An algebraic analysis of the two state Markov model on tripod trees.

Abstract:

:Methods of phylogenetic inference use more and more complex models to generate trees from data. However, even simple models and their implications are not fully understood. Here, we investigate the two-state Markov model on a tripod tree, inferring conditions under which a given set of observations gives rise to such a model. This type of investigation has been undertaken before by several scientists from different fields of research. In contrast to other work we fully analyse the model, presenting conditions under which one can infer a model from the observation or at least get support for the tree-shaped interdependence of the leaves considered. We also present all conditions under which the results can be extended from tripod trees to quartet trees, a step necessary to reconstruct at least a topology. Apart from finding conditions under which such an extension works we discuss example cases for which such an extension does not work.

journal_name

Math Biosci

journal_title

Mathematical biosciences

authors

Klaere S,Liebscher V

doi

10.1016/j.mbs.2012.03.001

subject

Has Abstract

pub_date

2012-05-01 00:00:00

pages

38-48

issue

1-2

eissn

0025-5564

issn

1879-3134

pii

S0025-5564(12)00032-6

journal_volume

237

pub_type

杂志文章
  • Dynamics of vaccination in a time-delayed epidemic model with awareness.

    abstract::This paper investigates the effects of vaccination on the dynamics of infectious disease, which is spreading in a population concurrently with awareness. The model considers contributions to the overall awareness from a global information campaign, direct contacts between unaware and aware individuals, and reported ca...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2017.09.007

    authors: Agaba GO,Kyrychko YN,Blyuss KB

    更新日期:2017-12-01 00:00:00

  • Incorporating bolus and infusion pharmacokinetics into the ICING insulin model.

    abstract::The ICING model has been successfully used to guide clinical decisions on insulin administration in critical illness. However, insulin pharmacokinetics in the ICING model can be improved to better describe both intravenous (IV) bolus and infusion insulin administration. Patient data from 217 Dynamic Insulin Sensitivit...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2016.08.005

    authors: Fisk L,Docherty PD,Pretty C,Chase JG

    更新日期:2016-11-01 00:00:00

  • Quantification of the effect of control strategies on classical swine fever epidemics.

    abstract::Emergency vaccination during an epidemic of classical swine fever virus (CSFV) has become a serious option because of the ethical problems of strategies with massive culling and the availability of a marker vaccine that reduces virus transmission. Here we present a model of between-herd CSFV transmission, which quanti...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2003.08.005

    authors: Klinkenberg D,Everts-van der Wind A,Graat EA,de Jong MC

    更新日期:2003-12-01 00:00:00

  • Robust model matching design methodology for a stochastic synthetic gene network.

    abstract::Synthetic biology has shown its potential and promising applications in the last decade. However, many synthetic gene networks cannot work properly and maintain their desired behaviors due to intrinsic parameter variations and extrinsic disturbances. In this study, the intrinsic parameter uncertainties and external di...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2010.12.007

    authors: Chen BS,Chang CH,Wang YC,Wu CH,Lee HC

    更新日期:2011-03-01 00:00:00

  • Prostate cancer: progression of prostate-specific antigen after external beam irradiation.

    abstract::This paper is concerned with the development of a stochastic path of prostate-specific antigen (PSA) level after radiation treatment for prostate cancer. PSA is a biomarker for prostate cancer, higher levels of which indicate the seriousness of the cancer progression. Following the deterministic modeling of the data b...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/s0025-5564(02)00215-8

    authors: Dayananda PW,Taylor JM,Whiting DG

    更新日期:2003-04-01 00:00:00

  • Dynamic population epidemic models.

    abstract::Most multipopulation epidemic models are of the contact distribution type, in which the locations of successive contacts are chosen independently from appropriate contact distributions. This paper is concerned with an alternative class of models, termed dynamic population epidemic models, in which infectives move amon...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/0025-5564(91)90011-7

    authors: Ball FG

    更新日期:1991-12-01 00:00:00

  • New perspectives on multilocus ancestry informativeness.

    abstract::We present an axiomatic approach for multilocus informativeness measures for determining the amount of information that a set of polymorphic genetic markers provides about individual ancestry. We then reveal several surprising properties of a decision-theoretic based measure that is consistent with the set of proposed...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2018.10.011

    authors: Tal O,Tran TD

    更新日期:2018-12-01 00:00:00

  • Dynamics of a predator-prey model with generalized Holling type functional response and mutual interference.

    abstract::Mutual interference and prey refuge are important drivers of predator-prey dynamics. The "exponent" or degree of mutual interference has been under much debate in theoretical ecology. In the present work, we investigate the interplay of the mutual interference exponent, and prey refuge, on the behavior of a predator-p...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2020.108407

    authors: Antwi-Fordjour K,Parshad RD,Beauregard MA

    更新日期:2020-08-01 00:00:00

  • Spatial Mendelian games.

    abstract::This paper considers complex models arising in sociobiology. These combine genetic and strategic aspects to model the effect of gene-linked strategies on the ability of individuals to survive to maturity, mate and produce offspring. Several important models considered in the literature are generalised and extended to ...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/s0025-5564(98)10011-1

    authors: Radcliffe J,Rass L

    更新日期:1998-08-01 00:00:00

  • A new necessary condition for Turing instabilities.

    abstract::Reactivity (a.k.a initial growth) is necessary for diffusion driven instability (Turing instability). Using a notion of common Lyapunov function we show that this necessary condition is a special case of a more powerful (i.e. tighter) necessary condition. Specifically, we show that if the linearised reaction matrix an...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2012.04.006

    authors: Elragig A,Townley S

    更新日期:2012-09-01 00:00:00

  • Exploration of the intercellular heterogeneity of topotecan uptake into human breast cancer cells through compartmental modelling.

    abstract::A mathematical multi-cell model for the in vitro kinetics of the anti-cancer agent topotecan (TPT) following administration into a culture medium containing a population of human breast cancer cells (MCF-7 cell line) is described. This non-linear compartmental model is an extension of an earlier single-cell type model...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2008.03.008

    authors: Cheung SY,Evans ND,Chappell MJ,Godfrey KR,Smith PJ,Errington RJ

    更新日期:2008-06-01 00:00:00

  • The natural history of renal cell carcinoma with pulmonary metastases illuminated through mathematical modeling.

    abstract::The goal of this study is to uncover some unobservable aspects of the individual-patient natural history of metastatic renal cell carcinoma (RCC) through mathematical modeling. We analyzed four clear cell RCC patients who at the time of primary tumor resection already had pulmonary metastases. Our description of the n...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2019.01.008

    authors: Hanin L,Jandrig B,Pavlova L,Seidel K

    更新日期:2019-03-01 00:00:00

  • An epidemic model with fatal risk.

    abstract::A new epidemic model is developed that describes the spread of an infectious disease with fatal risk. The model includes as extreme cases the standard general epidemic process (for diseases that confer immunity after infection) and the fatal epidemic process (for diseases that lead inevitably to death). Both determini...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/0025-5564(93)90019-7

    authors: Lefèvre C,Picard P

    更新日期:1993-09-01 00:00:00

  • Numerical solution of non-linear dual-phase-lag bioheat transfer equation within skin tissues.

    abstract::This paper deals with numerical modeling and simulation of heat transfer in skin tissues using non-linear dual-phase-lag (DPL) bioheat transfer model under periodic heat flux boundary condition. The blood perfusion is assumed temperature-dependent which results in non-linear DPL bioheat transfer model in order to pred...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2017.08.009

    authors: Kumar D,Kumar P,Rai KN

    更新日期:2017-11-01 00:00:00

  • A new five-parameter Birnbaum-Saunders distribution for modeling bicoid gene expression data.

    abstract::An extended version of Birnbaum-Saunders distribution with five parameters is introduced. Theoretical aspects of five-parameter Birnbaum-Saunders distribution and the maximum likelihood estimation of parameters are presented. The reliability and applicability of the proposed distribution is evaluated using both simula...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2019.108275

    authors: Hassani H,Kalantari M,Entezarian MR

    更新日期:2020-01-01 00:00:00

  • Stochastic models for the spread of HIV in a mobile heterosexual population.

    abstract::An important factor in the dynamic transmission of HIV is the mobility of the population. We formulate various stochastic models for the spread of HIV in a heterosexual mobile population, under the assumptions of constant and varying population sizes. We also derive deterministic and diffusion analogues for these mode...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2006.09.024

    authors: Sani A,Kroese DP,Pollett PK

    更新日期:2007-07-01 00:00:00

  • Intrinsic coherence resonance in excitable membrane patches.

    abstract::The influence of intrinsic channel noise on the spiking activity of excitable membrane patches is studied by use of a stochastic generalization of the Hodgkin-Huxley model. Internal noise stemming from the stochastic dynamics of individual ion channels does affect the electric properties of the cell-membrane patches. ...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2006.08.024

    authors: Schmid G,Hänggi P

    更新日期:2007-06-01 00:00:00

  • Which facilitates the evolution of cooperation more, retaliation or persistence?

    abstract::The existence of cooperation in this world is a mysterious phenomenon. One of the mechanisms that explain the evolution of cooperation is repeated interaction. If interactions between the same individuals repeat and individuals cooperate conditionally, cooperation can evolve. A previous study pointed out that if indiv...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2017.04.002

    authors: Kurokawa S

    更新日期:2017-07-01 00:00:00

  • Dynamics between infectious diseases with two susceptibility conditions: A mathematical model.

    abstract::This paper presents a novel epidemiological transmission model of a population affected by two different susceptible-infected-susceptible infectious diseases. For each disease, individuals fall into one of the two susceptibility conditions in which one of the diseases has the highest occurrence level. This model is un...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2019.01.005

    authors: Gutiérrez-Jara JP,Córdova-Lepe FD,Muñoz-Quezada MT

    更新日期:2019-03-01 00:00:00

  • Effect of red blood cell shape on oxygen transport in capillaries.

    abstract::A mathematical model of oxygen (O2) transport within a capillary utilizes axisymmetric red blood cell (RBC) shapes that were predicted theoretically by Zarda et al. in 1977. Chemical kinetics and both free and facilitated diffusion of O2 are accounted for in this time-dependent model. The finite-element method is used...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/0025-5564(93)90062-f

    authors: Wang CH,Popel AS

    更新日期:1993-07-01 00:00:00

  • Spatiotemporal dynamics of insect pest population under viral infection.

    abstract::The interrelationship between pathogen infection and host mobility is of great importance for successful spread of disease in spatial pest population. As spread of infection depends on horizontal transmission of pathogen, there are numerous factors like susceptibility, latent period, host movement that influence overa...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2013.03.009

    authors: Ghosh S,Bhattacharyya S

    更新日期:2013-07-01 00:00:00

  • Comparison of mathematical frameworks for modeling erythropoiesis in the context of malaria infection.

    abstract::Malaria is an infectious disease present all around the globe and responsible for half a million deaths per year. A within-host model of this infection requires a framework capable of properly approximating not only the blood stage of the infection but also the erythropoietic process that is in charge of overcoming th...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2015.08.020

    authors: Fonseca LL,Voit EO

    更新日期:2015-12-01 00:00:00

  • Robust control of uncertain nonlinear switched genetic regulatory networks with time delays: A redesign approach.

    abstract::In this paper, the problem of robust stability of nonlinear genetic regulatory networks (GRNs) is investigated. The developed method is an integral sliding mode control based redesign for a class of perturbed dissipative switched GRNs with time delays. The control law is redesigned by modifying the dissipativity-based...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2016.02.006

    authors: Moradi H,Majd VJ

    更新日期:2016-05-01 00:00:00

  • Similarity transformation approach to identifiability analysis of nonlinear compartmental models.

    abstract::Through use of the local state isomorphism theorem instead of the algebraic equivalence theorem of linear systems theory, the similarity transformation approach is extended to nonlinear models, resulting in finitely verifiable sufficient and necessary conditions for global and local identifiability. The approach requi...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/0025-5564(89)90024-2

    authors: Vajda S,Godfrey KR,Rabitz H

    更新日期:1989-04-01 00:00:00

  • A Mathematical Model of Countercurrent Exchange of Oxygen Between Paired Arterioles and Venules.

    abstract::A mathematical model is formulated for diffusive countercurrent exchange of oxygen between paired arterioles and venules. A closed form solution of the problem is obtained by linearizing the nonlinear oxyhemoglobin dissociation curve at the inlet PO2 in the vessel. The closed form solution is compared with the corresp...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/0025-5564(88)90022-3

    authors: Sharan M,Popel AS

    更新日期:1988-09-01 00:00:00

  • Comparing methods to quantify experimental transmission of infectious agents.

    abstract::Transmission of an infectious agent can be quantified from experimental data using the transient-state (TS) algorithm. The TS algorithm is based on the stochastic SIR model and provides a time-dependent probability distribution over the number of infected individuals during an epidemic, with no need for the experiment...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2007.04.009

    authors: Velthuis AG,De Jong MC,De Bree J

    更新日期:2007-11-01 00:00:00

  • A mechanical model of tumor encapsulation and transcapsular spread.

    abstract::In this paper, a mathematical modeling framework is presented which describes the growth, encapsulation, and transcapsular spread of solid tumors. The model is based on the physical forces and cellular interactions involved in tumorigenesis and is used to test and compare the active (foreign body hypothesis) and passi...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/s0025-5564(02)00118-9

    authors: Jackson TL,Byrne HM

    更新日期:2002-11-01 00:00:00

  • Spreading of excitation in 3-D models of the anisotropic cardiac tissue. I. Validation of the eikonal model.

    abstract::In this work we investigate, by means of numerical simulations, the performance of two mathematical models describing the spread of excitation in a three dimensional block representing anisotropic cardiac tissue. The first model is characterized by a reaction-diffusion system in the transmembrane and extracellular pot...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/0025-5564(93)90001-q

    authors: Franzone PC,Guerri L

    更新日期:1993-02-01 00:00:00

  • A model of HIV/AIDS with staged progression and amelioration.

    abstract::An epidemic model with multiple stages of infection is studied. The model allows for infected individuals to move from advanced stages of infection back to less advanced stages of infection. A threshold parameter which determines the local stability of the disease free equilibrium is found and interpreted. Under condi...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/s0025-5564(02)00149-9

    authors: McCluskey CC

    更新日期:2003-01-01 00:00:00

  • Analysis of a compartmental model of amyloid beta production, irreversible loss and exchange in humans.

    abstract::Amyloid beta (Aβ) peptides, and in particular Aβ42, are found in senile plaques associated with Alzheimer's disease. A compartmental model of Aβ production, exchange and irreversible loss was recently developed to explain the kinetics of isotope-labeling of Aβ peptides collected in cerebrospinal fluid (CSF) following ...

    journal_title:Mathematical biosciences

    pub_type: 杂志文章

    doi:10.1016/j.mbs.2014.11.004

    authors: Elbert DL,Patterson BW,Bateman RJ

    更新日期:2015-03-01 00:00:00