Vesicle shape transformations driven by confined active filaments

In active matter systems, deformable boundaries provide a mechanism to organize internal active stresses. To study a minimal model of such a system, we perform particle-based simulations of an elastic vesicle containing a collection of polar active filaments. The interplay between the active stress organization due to interparticle interactions and that due to the deformability of the confinement leads to a variety of filament spatiotemporal organizations that have not been observed in bulk systems or under rigid confinement, including highly-aligned rings and caps. In turn, these filament assemblies drive dramatic and tunable transformations of the vesicle shape and its dynamics. We present simple scaling models that reveal the mechanisms underlying these emergent behaviors and yield design principles for engineering active materials with targeted shape dynamics.

Performance scaling and trade-offs for collective motor-driven transport

Motor-driven intracellular transport of organelles, vesicles, and other molecular cargo is a highly collective process. An individual cargo is often pulled by a team of transport motors, with numbers ranging from only a few to several hundred. We explore the behavior of these systems using a stochastic model for transport of molecular cargo by an arbitrary number N of motors, finding analytic solutions for the N-dependence of the velocity, precision of forward progress, energy flows between different system components, and efficiency. In two opposing regimes, we show that these properties obey simple scaling laws with N. Finally, we explore trade-offs between performance metrics as N is varied, providing insight into how different numbers of motors might be well-matched to distinct contexts where different performance metrics are prioritized.

Exact solutions for steady granular flow in vertical chutes and pipes

Vertical chutes and pipes are a common component of many industrial apparatus used in the transport and processing of powders and grains. Here, a typical arrangement is considered first in which a hopper at the top feeds the chute and a converging outlet at the bottom controls the mass flux. Discrete element method (DEM) simulations reveal that steady uniform flow is only observed for intermediate flow rates, with jamming and unsteady waves dominating slow flows and non-uniform wall detachment in fast flow. Focusing on the steady uniform regimes, a progressive idealisation is carried out by matching with equivalent DEM simulations in periodic cells. These investigations justify a one-dimensional continuum modelling of the problem and provide key test data. Novel exact solutions are derived here for vertical flow using a linear version of the ‘ $\mu(I),\varPhi(I)$ -rheology’, for which the bulk friction $\mu$ and steady solid volume fraction $\varPhi$ depend on the inertial number I. Despite not capturing the full nonlinear complexities, the solutions match important aspects of the DEM flow fields and reveal simple scaling laws linking many quantities of interest. In particular, this study clearly demonstrates a linear relation between the chute width and the size of the shear zones at the walls. This finding contrasts with previous works on purely quasi-static flow, which instead predict a roughly constant shear zone width, a difference which implies that finite-size effects are minimal for the inertial flows studied here.

Probabilistic Analysis of the Obstruction of Water Sources Due to the Occurrence of Rainfall-Triggered Mass Movements

This paper presents a methodology for the probabilistic estimation of the obstruction of water streams generated by shallow mass movements triggered by rainfall. The study focuses on the Ovejas River, a tributary stream of the Medellín River, in the jurisdiction of the municipality of San Vicente in the department of Antioquia (Colombia). The occurrence of a mass movements was evaluated by deterministic and probabilistic methods based on the automation of processes of Geographic Information Systems (GIS) and spatial modeling. The spatial distribution of the mass movement hazard was estimated in terms of Factor of Safety (FoS) values by the deterministic method with physical basis SLIDE (Slope - Infiltration - Distributed Equilibrium), which allows the hazard zonation by calculating a FoS for rainfall-induced mass movements with different return periods. The rainfall regimes of the study area are estimated by means of a simple scaling Log Normal Model. On the other hand, the Probability of Failure (PF) analysis was performed under Rosenblueth’s punctual estimates method (PEM), which allows incorporating the uncertainty of the soil parameters. Subsequently, the resulting zones with high hazard that could detach and reach the Ovejas River channel are identified as sources for runout modeling by means of the Flow R model, thus estimating the extent of mass movement in probabilistic terms. In all the analyzed scenarios, the sliding material from the critical stability zones has a high probability of spreading to the riverbed of the main river. This analysis makes possible to identify those areas of the riverbed that should be analyzed with more detail and require possible intervention for the protection of the riverbed.

Mathematical Modelling to Determine the Greatest Height of Trees

This study aimed to analyse the critical height of a column whose weight varies vertically in order to obtain a simple scaling law for a tree where the weight distribution considered. We modelled trees as cantilevers that were fixed to the ground and formulated a self-buckling problem for various weight distributions. A formula for calculating the critical height was derived in a simple form that did not include special functions. We obtained a theoretical clarification of the effect of the weight distribution of heavy columns on the buckling behaviour. A widely applicable scaling law for trees was obtained. We found that an actual tree manages to distribute the weight of its trunk and branches along its vertical extent in a manner that adequately secures its critical height. The method and findings of this study are applicable to a wide range of fields, such as the simplification of complicated buckling problems and the study of tree shape quantification.

On testing structural identifiability by a simple scaling method: Relying on scaling symmetries can be misleading

A recent paper published in PLOS Computational Biology [1] introduces the Scaling Invariance Method (SIM) for analysing structural local identifiability and observability. These two properties define mathematically the possibility of determining the values of the parameters (identifiability) and states (observability) of a dynamic model by observing its output. In this note we warn that SIM considers scaling symmetries as the only possible cause of non-identifiability and non-observability. We show that other types of symmetries can cause the same problems without being detected by SIM, and that in those cases the method may lead one to conclude that the model is identifiable and observable when it is actually not.

The limitations, dangers, and benefits of simple methods for testing identifiability

In their Commentary paper, Villaverde and Massonis (On testing structural identifiability by a simple scaling method: relying on scaling symmetries can be misleading) have commented on our paper in which we proposed a simple scaling method to test structural identifiability. Our scaling invariance method (SIM) tests for scaling symmetries only, and Villaverde and Massonis correctly show the SIM may fail to detect identifiability problems when a model has other types of symmetries. We agree with the limitations raised by these authors but, also, we emphasize that the method is still valuable for its applicability to a wide variety of models, its simplicity, and even as a tool to introduce the problem of identifiability to investigators with little training in mathematics.

Probabilistic Projection of Subnational Life Expectancy

Projecting mortality for subnational units, or regions, is of great interest to practicing demographers. We seek a probabilistic method for projecting subnational life expectancy that is based on the national Bayesian hierarchical model used by the United Nations, and at the same time is easy to use. We propose three methods of this kind. Two of them are variants of simple scaling methods. The third method models life expectancy for a region as equal to national life expectancy plus a region-specific stochastic process which is a heteroskedastic first-order autoregressive process (AR(1)), with a variance that declines to a constant as life expectancy increases. We apply our models to data from 29 countries. In an out-of-sample comparison, the proposed methods outperformed other comparative methods and were well calibrated for individual regions. The AR (1) method performed best in terms of crossover patterns between regions. Although the methods work well for individual regions, there are some limitations when evaluating within-country variation. We identified four countries for which the AR(1) method either underestimated or overestimated the predictive between-region within-country standard deviation. However, none of the competing methods work better in this regard than the AR(1) method. In addition to providing the full distribution of subnational life expectancy, the methods can be used to obtain probabilistic forecasts of age-specific mortality rates.

How Fast Does the Clock of Finance Run?—A Time-Definition Enforcing Stationarity and Quantifying Overnight Duration

A definition of time based on the assumption of scale invariance may enhance and simplify the analysis of historical series with cyclically recurrent patterns and seasonalities. By enforcing simple-scaling and stationarity of the distributions of returns, we identify a successful protocol of time definition in finance, functional from tens of minutes to a few days. Within this time definition, the significant reduction of cyclostationary effects allows analyzing the structure of the stochastic process underlying the series on the basis of statistical sampling sliding along the whole time series. At the same time, the duration of periods in which markets remain inactive is properly quantified by the novel clock, and the corresponding returns (e.g., overnight or weekend) can be consistently taken into account for financial applications. The method is applied to the S&P500 index recorded at a 1 min frequency between September 1985 and June 2013.