Mangrove restoration efforts have been ongoing, but with varying levels of success, requiring spatial and temporal monitoring to better understand the stocks and drivers of success. Here, we used multi-spectral remote sensing and spatial regression techniques to examine mangrove distribution and restoration potential in the Vietnamese Southern Coastal (VSC) region from 1988 to 2023, an area where multiple episodes of mangrove restoration have been attempted over the past decades. Our results show that 51.5% of the mangrove area has recovered from previous losses, while 48.5% has been lost during the 1988–2023 period. Significant gains were observed between 2018 and 2023, accounting for 77.8% of the total restoration. However, over 40,000 ha of mangroves were lost during each decade between 1988 and 2018, primarily due to land-use changes. Regression analyses estimated a sustainable mangrove cover increase of 9.9% (23,407 ha) and persistence of 22.5% (52,936 ha), mainly in protected areas and low-impact zones. Conversely, 9.8% (23,056 ha) of mangroves in erosion-prone and human-disturbed regions face continued decline. Our study demonstrated the effectiveness of integrating long-term Normalised Difference Vegetation Index time-series analysis with spatial regression to monitor mangrove ecosystems. These techniques offered a scalable framework for global mangrove monitoring and restoration planning, supporting evidence-based conservation policies.

Understanding core statistical properties and data features in mortality data are fundamental to the development of machine learning methods for demographic and actuarial applications of mortality projection. The study of statistical features in such data forms the basis for classification, regression and forecasting tasks. In particular, the understanding of key statistical structure in such data can aid in improving accuracy in undertaking mortality projection and forecasting when constructing life tables. The ability to accurately forecast mortality is a critical aspect for the study of demography, life insurance product design and pricing, pension planning and insurance-based decision risk management. Though many stylised facts of mortality data have been discussed in the literature, we provide evidence for a novel statistical feature that is pervasive in mortality data at a national level that is as yet unexplored. In this regard, we demonstrate in this work a strong evidence for the existence of long memory features in mortality data, and second that such long memory structures display multifractality as a statistical feature that can act as a discriminator of mortality dynamics by age, gender and country. To achieve this, we first outline the way in which we choose to represent the persistence of long memory from an estimator perspective. We make a natural link between a class of long memory features and an attribute of stochastic processes based on fractional Brownian motion. This allows us to use well established estimators for the Hurst exponent to then robustly and accurately study the long memory features of mortality data. We then introduce to mortality analysis the notion from data science known as multifractality. This allows us to study the long memory persistence features of mortality data on different timescales. We demonstrate its accuracy for sample sizes commensurate with national-level age term structure historical mortality records. A series of synthetic studies as well a comprehensive analysis of real mortality death count data are studied in order to demonstrate the pervasiveness of long memory structures in mortality data, both mono-fractal and multifractal functional features are verified to be present as stylised facts of national-level mortality data for most countries and most age groups by gender. We conclude by demonstrating how such features can be used in kernel clustering and mortality model forecasting to improve these actuarial applications.

We propose a new multifractional stochastic process which allows for self-exciting behavior, similar to what can be seen for example in earthquakes and other self-organizing phenomena. The process can be seen as an extension of a multifractional Brownian motion, where the Hurst function is dependent on the past of the process. We define this by means of a stochastic Volterra equation, and we prove existence and uniqueness of this equation, as well as giving bounds on the p-order moments, for all $p\geq1$. We show convergence of an Euler–Maruyama scheme for the process, and also give the rate of convergence, which is dependent on the self-exciting dynamics of the process. Moreover, we discuss various applications of this process, and give examples of different functions to model self-exciting behavior.

One of the main concerns about the fast spreading coronavirus disease 2019 (Covid-19) pandemic is how to intervene. We analysed severe acute respiratory syndrome-coronavirus-2 (SARS-CoV-2) isolates data using the multifractal approach and found a rich in viral genome diversity, which could be one of the root causes of the fast Covid-19 pandemic and is strongly affected by pressure and health index of the hosts inhabited regions. The calculated mutation rate (mr) is observed to be maximum at a particular pressure, beyond which mr maintains diversity. Hurst exponent and fractal dimension are found to be optimal at a critical pressure (Pm), whereas, for P > Pm and P < Pm, we found rich genome diversity relating to complicated genome organisation and virulence of the virus. The values of these complexity measurement parameters are found to be increased linearly with health index values.

The daily time series Flare Index (FI) data of Northern Hemisphere, Southern Hemisphere and Total Disk for Solar Cycle 21- 23 and 24 up to Dec. 2014 has been pre-processed using a 2nd order exponential smoothing algorithm to remove orthogonal noise. The smoothed data in each case is processed for scaling analysis using Rescaled-Range Analysis as well as Finite Variance Scaling Method in order to search for the Hurst exponent. As the value of H obtained from our analysis lies in between 0 and 1, so it can be said that the signal may behave like Fractional Brownian Motion. Also, it is observed that H is less than 0.5 which indicates the data is anti-persistent in nature and it has a strong negative correlation within the signal. The value of H also indicates the oscillating features of the signal which might have some fundamental periodicities in the Suns atmosphere.

An approach to time series model identification is described which involves the simultaneous use of frequency, time and quantile domain algorithms; the approach is called quantile spectral analysis. It proposes a framework to integrate the analysis of long-memory (non-stationary) time series with the analysis of short-memory (stationary) time series.

Necessary and sufficient conditions for the so-called Hurst effect are given in the case of a weakly dependent stationary sequence of random variables perturbed by a trend. As a consequence of this general result it is shown that the Hurst effect is present in the case of weakly dependent random variables with a small monotonic trend of the form f(n) = c(m + n)ß, where m is an arbitrary non-negative parameter and c is not 0. For – ½ < ß < 0 the Hurst exponent is shown to be precisely given by 1 + ß. For ß ≦ – ½ and for ß = 0 the Hurst exponent is 0.5, while for ß > 0 it is 1. This simple mathematical model, motivated by empirical evidence in various geophysical records, demonstrates the presence of the Hurst effect in a direction not explored before.