Martin G. Riedler

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In this paper, we present a mathematical description for excitable biological membranes, in particular neuronal membranes. We aim to model the (spatio-) temporal dynamics, e.g., the travelling of an action potential along the axon, subject to noise, such as ion channel noise. Using the framework of Piecewise Deterministic Processes (PDPs) we provide an(More)
We study the effect of additive noise on integro-differential neural field equations. In particular, we analyze an Amari-type model driven by a Q-Wiener process, and focus on noise-induced transitions and escape. We argue that proving a sharp Kramers' law for neural fields poses substantial difficulties, but that one may transfer techniques from stochastic(More)
Hybrid systems, and Piecewise Deterministic Markov Processes in particular, are widely used to model and numerically study systems exhibiting multiple time scales in biochemical reaction kinetics and related areas. In this paper an almost sure convergence analysis for numerical simulation algorithms for PiecewiseDeterministicMarkov Processes is presented.(More)
In this study, we consider limit theorems for microscopic stochastic models of neural fields. We show that the Wilson-Cowan equation can be obtained as the limit in uniform convergence on compacts in probability for a sequence of microscopic models when the number of neuron populations distributed in space and the number of neurons per population tend to(More)
We present limit theorems for a sequence of Piecewise Deterministic Markov Processes (PDMPs) taking values in a separable Hilbert space. This class of processes provides a rigorous framework for stochastic spatial models in which discrete random events are globally coupled with continuous space-dependent variables solving partial differential equations,(More)
The Particle Therapy Patient Scheduling Problem arises in radiotherapy used for cancer treatment. Previous contributions in the existing literature primarily dealt with photon and electron therapy with a one-to-one correspondence of treatment rooms and accelerators. In particle therapy, however, a single accelerator serves multiple rooms in an interleaved(More)
The net synthesis of ATP in dark anaerobic cells of Anacystis nidulans subjected to acid jumps and/or valinomycin pulses was characterized thermodynamically and kinetically. Maximum initial rates of 75 nmol ATP/min per mg dry weight at an applied proton motive force of -350 mV were obtained, the flow-force relationship (rate of ATP synthesis vs applied(More)
The Particle Therapy Patient Scheduling Problem (PTPSP) arises in modern cancer treatment facilities that provide particle therapy and consists of scheduling a set of therapies within a planning horizon of several months. A particularity of PTPSP compared to classical radiotherapy scheduling is that therapies need not only be assigned to days but also(More)