Nucleation for one-dimensional long-range Ising models

In this note we study metastability phenomena for a class of long-range Ising models in one-dimension. We prove that, under suitable general conditions, the configuration -1 is the only metastable state and we estimate the mean exit time. Moreover, we illustrate the theory with two examples (exponentially and polynomially decaying interaction) and we show that the critical droplet can be macroscopic or mesoscopic, according to the value of the external magnetic field.Comment: 15 pages, 3 figure

Competitive nucleation in reversible probabilistic cellular automata

The problem of competitive nucleation in the framework of probabilistic cellular automata is studied from the dynamical point of view. The dependence of the metastability scenario on the self-interaction is discussed.An intermediate metastable phase, made of two flip-flopping chessboard configurations, shows up depending on the ratio between the magnetic field and the self-interaction. A behavior similar to the one of the stochastic Blume-Capel model with Glauber dynamics is found

Sharp asymptotics for stochastic dynamics with parallel updating rule with self-interaction

In this paper we study metastability for a stochastic dynamics with a parallel updating rule in particular for a probabilistic cellular automata. The problem is addressed in the Freidlin Wentzel regime, i.e., finite volume, small magnetic field, and in the limit when temperature tends to zero. We are interested in how the system nucleates, i.e., in properties of the transition from the metastable state (the configuration with all minuses) to the stable state (the configuration with all pluses). In this paper we show that the nucleation time divided by its average converges to an exponential random variable and we express the proportionality constant for the average nucleation time in terms of parameters of the model. Our approach combines geometric and potential theoretic arguments. A special feature of parallel dynamics is the existence of many fixed points and cyclic pairs of the zero temperature dynamics, in which the system can be trapped in its way to the stable phase. These cyclic points are corresponding to chessboard kind of configurations that under the parallel dynamics alternate between even and odd

Marginal structural models with dose-delay joint-exposure for assessing variations to chemotherapy intensity

Marginal structural models are causal models designed to adjust for time-dependent confounders in observational studies with dynamically adjusted treatments. They are robust tools to assess causality in complex longitudinal data. In this paper, a marginal structural model is proposed with an innovative dose-delay joint-exposure model for Inverse-Probability-of-Treatment Weighted estimation of the causal effect of alterations to the therapy intensity. The model is motivated by a precise clinical question concerning the possibility of reducing dosages in a regimen. It is applied to data from a randomised trial of chemotherapy in osteosarcoma, an aggressive primary bone-tumour. Chemotherapy data are complex because their longitudinal nature encompasses many clinical details like composition and organisation of multi-drug regimens, or dynamical therapy adjustments. This manuscript focuses on the clinical dynamical process of adjusting the therapy according to the patient’s toxicity history, and the causal effect on the outcome of interest of such therapy modifications. Depending on patients’ toxicity levels, variations to therapy intensity may be achieved by physicians through the allocation of either a reduction or a delay of the next planned dose. Thus, a negative feedback is present between exposure to cytotoxic agents and toxicity levels, which acts as time-dependent confounders. The construction of the model is illustrated highlighting the high complexity and entanglement of chemotherapy data. Built to address dosage reductions, the model also shows that delays in therapy administration should be avoided. The last aspect makes sense from the cytological point of view, but it is seldom addressed in the literature

Non-parametric estimation of transition probabilities in non-Markov multi-state models: The landmark Aalen-Johansen estimator

Development and application of statistical models for medical scientific researc

Unveiling the capabilities of bipolar conical channels in neuromorphic iontronics

Conical channels filled with an aqueous electrolyte have been proposed as promising candidates for iontronic neuromorphic circuits. This is facilitated by a novel analytical model for the internal channel dynamics [Kamsma et al., arXiv:2301.06158, 2023], the relative ease of fabrication of conical channels, and the wide range of achievable memory retention times by varying the channel lengths. In this work, we demonstrate that the analytical model for conical channels can be generalized to channels with an inhomogeneous surface charge distribution, which we predict to exhibit significantly stronger current rectification and more pronounced memristive properties in the case of bipolar channels, i.e. channels where the tip and base carry a surface charge of opposite sign. Additionally, we show that the use of bipolar conical channels in a previously proposed iontronic circuit features hallmarks of neuronal communication, such as all-or-none action potentials and spike train generation. Bipolar channels allow, however, for circuit parameters in the range of their biological analogues, and exhibit membrane potentials that match well with biological mammalian action potentials, further supporting its potential for bio-compatibility

Iontronic Neuromorphic Signaling with Conical Microfluidic Memristors

Experiments have shown that the conductance of conical channels, filled with an aqueous electrolyte, can strongly depend on the history of the applied voltage. These channels hence have a memory and are promising elements in brain-inspired (iontronic) circuits. We show here that the memory of such channels stems from transient concentration polarization over the ionic diffusion time. We derive an analytic approximation for these dynamics which shows good agreement with full finite-element calculations. Using our analytic approximation, we propose an experimentally realizable Hodgkin-Huxley iontronic circuit where micrometer cones take on the role of sodium and potassium channels. Our proposed circuit exhibits key features of neuronal communication such as all-or-none action potentials upon a pulse stimulus and a spike train upon a sustained stimulus

Iontronic Neuromorphic Signaling with Conical Microfluidic Memristors

Experiments have shown that the conductance of conical channels, filled with an aqueous electrolyte, can strongly depend on the history of the applied voltage. These channels hence have a memory and are promising elements in brain-inspired (iontronic) circuits. We show here that the memory of such channels stems from transient concentration polarization over the ionic diffusion time. We derive an analytic approximation for these dynamics which shows good agreement with full finite-element calculations. Using our analytic approximation, we propose an experimentally realisable Hodgkin-Huxley iontronic circuit where micrometer cones take on the role of sodium and potassium channels. Our proposed circuit exhibits key features of neuronal communication such as all-or-none action potentials upon a pulse stimulus and a spike train upon a sustained stimulus

Is the IMF in ellipticals bottom-heavy? Clues from their chemical abundances

© 2018 The Author(s). Published by Oxford University Press on behalf of the Royal Astronomical Society.We tested the implementation of different initial mass functions (IMFs) in our model for the chemical evolution of ellipticals, with the aim of reproducing the observed relations of [Fe/H] and [Mg/Fe] abundances with galaxy mass in a sample of early-type galaxies selected from the SPIDER-SDSS catalogue. Abundances in the catalogue were derived from averaged spectra, obtained by stacking individual spectra according to central velocity dispersion, as a proxy of galaxy mass. We tested IMFs already used in a previous work, as well as two new models, based on low-mass tapered (‘bimodal’) IMFs, where the IMF becomes either (1) bottom-heavy in more massive galaxies, or (2) is time-dependent, switching from top-heavy to bottom-heavy in the course of galactic evolution. We found that observations could only be reproduced by models assuming either a constant, Salpeter IMF, or a time-dependent distribution, as other IMFs failed. We further tested the models by calculating their M/L ratios. We conclude that a constant, time-independent bottom-heavy IMF does not reproduce the data, especially the increase of the [α/Fe] ratio with galactic stellar mass, whereas a variable IMF, switching from top to bottom-heavy, can match observations. For the latter models, the IMF switch always occurs at the earliest possible considered time, i.e. tswitch = 0.1 Gyr.Peer reviewe