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We develop a new quantile-based panel data framework to study the nature of income persistence and the transmission of income shocks to consumption. Log-earnings are the sum of a general Markovian persistent component and a transitory innovation. The persistence of past shocks to earnings is allowed to vary according to the size and sign of the current shock. Consumption is modeled as an age-dependent non-linear function of assets, unobservable tastes, and the two earnings components. We establish the nonparametric identification of the nonlinear earnings process and of the consumption policy rule. Exploiting the enhanced consumption and asset data in recent waves of the Panel Study of Income Dynamics, we find that the earnings process features nonlinear persistence and conditional skewness. We confirm these results using population register data from Norway. We then show that the impact of earnings shocks varies substantially across earnings histories, and that this nonlinearity drives heterogeneous consumption responses. The framework provides new empirical measures of partial insurance in which the transmission of income shocks to consumption varies systematically with assets, the level of the shock, and the history of past shocks.

The discrete complex Ginzburg–Landau equation is a fundamental model for the dynamics of nonlinear lattices incorporating competitive dissipation and energy gain effects. Such mechanisms are of particular importance for the study of survival/destruction of localised structures in many physical situations. In this work, we prove that in the discrete complex Ginzburg–Landau equation dissipative solitonic waveforms persist for significant times by introducing a dynamical transitivity argument. This argument is based on a combination of the notions of “inviscid limits” and of the “continuous dependence of solutions on their initial data”, between the dissipative system and its Hamiltonian counterparts. Thereby, it establishes closeness of the solutions of the Ginzburg–Landau lattice to those of the conservative ideals described by the Discrete Nonlinear Schrödinger and Ablowitz–Ladik lattices. Such a closeness holds when the initial conditions of the systems are chosen to be sufficiently small in the suitable metrics and for small values of the dissipation or gain strengths. Our numerical findings are in excellent agreement with the analytical predictions for the dynamics of the dissipative bright, dark or even Peregrine-type solitonic waveforms.

Neuro-degenerative disease is a common progressive nervous system disorder that leads to serious clinical consequences. Gait rhythm dynamics analysis is essential for evaluating clinical states and improving quality of life for neuro-degenerative patients. The magnitude of stride-to-stride fluctuations and corresponding changes over time—gait dynamics—reflects the physiology of gait, in quantifying the pathologic alterations in the locomotor control system of health subjects and patients with neuro-degenerative diseases. Motivated by algebra topology theory, a topological data analysis-inspired nonlinear framework was adopted in the study of the gait dynamics. Meanwhile, the topological representation–persistence landscapes were used as input of classifiers in order to distinguish different neuro-degenerative disease type from healthy. In this work, stride-to-stride time series from healthy control (HC) subjects are compared with the gait dynamics from patients with amyotrophic lateral sclerosis (ALS), Huntington’s disease (HD), and Parkinson’s disease (PD). The obtained results show that the proposed methodology discriminates healthy subjects from subjects with other neuro-degenerative diseases with relatively high accuracy. In summary, our study is the first attempt to provide a topological representation-based method into the disease classification with gait rhythms measured from the stride intervals to visualize gait dynamics and classify neuro-degenerative diseases. The proposed method could be potentially used in earlier interventions and state monitoring.

In this paper, we propose and analyze a detailed mathematical model describing the dynamics of a prey-predator model under the influence of an SIS infectious disease by using nonlinear differential equations. We use the functional response of ratio-dependent Michaelis-Menten type to describe the predation strategy. In the presence of the disease, prey and predator population are divided into two disjointed classes, namely infected and susceptible. The first one is governed through due predation interaction, and the second one is governed through the propagation of disease in the prey and predator population via predation. Our aim is to analyze the effect of predation on the dynamic of the disease transmission. Important mathematical results resulting from the transmission of the disease under influence of predation are offered. First, results concerning boundedness, uniform persistence, existence and uniqueness of solutions have been developed. In addition, many thresholds have been computed and used to investigate local and global stability analysis by using Routh-Hurwitz criterion and Lyapunov principle. We also establish the Hopf bifurcation to highlight periodic fluctuation with persistence of the disease or without disease in the prey and predator population. Finally, numerical simulations are carried out to illustrate the feasibility of the theoretical results.

Stride-to-stride fluctuations during walking reflect age-related changes in gait adaptability and are estimated with nonlinear measures that confine data collection to controlled settings. Smartphones, with their embedded accelerometers, may provide accessible gait analysis throughout the day. This study investigated age-related differences in linear and nonlinear gait measures estimated from a smartphone accelerometer (SPAcc) in an unconstrained, free-living environment. Thirteen young adults (YA) and 11 older adults (OA) walked within a shopping mall with a SPAcc placed in their front right pants pocket. The inter-stride interval, calculated as the time difference between ipsilateral heel contacts, was used for dependent measures calculations. One-way repeated-measures analysis of variance revealed significant (p < 0.05) age-related differences (mean: YA, OA) for stride-time standard deviation (0.04 s, 0.05 s) and coefficient of variation (3.47%, 4.16%), sample entropy (SaEn) scale 1 (1.70, 1.86) and scale 3 (2.12, 1.80), and statistical persistence decay (31 strides, 23 strides). The fractal scaling index was not different between groups (0.93, 0.95), but exceeded those typically found in controlled settings, suggesting an upregulation in adaptive behaviour likely to accommodate the increased challenge of free-living walking. These findings support the SPAcc as a viable telehealth instrument for remote monitoring of gait dynamics, with implications for unsupervised fall-risk assessment.

Persistence and permanence are properties of dynamical systems that describe the long-term behavior of the solutions and in particular specify whether positive solutions approach the boundary of the positive orthant. Mass-action systems (or more generally power-law systems) are very common in chemistry, biology, and engineering and are often used to describe the dynamics in interaction networks. We prove that two-species mass-action systems derived from weakly reversible networks are both persistent and permanent, for any values of the reaction rate parameters. Moreover, we prove that a larger class of networks, called endotactic networks, also give rise to permanent systems, even if the reaction rate parameters vary in time (to allow for the influence of external signals). These results also apply to power-law systems and other nonlinear dynamical systems. In addition, ideas behind these results allow us to prove the global attractor conjecture for three-species systems.

The Wet Bulb Globe Temperature (WBGT) is an international standard heat index used by the health, industrial, sports, and climate sectors to assess thermal comfort during heat extremes. Observations of its components, the globe and the wet bulb temperature (WBT), are however sparse. Therefore WBGT is difficult to derive, making it common to rely on approximations, such as the ones developed by Liljegren et al. (2008, https://doi.org/10.1080/15459620802310770, WBGTLiljegren${\\mathrm{W}\\mathrm{B}\\mathrm{G}\\mathrm{T}}_{\\mathrm{L}\\mathrm{i}\\mathrm{l}\\mathrm{j}\\mathrm{e}\\mathrm{g}\\mathrm{r}\\mathrm{e}\\mathrm{n}}$ ) and by the American College of Sports Medicine (WBGTACSM87${\\mathrm{W}\\mathrm{B}\\mathrm{G}\\mathrm{T}}_{\\mathrm{A}\\mathrm{C}\\mathrm{S}\\mathrm{M}87}$ ). In this study, a global data set is created by implementing an updated WBGT method using ECMWF ERA5 gridded meteorological variables and is evaluated against existing WBGT methods. The new method, WBGTBrimicombe${\\mathrm{W}\\mathrm{B}\\mathrm{G}\\mathrm{T}}_{\\mathrm{B}\\mathrm{r}\\mathrm{i}\\mathrm{m}\\mathrm{i}\\mathrm{c}\\mathrm{o}\\mathrm{m}\\mathrm{b}\\mathrm{e}}$ , uses globe temperature calculated using mean radiant temperature and is found to be accurate in comparison to WBGTLiljegren${\\mathrm{W}\\mathrm{B}\\mathrm{G}\\mathrm{T}}_{\\mathrm{L}\\mathrm{i}\\mathrm{l}\\mathrm{j}\\mathrm{e}\\mathrm{g}\\mathrm{r}\\mathrm{e}\\mathrm{n}}$across three heatwave case studies. In addition, it is found that WBGTACSM87${\\mathrm{W}\\mathrm{B}\\mathrm{G}\\mathrm{T}}_{\\mathrm{A}\\mathrm{C}\\mathrm{S}\\mathrm{M}87}$is not an adequate approximation of WBGT. Our new method is a candidate for a global forecasting early warning system. Plain Language Summary The Wet Bulb Globe Temperature (WBGT) is an international standard for how we measure the effect of heat on the human body. It is used across sectors in health, industry, sports, and climate to calculate how we feel and how our body responds during heat extremes. Its calculation has historically relied on globe thermometer and wet bulb temperature observations, which are however not widely available. This has made WBGT difficult to calculate and meant approximations have been created. Here we formulate a new WBGT method that can be used with global gridded data that are freely available and we compare it against other methods in common use. We find that our method is accurate when compared to the existing gold standard WBGT method. Key Points We create an accurate method for calculating Wet Bulb Globe Temperature (WBGT) using Mean Radiant Temperature termed WBGTBrimicombe It is found that WBGTamsc87 also known as WBGTsimple is not an accurate approximation of WBGT WBGTBrimicombe can assist with robust heat stress standards across sectors including in public and occupational health

Population persistence in the marine environment is driven by patterns of ocean circulation, larval dispersal, ecological interactions, and demographic rates. For habitat-forming organisms in particular, understanding the relationship between larval connectivity and meta-population dynamics aids in planning for marine spatial management. Here, we estimate networks of connectivity between fringing coral reefs in the northwest shelf of Australia by combining a particle tracking model based on shelf circulation with models of subpopulation dynamics of individual reefs. Coral cover data were used as a proxy for overall habitat quality, which can change as a result of natural processes, human-driven impacts, and management initiatives. We obtain three major results of conservation significance. First, the dynamics of the ecological network result from the interplay between network connectivity and ecological processes on individual reefs. The maximum coral cover a zone can sustain imposes a significant nonlinearity on the role an individual reef plays within the dynamics of the network, and thus on the impact of conservation interventions on specific reefs. Second, the role of an individual reef within these network dynamics changes considerably depending on the overall state of the system: a reef’s role in sustaining the system’s state can be different from the same reef’s role in helping the system recover following major disturbance. Third, patterns of network connectivity change significantly as a function of yearly shelf circulation trends, and nonlinearity in network dynamics make mean connectivity a poor representation of yearly variations. From a management perspective, the priority list of reefs that are targets for management interventions depends crucially on what type of stressors (system-wide vs. localized) need addressing. This choice also depends not only on the ultimate purpose of management, but also on future oceanographic, climate change, and development scenarios that will determine the network connectivity and habitat quality.