scholarly journals Species Dynamics in the Two-Parameter Poisson-Dirichlet Diffusion Model

2014 ◽  
Vol 51 (1) ◽  
pp. 174-190 ◽  
Author(s):  
Matteo Ruggiero
Keyword(s):  
Mathematical Properties ◽  
State Dependent ◽  
Continuous State ◽  
Continuous State Branching Process ◽  
Biological Interpretation ◽  
Species Dynamics ◽  
The One ◽  
Branching Process With Immigration ◽  
Parameter Case ◽  
Two Parameter

The recently introduced two-parameter infinitely-many-neutral-alleles model extends the celebrated one-parameter version (which is related to Kingman's distribution) to diffusive two-parameter Poisson-Dirichlet frequencies. In this paper we investigate the dynamics driving the species heterogeneity underlying the two-parameter model. First we show that a suitable normalization of the number of species is driven by a critical continuous-state branching process with immigration. Secondly, we provide a finite-dimensional construction of the two-parameter model, obtained by means of a sequence of Feller diffusions of Wright-Fisher flavor which feature finitely many types and inhomogeneous mutation rates. Both results provide insight into the mathematical properties and biological interpretation of the two-parameter model, showing that it is structurally different from the one-parameter case in that the frequency dynamics are driven by state-dependent rather than constant quantities.

scholarly journals Species Dynamics in the Two-Parameter Poisson-Dirichlet Diffusion Model

2014 ◽  
Vol 51 (01) ◽  
pp. 174-190 ◽  
Author(s):  
Matteo Ruggiero
Keyword(s):  
Mathematical Properties ◽  
State Dependent ◽  
Continuous State ◽  
Continuous State Branching Process ◽  
Biological Interpretation ◽  
Species Dynamics ◽  
The One ◽  
Branching Process With Immigration ◽  
Parameter Case ◽  
Two Parameter

The recently introduced two-parameter infinitely-many-neutral-alleles model extends the celebrated one-parameter version (which is related to Kingman's distribution) to diffusive two-parameter Poisson-Dirichlet frequencies. In this paper we investigate the dynamics driving the species heterogeneity underlying the two-parameter model. First we show that a suitable normalization of the number of species is driven by a critical continuous-state branching process with immigration. Secondly, we provide a finite-dimensional construction of the two-parameter model, obtained by means of a sequence of Feller diffusions of Wright-Fisher flavor which feature finitely many types and inhomogeneous mutation rates. Both results provide insight into the mathematical properties and biological interpretation of the two-parameter model, showing that it is structurally different from the one-parameter case in that the frequency dynamics are driven by state-dependent rather than constant quantities.

Distributions of jumps in a continuous-state branching process with immigration

2016 ◽  
Vol 53 (4) ◽  
pp. 1166-1177 ◽  
Author(s):  
Xin He ◽  
Zenghu Li
Keyword(s):  
Branching Process ◽  
Lévy Measure ◽  
Borel Set ◽  
Jump Size ◽  
Distributional Properties ◽  
Continuous State ◽  
Continuous State Branching Process ◽  
Jump Time ◽  
Branching Process With Immigration

Abstract We study the distributional properties of jumps in a continuous-state branching process with immigration. In particular, a representation is given for the distribution of the first jump time of the process with jump size in a given Borel set. From this result we derive a characterization for the distribution of the local maximal jump of the process. The equivalence of this distribution and the total Lévy measure is then studied. For the continuous-state branching process without immigration, we also study similar problems for its global maximal jump.

Asymptotic Formulae for the Eigenvalues of a Two Parameter System of Ordinary Differential Equations of the Second Order

1975 ◽  
Vol 17 (5) ◽  
pp. 657-665 ◽  
Author(s):  
M. Faierman
Keyword(s):  
Differential Equations ◽  
Mathematical Physics ◽  
Parameter System ◽  
Eigenvalues And Eigenfunctions ◽  
Asymptotic Formulae ◽  
Sturm Liouville ◽  
The One ◽  
Work Done ◽  
Parameter Case ◽  
Two Parameter

The origin and importance of multiparameter Sturm-Liouville problems in mathematical physics has recently been discussed by Atkinson [1, sects. 3 and 4], [2, introduction]. In spite of the importance of such problems, and in spite of the work done in this field by such early investigators as Klein and Hilbert, Atkinson points out that in recent years this field has been relatively neglected in contrast to the single parameter case. As an example, he states that as opposed to the one parameter case, the detailed behaviour of the eigenvalues and eigenfunctions in the multiparameter Sturm-Liouville case is still far from clear.

scholarly journals Exact simulation of the genealogical tree for a stationary branching population and application to the asymptotics of its total length

2021 ◽  
Vol 53 (2) ◽  
pp. 537-574
Author(s):  
Romain Abraham ◽  
Jean-François Delmas
Keyword(s):  
Fixed Time ◽  
Genealogical Tree ◽  
Total Length ◽  
Constant Size ◽  
Continuous State ◽  
Continuous State Branching Process ◽  
Size Population ◽  
Quadratic Branching ◽  
Branching Process With Immigration ◽  
Extant Population

AbstractWe consider a model of a stationary population with random size given by a continuous-state branching process with immigration with a quadratic branching mechanism. We give an exact elementary simulation procedure for the genealogical tree of n individuals randomly chosen among the extant population at a given time. Then we prove the convergence of the renormalized total length of this genealogical tree as n goes to infinity; see also Pfaffelhuber, Wakolbinger and Weisshaupt (2011) in the context of a constant-size population. The limit appears already in Bi and Delmas (2016) but with a different approximation of the full genealogical tree. The proof is based on the ancestral process of the extant population at a fixed time, which was defined by Aldous and Popovic (2005) in the critical case.

scholarly journals First passage upwards for state-dependent-killed spectrally negative Lévy processes

2019 ◽  
Vol 56 (2) ◽  
pp. 472-495 ◽  
Author(s):  
Matija Vidmar
Keyword(s):  
Branching Processes ◽  
First Passage Time ◽  
Passage Time ◽  
Additive Functional ◽  
First Passage ◽  
State Dependent ◽  
Continuous State ◽  
The Laplace Transform ◽  
Exit Probability ◽  
The One

AbstractFor a spectrally negative Lévy process X, killed according to a rate that is a function ω of its position, we complement the recent findings of [12] by analysing (in greater generality) the exit probability of the one-sided upwards passage problem. When ω is strictly positive, this problem is related to the determination of the Laplace transform of the first passage time upwards for X that has been time-changed by the inverse of the additive functional $$\int_0^ \cdot \omega ({X_u}){\kern 1pt} {\rm{d}}u$$. In particular, our findings thus shed extra light on related results concerning first passage times downwards (resp. upwards) of continuous-state branching processes (resp. spectrally negative positive self-similar Markov processes).

Two-parameter Quantum Affine Algebra $U_{r,s}(\widehat{\frak{sl}}_2)$

2013 ◽  
Vol 20 (03) ◽  
pp. 507-514 ◽  
Author(s):  
Honglian Zhang ◽  
Ruzhi Pang
Keyword(s):  
Quantum Affine Algebra ◽  
Affine Algebra ◽  
Evaluation Representation ◽  
The One ◽  
Parameter Case ◽  
Two Parameter

We give two realizations of the two-parameter quantum affine algebra [Formula: see text] and prove that its structure is isomorphic to the one-parameter case. In particular, the evaluation representation of [Formula: see text] is obtained.

Subjective Time Preference and Willingness to Pay for an Energy-Saving Durable Good

2001 ◽  
Vol 32 (3) ◽  
pp. 133-141 ◽  
Author(s):  
Gerrit Antonides ◽  
Sophia R. Wunderink
Keyword(s):  
Willingness To Pay ◽  
Energy Saving ◽  
Subjective Time ◽  
Durable Good ◽  
Discount Function ◽  
Hyperbolic Discount ◽  
The One ◽  
Two Parameter ◽  
Difference Effect ◽  
Better Than

Summary: Different shapes of individual subjective discount functions were compared using real measures of willingness to accept future monetary outcomes in an experiment. The two-parameter hyperbolic discount function described the data better than three alternative one-parameter discount functions. However, the hyperbolic discount functions did not explain the common difference effect better than the classical discount function. Discount functions were also estimated from survey data of Dutch households who reported their willingness to postpone positive and negative amounts. Future positive amounts were discounted more than future negative amounts and smaller amounts were discounted more than larger amounts. Furthermore, younger people discounted more than older people. Finally, discount functions were used in explaining consumers' willingness to pay for an energy-saving durable good. In this case, the two-parameter discount model could not be estimated and the one-parameter models did not differ significantly in explaining the data.

Theoretical accuracy of the last squares method in the isotope dilution analysis

1984 ◽  
Vol 49 (4) ◽  
pp. 805-820
Author(s):  
Ján Klas
Keyword(s):  
Least Squares ◽  
Isotope Dilution ◽  
Least Squares Method ◽  
Isotope Dilution Analysis ◽  
Straight Line ◽  
The One ◽  
Two Parameter ◽  
Theoretical Accuracy

The accuracy of the least squares method in the isotope dilution analysis is studied using two models, viz a model of a two-parameter straight line and a model of a one-parameter straight line.The equations for the direct and the inverse isotope dilution methods are transformed into linear coordinates, and the intercept and slope of the two-parameter straight line and the slope of the one-parameter straight line are evaluated and treated.

scholarly journals Stability of a one-dimensional morphoelastic model for post-burn contraction

2021 ◽  
Vol 83 (3) ◽  
Author(s):  
Ginger Egberts ◽  
Fred Vermolen ◽  
Paul van Zuijlen
Keyword(s):  
Wound Healing ◽  
Residual Stresses ◽  
Truncation Error ◽  
Signaling Molecules ◽  
Discrete Problem ◽  
One Dimensional ◽  
Stability Constraint ◽  
Biological Interpretation ◽  
The Stability ◽  
The One

AbstractTo deal with permanent deformations and residual stresses, we consider a morphoelastic model for the scar formation as the result of wound healing after a skin trauma. Next to the mechanical components such as strain and displacements, the model accounts for biological constituents such as the concentration of signaling molecules, the cellular densities of fibroblasts and myofibroblasts, and the density of collagen. Here we present stability constraints for the one-dimensional counterpart of this morphoelastic model, for both the continuous and (semi-) discrete problem. We show that the truncation error between these eigenvalues associated with the continuous and semi-discrete problem is of order $${{\mathcal {O}}}(h^2)$$ O ( h 2 ) . Next we perform numerical validation to these constraints and provide a biological interpretation of the (in)stability. For the mechanical part of the model, the results show the components reach equilibria in a (non) monotonic way, depending on the value of the viscosity. The results show that the parameters of the chemical part of the model need to meet the stability constraint, depending on the decay rate of the signaling molecules, to avoid unrealistic results.

scholarly journals Backbone Decomposition of Multitype Superprocesses

2021 ◽  
Author(s):  
Dorottya Fekete ◽  
Sandra Palau ◽  
Juan Carlos Pardo ◽  
Jose Luis Pérez
Keyword(s):  
Branching Processes ◽  
Easy Consequence ◽  
Continuous State ◽  
The One

AbstractIn this paper, we provide a construction of the so-called backbone decomposition for multitype supercritical superprocesses. While backbone decompositions are fairly well known for both continuous-state branching processes and superprocesses in the one-type case, so far no such decompositions or even description of prolific genealogies have been given for the multitype cases. Here we focus on superprocesses, but by turning the movement off, we get the prolific backbone decomposition for multitype continuous-state branching processes as an easy consequence of our results.

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