instead of linear?
  • Bernie Cohen added an answer:
    Can we define organisation and formalize it in a manner that supports the explanation of life phenomena?
    Organisation, its omni-presence, preservation and dependence, is possible the distinctive aspect of biological phenomena. Achieving a consensus about what is organisation and how can it be used to generate biological explanations would greatly benefit the development of (theoretical) biology.
    Bernie Cohen · City University London
    The enterprise modelling framework called 'Projective Analysis' (or PAN) provides a structure for organisation that is consistent with the reflexivity in Rosen's categorical model, with the third order cybernetics in Maturana's later work and with the Lacanian/Freudian accounts of consciousness. It also provides a full set of computational tools for eliciting, composing and analysing people's models of the organisations they inhabit and for indicating the 'holes' in these models. See the papers and blogs at www.brl.com and www.asymmetricdesign.com.
  • Adil AL-Rammahi added an answer:
    Which is the best solution for solving highly non-linear numerical problems like phase change?
    Out of the solvers available like MUMPS, PARADISO, SPOOLES, etc. which is best suited for solving highly non-linear problems
    Adil AL-Rammahi · University Of Kufa
    B-Spline method is best yet.
  • Peter T. Breuer added an answer:
    Which open source software could be recommended for mathematical modelling of electronic systems ?
    Trying to develop a model for all to use, thus open source software.
    Peter Breuer · University of Birmingham
    Electronic? Or digital? "Mathematical", I'm not sure of. I've always written my own code. But for simulation of digital systems in a GUI there are several packages available. Tkgate, logisim, geda, ngspice, octave-ocs, ... You might check out the "electronics" section of debian's archive. Looks like 100+ packages. "apt-get install science-electronics" would be a good start.
  • Augusto Carreira added an answer:
    Can anyone suggest software to build causal loop diagrams for system analysis?
    I do a lot of modelling and system analysis. The best mean for that is paper, however, it would be handy to have a piece of software to build these diagrams on a computer for publication, presentations, or for teaching. Up until now I have used vector image software such as Inkscape or Adobe Illustrator.
    Augusto Carreira · Technical University of Lisbon
    Vensim PLE is usually enough for CLD's but is not enough as a full fledged SD modelling tool (for instance, PLE does not use use max and min values for stocks in the equation editor, in spite of the possibility of entering such values).
  • Divo Dharma Silalahi added an answer:
    Is there any software or method to solve an epidemic model with age structure?
    How do we do discrete modelling, especially to choose the infection incidence rate/beta(a) and the initial functions in a simple SIR model?
    Divo Silalahi · PT Sinar Mas Agro Resources and Technology (SMART) Tbk
    try this Jun, it is an online solver http://www.warrenweckesser.net/solvers/menu_sir.html
  • Soumya Banerjee added an answer:
    How to draw phase portrait plots for delay differential equations in matlab?
    Quiver function is being used for phase portrait plots obtained using ode. Is there a way for plotting phase portraits and vector fields for autonomous system of delay differential equations in matlab?
  • Barry Croke added an answer:
    What is the difference among Deterministic model, Stochastic model and Hybrid model?
    How to develop hybrid model?
    Barry Croke · Australian National University
    G'day Luciane, Your definition of a deterministic and stochastic model are not correct. Deterministic models can be black box models. Also, a stochastic model can be generated by first principles (e.g. if the underlying processes are random), while a deterministic model can be generated by a conceptual understanding of the processes (an approach widely used in Hydrology). A deterministic model is one that uses numbers as inputs, and produces numbers as outputs. A stochastic model includes a random component that uses a distribution as one of the inputs, and results in a distribution for the output. These distributions may reflect the uncertainty in what the input should be (e.g. a deterministic input plus noise), or may reflect a random process (i.e. a stochastic input).
  • Yasodha Gayathri added an answer:
    Reference material for conducting Multi Criteria Analysis in evaluation?
    I need reference material for using MCA as tool for decision making in conservation studies. Could anyone please give me reference material which enable me to develop a mathematical model?
    Yasodha Gayathri · Tamil Nadu Agricultural University
    Thank you Kostas Katselidis
  • Hans Mair added an answer:
    Which results do you trust more: results from a verified model or results from field experiments?
    R. G. Allen reported: Some years ago, when computer modeling was in its infancy, a common cautionary advice was to "do not trust any model until it has been validated using independent data." Today, with some of the more common mathematical models becoming proven and trustworthy, the corollary of this expression is commonly advocated, where "one should not trust any data until they are validated using a model!" Certainly, some place in between these two cautionary advocations is appropriate. Often a valid model can be valuable for evaluating data to identify errors, outliers and biases. Of course, valid data are required for selecting or calibrating a particular model.
    Hans Mair · Johns Hopkins University
    There is an appropriate place between the two cautionary advocations, because both are "wrong." Models are not simply "validated" using independent data, and experimental data are not "validated" via models. That approach to validity is misguided and unscientific. The engineering approach to developing theories and models is based on the recognition that "all models are wrong" - i.e., all models are inexact. The objective is to assess HOW inexact, in order to make an educated assessment of the appropriateness or suitability of that model for a specific application. The validation process - usually defined as assessing "... the degree of accuracy..." - becomes corrupted when assumptions about validity drive misguided conclusions like "proof." Do not trust any model until the validation process has quantified acceptable accuracy - and inaccuracy - of the model for its intended purposes. Do not trust your interpretation of experimental data - especially of complex systems - until the accuracies and inaccuracies of your model are sufficiently quantified, and uncertainties inherent in the data are sufficiently quantified.
  • Azizi Ahmadi added an answer:
    What are the limitations of saint venant equations?
    River modeling
    Azizi Ahmadi · University Malaysia Sarawak
    Thank you so much for your answer.
  • Soumen Deb added an answer:
    What are the basic theories in mathematical modeling of SiGe heterostructure MOSFET?
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    Soumen Deb · National Institute of Technology, Silchar
    Thank u sir, Mohapatra, actually I m using a heterostructure channel in lateral direction, not in vertical direction, hence no supporting literature I m not getting, nd madam Srikanth I m typically working on 24 nm SOI DG MOSFET, and the books and u r referring are concerned with only basic and long channel devices, any ways thanks for concern, Sir Mohapatra I would be looking forward to your suggestion in future as well ...
  • Xin Zhang added an answer:
    Mathematical model for antibody-antigen interaction in ELISA?
    Does anyone have a good resource to share on describing the colorimetric signal in sandwich ELISA mathematically as a function of antibody- and antigen concentration and other variables? In order to better understand what's actually happening in the microplate, I am looking for something to start from that represents the current knowledge. A recent paper, review or textbook paper would be fine.
    Xin Zhang · Dublin City University
    Langmuir equation is used to simulate the kinetics of antigen-antibody binding. It is a ODE equation, so the software such as Matlab or Comsol can be used to solve the equations.
  • Roselyn Kaondera asked a question:
    Can someone assist me with some notes on modelling hiv vertical transmission?
    I am an MPhil student. I need material to understand the concepts better for my research. Papers and notes are welcome
  • Mahfuz Judeh added an answer:
    What are the limits of measurement in science?
    When I was in high school Bohr's atom of shells, s and p orbitals was introduced in chemistry. Realization was automatic that the world was explained according to theory that was verified by experiment. Through college and graduate school, looking for more complete explanation, theory is challanged but it is not brought to question "what is an electron or proton, if they have mass but are visible only in the sense that they emit light energy as photons that also have mass, "spots of light in orbit around nuclei?, the atom a solar system in minature"? Physicists will say this is not the picture they have evolved, but all that remains is the image of equations on a chalkboard, at best 'the image of things of a particle nature in alteration with things of a light nature'. Can a pieced-together stepwise reality of this nature be accepted? In the Feyman quote below pieces are added that can break any of the established laws "they are not directly observeable" or affect "causality". In this same meaning though neither electrons, protons, photons or atoms are observable and their causal effects are but a matter of humanly constructed theory and similarly based experimental apparatus. The possibility exists that theory and theory based apparatus entail one another and all that might be gotten is that the real universe is identical in this respect...i.e. existence entails the experienced universe and visa-verse. "You found out in the last lecture that light doesn't go only in straight lines; now, you find out that it doesn't go only at the speed of light! It may surprise you that there is an amplitude for a photon to go at speeds faster or slower than the conventional speed, c." These virtual photons, however, do not violate causality or special relativity, as they are not directly observable and information cannot be transmitted causally in the theory." (from "Varying c in quantum theory" http://www.researchgate.net/go.Deref.html?url=http%3A%2F%2Fen.wikipedia.org%2Fwiki%2FVariable_speed_of_light)
    Mahfuz Judeh · Applied Science Private University
    Measurements include many limitations. In scales, we can`t discriminate between two values that fall between the marked divisions of the measuring scale. In addition to scaling errors, there are also sampling errors, It is important for researchers to be aware of these errors.
  • Hemanta K. Baruah added an answer:
    What is the difference between fiducial empirical distribution and the empirical distribution function?
    Fiducial empirical distribution vs. the empirical distribution function?
    Hemanta Baruah · Bodoland University
    Dear Samah, I would like to advise you to go through the Glivenko-Cantelli Theorem on Convergence of Empirical Probability Distribution Functions. This theorem would be available in chapters on Order Statistics in standard text books. When you would understand this classical theorem, you will get the answer to your question automatically.
  • Hans H. Diebner added an answer:
    Does anyone know of codes or software tools to perform discrete (time series) chaos analysis?
    I will have recorded acoustic files and desire to perform chaos analysis on the acoustic data. I am also looking to analyze the signals for energy in time-frequency such as using a Gabor Transform technique that has been done on bat echolocation signals, phase space, Lyapunov exponent, capacity dimension, etc. Anyway, does anyone know of where to find the codes or software tools such as in Matlab or some other source to conduct the analysis? Any current literature related to the algorithms would also be appreciated. Any suggestions are welcome as well. Thank you.
    Hans Diebner · Technische Universität Dresden
    The Matlab plugin OpenTSTool is nice but no longer maintained since 2009, I'm afraid. Nevertheless, for a Matlab user still an option. http://www.physik3.gwdg.de/tstool/HTML/index.html
  • Santhosh P Mathew added an answer:
    How to segment a medical image using Markov Random field?
    How to segment a medical image using Markov Random field?
  • Santanu Biswas added an answer:
    Any ideas about the stability of two solutions in a nonlinear system?
    Suppose a non linear system has at least 2 positive periodic solutions in a bounded domain. If one can show that the system is globally asymptotically stable, then is it a contradiction to the previous statement? If not, what can one say about the other solution? Can anybody suggest me any relevant references?
    Santanu Biswas · Indian Statistical Institute
    Thank you sir
  • Vijayalakshmi Murali asked a question:
    Can anyone help solve the trajectory equation for water riochet of a projectile?
    I have written a code but the number of bounces increasing with velocity which is not happening with present codes.
  • Viktor Kotolupov added an answer:
    What are possible mathematical models for cancer and cell migration?
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    Viktor Kotolupov · Russian Academy of Sciences
    http://link.springer.com/article/10.1134%2FS0022093013020175

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