Sander C. Hille
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View article: Approximating a Spatially‐Heterogeneously Mass‐Emitting Object by Multiple Point Sources in a Diffusion Model
Approximating a Spatially‐Heterogeneously Mass‐Emitting Object by Multiple Point Sources in a Diffusion Model Open
Various biological cells secrete diffusing chemical compounds into their environment for communication purposes. Secretion usually takes place over the cell membrane in a spatially heterogeneous manner. Mathematical models of these process…
View article: Law of the Iterated Logarithm for Markov Semigroups with Exponential Mixing in the Wasserstein Distance
Law of the Iterated Logarithm for Markov Semigroups with Exponential Mixing in the Wasserstein Distance Open
In this paper, we establish the law of the iterated logarithm for a wide class of non-stationary, continuous-time Markov processes evolving on Polish spaces. Specifically, our result applies to certain additive functionals of processes gov…
View article: Mathematical analysis of long‐distance polar auxin transport data of pin mutants questions the role of <scp>PIN1</scp> as postulated in the chemi‐osmotic theory
Mathematical analysis of long‐distance polar auxin transport data of pin mutants questions the role of <span>PIN1</span> as postulated in the chemi‐osmotic theory Open
The plant hormone auxin (Indole‐3‐Acetic Acid, IAA) is a key player in nearly every aspect of plant growth and development ranging from cell division and cell elongation to embryogenesis and root formation. The IAA level in specific tissue…
View article: Invariance properties of the solution operator for measure-valued semilinear transport equations
Invariance properties of the solution operator for measure-valued semilinear transport equations Open
We provide conditions under which we prove for measure-valued transport equations with non-linear reaction term in the space of finite signed Radon measures, that positivity is preserved, as well as absolute continuity with respect to Lebe…
View article: Approximation of a compound-exchanging cell by a Dirac point
Approximation of a compound-exchanging cell by a Dirac point Open
Communication between single cells or higher organisms by means of diffusive compounds is an important phenomenon in biological systems. Modelling therefore often occurs, most straightforwardly by a diffusion equation with suitable flux bo…
View article: Unique ergodicity for noninvertible function systems on an interval
Unique ergodicity for noninvertible function systems on an interval Open
We study random dynamical systems of certain continuous functions on the unit interval. We use bounded variation to provide sufficient conditions for unique ergodicity of these systems. Several classes of examples are provided.
View article: Approximation of a compound-exchanging cell by a Dirac point
Approximation of a compound-exchanging cell by a Dirac point Open
Communication between single cells or higher organisms by means of diffusive compounds is an important phenomenon in biological systems. Modelling therefore often occurs, most straightforwardly by a diffusion equation with suitable flux bo…
View article: Proximality, stability, and central limit theorem for random maps on an interval
Proximality, stability, and central limit theorem for random maps on an interval Open
Stochastic dynamical systems consisting of non-invertible continuous maps on an interval are studied. It is proved that if they satisfy the recently introduced so-called $μ$-injectivity and some mild assumptions, then proximality, asymptot…
View article: Norming and dense sets of extreme points of the unit ball in spaces of bounded Lipschitz functions
Norming and dense sets of extreme points of the unit ball in spaces of bounded Lipschitz functions Open
On spaces of finite signed Borel measures on a metric space one has introduced the Fortet-Mourier and Dudley norms, by embedding the measures into the dual space of the Banach space of bounded Lipschitz functions, equipped with different –…
View article: Using multiple Dirac delta points to describe inhomogeneous flux density over a cell boundary in a single-cell diffusion model
Using multiple Dirac delta points to describe inhomogeneous flux density over a cell boundary in a single-cell diffusion model Open
Biological cells can release compounds into their direct environment, generally inhomogeneously over their cell membrane, after which the compounds spread by diffusion. In mathematical modelling and simulation of a collective of such cells…
View article: Quality of approximating a mass-emitting object by a point source in a diffusion model
Quality of approximating a mass-emitting object by a point source in a diffusion model Open
For the sake of computational efficiency and for theoretical purposes, in mathematical modelling, the DiracDelta distributions are often utilized as a replacement for cells or vesicles, since the size of cells or vesicles is much smaller tha…
View article: Explicit expressions and computational methods for the Fortet–Mourier distance of positive measures to finite weighted sums of Dirac measures
Explicit expressions and computational methods for the Fortet–Mourier distance of positive measures to finite weighted sums of Dirac measures Open
Explicit expressions and computational approaches are given for the Fortet–Mourier distance between a positively weighted sum of Dirac measures on a metric space and a positive finite Borel measure. Explicit expressions are given for the d…
View article: Norming and dense sets of extreme points of the unit ball in spaces of bounded Lipschitz functions
Norming and dense sets of extreme points of the unit ball in spaces of bounded Lipschitz functions Open
On spaces of finite signed Borel measures on a metric space one has introduced the Fortet-Mourier and Dudley norms, by embedding the measures into the dual space of the Banach space of bounded Lipschitz functions, equipped with different -…
View article: Quality of approximating a mass-emitting object by a point source in a diffusion model
Quality of approximating a mass-emitting object by a point source in a diffusion model Open
For the sake of computational efficiency and for theoretical purposes, in mathematical modelling, the Dirac Delta distributions are often utilized as a replacement for cells or vesicles, since the size of cells or vesicles is much smaller …
View article: Bidirectional crosstalk between epithelial–mesenchymal plasticity and IFN <i>γ</i> -induced PD-L1 expression promotes tumour progression
Bidirectional crosstalk between epithelial–mesenchymal plasticity and IFN <i>γ</i> -induced PD-L1 expression promotes tumour progression Open
Epithelial–mesenchymal transition (EMT) and immunoevasion through upregulation of programmed death-ligand 1 (PD-L1) are important drivers of cancer progression. While EMT has been proposed to facilitate PD-L1-mediated immunosuppression, mo…
View article: Explicit expressions and computational methods for the Fortet-Mourier distance to finite weighted sums of Dirac measures
Explicit expressions and computational methods for the Fortet-Mourier distance to finite weighted sums of Dirac measures Open
Explicit expressions and computational approaches are given for the Fortet-Mourier distance between a positively weighted sum of Dirac measures on a metric space and a positive finite Borel measure. Explicit expressions are given for the d…
View article: Bidirectional crosstalk between epithelial-mesenchymal plasticity and IFNγ-induced PD-L1 expression promotes tumor progression
Bidirectional crosstalk between epithelial-mesenchymal plasticity and IFNγ-induced PD-L1 expression promotes tumor progression Open
Epithelial-Mesenchymal Transition (EMT) and immunoevasion through upregulation of Programmed Death-Ligand 1 (PD-L1) are important drivers of cancer progression. While EMT has been proposed to facilitate PD-L1-mediated immunosuppression, th…
View article: Equivalence of equicontinuity concepts for Markov operators derived from a Schur-like property for spaces of measures
Equivalence of equicontinuity concepts for Markov operators derived from a Schur-like property for spaces of measures Open
Various equicontinuity properties for families of Markov operators have been – and still are – used in the study of existence and uniqueness of invariant probability for these operators, and of asymptotic stability. We prove a general resu…
View article: The law of the iterated logarithm for a piecewise deterministic Markov process assured by the properties of the Markov chain given by its post-jump locations
The law of the iterated logarithm for a piecewise deterministic Markov process assured by the properties of the Markov chain given by its post-jump locations Open
In the paper we consider some piecewise deterministic Markov process whose continuous component evolves according to semiflows, which are switched at the jump times of a Poisson process. The associated Markov chain describes the states of …
View article: Existence and differentiability in parameter of the measure solution to a perturbed non-linear transport equation
Existence and differentiability in parameter of the measure solution to a perturbed non-linear transport equation Open
We consider a perturbation in the non-linear transport equation on measures i.e. both initial condition $μ_0$ and the solution $μ_t^h$ are bounded Radon measures $\mathcal{M}(\mathbb{R}^d)$. The perturbations occur in the velocity field an…
View article: Special issue: Mathematical Modeling with Measures
Special issue: Mathematical Modeling with Measures Open
The special issue is available from: http://www.aimspress.com/newsinfo/1132.html.
View article: Continuous dependence of an invariant measure on the jump rate of a piecewise-deterministic Markov process
Continuous dependence of an invariant measure on the jump rate of a piecewise-deterministic Markov process Open
We investigate a piecewise-deterministic Markov process, evolving on a Polish metric space, whose deterministic behaviour between random jumps is governed by some semi-flow, and any state right after the jump is attained by a randomly sele…
View article: Differentiability in perturbation parameter of measure solutions to perturbed transport equation
Differentiability in perturbation parameter of measure solutions to perturbed transport equation Open
We consider a linear perturbation in the velocity field of the transport equation. We investigate solutions in the space of bounded Radon measures and show that they are differentiable with respect to the perturbation parameter in a proper…
View article: Differentiability in perturbation parameter of measure solutions to perturbed transport equation
Differentiability in perturbation parameter of measure solutions to perturbed transport equation Open
We consider a linear perturbation in the velocity field of the transport equation. We investigate solutions in the space of bounded Radon measures and show that they are differentiable with respect to the perturbation parameter in a proper…
View article: A novel expected hypervolume improvement algorithm for Lipschitz multi-objective optimisation: Almost Shubert’s algorithm in a special case
A novel expected hypervolume improvement algorithm for Lipschitz multi-objective optimisation: Almost Shubert’s algorithm in a special case Open
An algorithm is proposed for multi-objective optimisation of Lipschitz objective functions that each satisfy a Lipschitz condition of which a Lipschitz constant is a priori known. The number of function evaluations is reduced by determini…
View article: Relative Contribution of PIN-Containing Secretory Vesicles and Plasma Membrane PINs to the Directed Auxin Transport: Theoretical Estimation
Relative Contribution of PIN-Containing Secretory Vesicles and Plasma Membrane PINs to the Directed Auxin Transport: Theoretical Estimation Open
The intercellular transport of auxin is driven by PIN-formed (PIN) auxin efflux carriers. PINs are localized at the plasma membrane (PM) and on constitutively recycling endomembrane vesicles. Therefore, PINs can mediate auxin transport eit…
View article: Relative Contribution of PIN-containing Secretory Vesicles and Plasma Membrane PINs to the Directed Auxin Transport: Theoretical Estimation
Relative Contribution of PIN-containing Secretory Vesicles and Plasma Membrane PINs to the Directed Auxin Transport: Theoretical Estimation Open
Intercellular transport of auxin is driven by PIN-formed (PIN) proteins. PINs are localized at the plasma membrane (PM) and on constitutively recycling endomembrane vesicles. Therefore, PINs can mediate auxin transport either by direct tra…
View article: Lie-Trotter product formula for locally equicontinuous and tight Markov semigroup
Lie-Trotter product formula for locally equicontinuous and tight Markov semigroup Open
In this paper we prove a Lie-Trotter product formula for Markov semigroups in spaces of measures. We relate our results to "classical" results for strongly continuous linear semigroups on Banach spaces or Lipschitz semigroups in metric spa…