Browsing by Author "Anton, Cristina"

Now showing 1 - 10 of 10
  • Thumbnail Image
    Item
    Clustering of time series cytotoxicity data
    (2020) Richard, Dan; Anton, Cristina
    To study the effect of various toxicants on cells’ growth, the Alberta Centre for Toxicology did several in-vitro experiments, and concentration response curves (TCRCs) were generated. Each TCRC represents a time series that gives the temporal evolution of the number of cells, after exposure to a chemical with a certain concentration. Here we use the wavelet transform to extract important features from the original TCRC data, and we apply self organizing maps to classify the toxicants according to their adverse biological response.
  • Thumbnail Image
    Item
    Explicit pseudo-symplectic methods based on generating functions for stochastic Hamiltonian systems
    (2020) Anton, Cristina
    We propose a systematic approach to construct explicit pseudo-symplectic schemes for stochastic Hamiltonian systems. This method is based on generating functions, so it is an extension of the techniques used for constructing high-order symplectic schemes for stochastic Hamiltonian systems. We study the order of convergence of the proposed explicit pseudo-symplectic schemes. The excellent long term performance of the pseudo-symplectic schemes is verified numerically.
  • Thumbnail Image
    Item
    Forecasting CAD/USD exchange rate
    (2023) Wu, Joyce; Anton, Cristina
    The exchange rate of Canadian dollars was closely bound up with the US dollars for the past decades. The last time that the Canadian dollar was worth more than the US dollar was in July 2011. It then experienced its fastest decline in modern-day history as commodity prices rapidly deteriorated. We use time series analysis to study the variation of CAD/USD exchange rate since 2010. We fit an ARIMA model and analyze how different economic and social policies in both countries affect the exchange rate.
  • Thumbnail Image
    Item
    MacEwan University WiFi analysis
    (2016) Prince, James; Yong, Alan; Anton, Cristina
    One of the worst feelings in the world is waiting for a slow Internet connection. While this may be more a reflection of our impaired society than a faulty modem, this study will shed some light as to soothe these pains while on MacEwan University Campus. MacEwan University has recently undergone a "WiFi Renovation", with many new WiFi units installed all throughout the school. The goal of this experiment is to find where in the school are the strongest and weakest connections. This will be an interesting reflection on the new system effectiveness and coverage. The factors that will be tested for are the Location in the school, Time of Day, Day of the Week and Type of Device used, and blocking will be done on the last four factors. To measure the connection quality, a file of a pre-determined size will be downloaded and the time taken will be recorded. Alan will be using an Apple Iphone, and James will be using a Samsung Galaxy S3, which will eliminate the chance of a newer device being different than an older one, or an Apple device vs an Android. This study will determine which factors are significant, and which factor combination yields the best results in terms of WiFi connectivity. This method of mapping a WiFi system will be useful to students and to the IT management of the University because the results of this study will provide the school with information which will help plan for future changes to WiFi layout. An easy extension of the methodology of this experiment could be developed and used to assess any WiFi or cellular device service. The results from this experiment alone will be interesting, but a larger application of the method could be groundbreaking.
  • Thumbnail Image
    Item
    Moving limit cycles model of an economic system
    (2017) Kryuchkov, Vladimir; Solomonovich, Mark; Anton, Cristina
    We consider a model explaining the dependence between the productivity of labor (PL) and the fixed capital per worker (FC) in an economic system. The core of the model is a nonlinear oscillator with a limit cycle as an attractor. We run numerical simulations of the dynamics specific to this non-autonomous model to compare with the actual data recorded for the years 1987–2001 for the enterprise Omsk Bacon. Based on the numerical analysis we can conclude that the interior dynamics is not affected by exterior perturbations. The numerical simulations can help the managers of the enterprise to take the right steps to avoid stagnation.
  • Thumbnail Image
    Item
    Parameter estimation and prediction for time-dependent concentration response curves for cytotoxicity assessment
    (2016) Anton, Cristina
    We propose a model based on the logistic equation and linear kinetics to study the effect of toxicants with various initial concentrations on a cells' population. To efficiently estimate the model's parameters, we design an Expectation Maximization algorithm. The model is validated by showing that it accurately represents the information provided by in-vitro experiments.
  • Thumbnail Image
    Item
    Pseudo-symplectic methods for stochastic Hamiltonian systems
    (2018) Anton, Cristina
    We propose a systematic approach to construct explicit pseudo-symplectic schemes for stochastic Hamiltonian systems. This method is based on generating functions, so it is an extension of the techniques used for constructing high-order symplectic schemes for stochastic Hamiltonian systems. We study the order of convergence of the proposed explicit pseudo-symplectic schemes. The excellent long term performance of the pseudo-symplectic schemes is verified numerically.
  • Thumbnail Image
    Item
    Stochastic dynamics and survival analysis of a cell population model with random perturbations
    (2018) Anton, Cristina; Yong, Alan
    We consider a model based on the logistic equation and linear kinetics to study the effect of toxicants with various initial concentrations on a cell population. To account for parameter uncertainties, in our model the coefficients of the linear and the quadratic terms of the logistic equation are affected by noise. We show that the stochastic model has a unique positive solution and we find conditions for extinction and persistence of the cell population. In case of persistence we find the stationary distribution. The analytical results are confirmed by Monte Carlo simulations.
  • Thumbnail Image
    Item
    The influence of noise in cytoxicity assessment
    (2016) Yong, Alan; Anton, Cristina
    Industrial activity produces many chemicals that may be hazardous to human health or the environment. Traditionally, experiments can be carried out on live subjects (in vivo), but this is both expensive and raises significant ethical concerns. Rather than conducting these assays, we might try using mathematical or computational models to assess the effect of these toxicants (1). With in vitro assays at the Alberta Centre of Toxicology using the xCelligence Real-Time Cell Analysis HT system, time-dependent response curves (TCRCs) were generated. These experimentally-derived curves reflect the response of human cells to these toxicants. The goal was to find a mathematical model that could accurately reproduce these curves (2). Depending on the value of various parameters of the toxicant – such as its toxicity and how fast cells absorb it – there are generally two possible equilibria dependent on the toxicant's initial external concentration: a cell line may persevere and survive; or the concentration may be large enough to cause extinction of the cell population. Data from the TCRCs were used to generate a deterministic model. That is, a given set of parameter values will always generate the same cell fate. However, there is inherently uncertainty in the value of these parameters. To assess the influence of this noise on the external concentration of toxicant at which some population of cells would reach survival or extinction equilibria, a new model was created with additional variables for this uncertainty. Several simulations were run with this extended model. The information generated will be useful for planning further experiments regarding cytotoxicity, and for numerically generating TCRCs for clustering and classification.
  • Thumbnail Image
    Item
    Weak backward error analysis for stochastic Hamiltonian systems
    (2019) Anton, Cristina
    This paper presents a study of the approximation error corresponding to a symplectic scheme of weak order one for a stochastic autonomous Hamiltonian system. A backward error analysis is done at the level of the Kolmogorov equation associated with the initial stochastic Hamiltonian system. An expansion of the weak error and expansions of the ergodic averages and of the invariant measures associated with the numerical scheme are obtained in terms of powers of the discretization step size and the solutions of the modified Kolmogorov equation.