We define the notions of strong and strict recurrency for actions of countable ordered groups on $\sigma$-finite non atomic measure spaces with quasi-invariant measures. We show that strong recurrency is equivalent to non existence of weakly wandering sets of positive measure. We also show that for certain p.m.p ergodic actions the system is not strictly recurrent, which shows that strong and strict recurrency are not equivalent.

In modern mathematics, many concepts and ideas are described in terms of category theory. From this viewpoint, it is desirable to analyze what can be determined if, instead of the basic category of sets, we consider a similar category of fuzzy sets. In this paper, we describe a natural fuzzy analog of the category of sets and functions, and we show that, in this category, fuzzy relations (a natural fuzzy analogue of functions) can be determined in category terms -- of course, modulo 1-1 mapping of the corresponding universe of discourse and 1-1 re-scaling of fuzzy degrees.

The notion of oriented set is the basic elementary concept of the theory of changeable sets. The main motivation for the introduction of changeable sets was the sixth Hilbert problem, that is, the problem of mathematically rigorous formulation of the fundamentals of theoretical physics. In the present paper the necessary and sufficient condition of the existence of one-point time on an oriented set is established. From the intuitive point of view, one-point time is the time associated with the evolution of a system consisting of only one object (for example, from one material point). Namely, it is proven that the one-point time exists on the oriented set if and only if this oriented set is a quasi-chain. Also, using the obtained result, the problem of describing all possible images of linearly ordered sets is solved. This problem naturally arises in the theory of ordered sets.

Among many research areas to which Ron Yager contributed are decision making under uncertainty (in particular, under interval and fuzzy uncertainty) and aggregation – where he proposed, analyzed, and utilized the use of Ordered Weighted Averaging (OWA). The OWA algorithm itself provides only a specific type of data aggregation. However, it turns out that if we allows several OWA stages one after another, we get a scheme with a universal approximation property – moreover, a scheme which is perfectly equivalent to deep neural networks. In this sense, Ron Yager can be viewed as a (grand)father of deep learning. We also show that the existing schemes for decision making under uncertainty are also naturally interpretable in OWA terms.

During March and April 2020, the European Union (EU) was the center of the COVID-19 pandemic. Many National Governments imposed severe lockdown policies to mitigate the health crisis. The European Parliament commissioned a survey to analyse the citizens’ attitudes over a number of issues related to the COVID-19 pandemic. 21804 European citizens in 21 EU countries responded the survey between 23 April and 1 May 2020. The paper analyses empirically the individual satisfaction that European citizens have experienced over the measures taken by the respective National Governments to control the COVID-19 pandemic. The analysis is based on a micro-econometric model (ordered probit) that explains the citizens’ satisfaction by a number of attitudes and sociodemographic factors. Our results reveal that Spaniards are the least satisfied citizens in comparison with Danes, Irelanders, Greeks and Croats who are the most satisfied nationals. The years of education and the social class also play a determinant role. We also find that the most important determinant is the political support to the Government, and that those who are more worried by the economy and the protection of individual rights are usually more critic with the measures than those who are more worried by the health consequences.

Background: According to the National Highway Traffic Safety Administration, 116 pedestrians were killed in motor vehicle crashes in Ohio in 2015. However, no study to date has analyzed crashes in Ohio exploring the factors contributing to the pedestrian injury severity resulting from motor vehicle crashes. This study fills this gap by investigating the crashes involving pedestrians exclusively in Ohio. Materials and Methods: This study uses the crash data from the Highway Safety Information System, from 2009 to 2013. The explanatory factors include the pedestrian, driver, vehicle, crash, and roadway characteristics. Both fixed- and random-parameters ordered probit models of injury severity (where possible outcomes are major, minor, and possible/no injury) were estimated. Results: The model results indicate that being older pedestrian (65 and over), younger driver (less than 24), driving under influence (DUI), being struck by truck, dark-unlighted roadways, six-lane roadways, and speed limit of 40 mph and 50 mph were associated with more severe injuries to the pedestrians. Conversely, older driver (65 and over), passenger car, crash occurring in urban locations, daytime traffic off-peak (10 AM to 3:59 PM), weekdays, and daylight condition were associated with less severe injuries. Conclusion: This study provides specific safety recommendations so that effective countermeasures could be developed and implemented by the policy makers, which in turn will improve overall highway safety.

In this paper, we introduced a generalized ∆-implicit locally contractive condition and give some examples to support it and to show its significance in fixed point theory. We prove that the mappings satisfying generalized ∆-implicit locally contractive condition admits a common fixed point, where, the ordered multiplicative GM−metric space is chosen as underlying space. The obtained fixed point theorems generalize many earlier fixed point theorems on implicit locally contractive mappings. In addition, some nontrivial and interesting examples are provided to support our findings. To demonstrate the originality of our new main result, we apply it to show existence of solutions to a system of nonlinear -Volterra type- integral equations.

The paper proposes a human explainable artificial intelligence approach for mapping the status of environmental phenomena from multisource geo data. It is both knowledge and data driven: it exploits remote sensing expert’s knowledge to define the contributing factors from which partial evidence of the environmental status can be computed. Furthermore, it aggregates the partial evidences to compute a map of the environmental status by adapting to a region of interest through a learning mechanism exploiting Volunteered Geographic Information (VGI), both from in situ observations and photointerpretation. The approach is capable to capture the specificities of local context as well as to cope with the subjectivity and incompleteness of expert’s knowledge. The proposal is exemplified to map the status of standing water areas (i.e. water bodies and river, human driven or natural hazard flooding) by considering satellite data and geotagged observations. Results of the validation experiments were performed in three areas of Northern Italy, characterized by distinct ecosystems. Results of the proposed methodological framework showed better performances than traditional approaches based on single spectral indexes thresholding. The use of expert’s knowledge, possibly imprecise/uncertain and incomplete, the need of few ground truth data for learning, and finally the explainability of learned rules are the distinguishing characteristics of the proposal with respect to traditional machine learning methods.

This paper identifies the characteristics of the farmer that affect the degree of farmer’s perceived-impact of climate change (CC). We use data from the Indonesian Rice Farm Household survey consisting of 87,330 farmers. An ordered probit regression model was used to estimate the effect of each variable on the degree of perceived-impact of CC. The results of this study confirm the previous empirical studies. Several variables that have been identified as having a positive effect on farmer adaptation practices such as farmer education, land tenure, irrigation infrastructure, cropping system, chemical fertilizer application, access to extension services and participation in farmer group affect the degree of CC perceived-impact negatively. However, a different result was found in the estimation of the gender variable. We found that female farmer has a higher resilience toward CC than the male farmer does. Furthermore, the female farmer has a more positive perception about future farming conditions than the male does. Finally, we suggest that the implementation of national adaptation policy should prioritize more to the farmer with insecure land tenure and utilize and expand the channel of agricultural extension services to deliver the planned adaptation policy.

Balanced and coordinated economic development across regions is a critical goal of regional economic development and new-type urbanization in China. However, few studies have examined economic growth convergence clubs at the county level. To extend the research on convergence clubs, this research applies a log t convergence test and a dynamic spatial ordered Probit model (DSOP) to endogenously identify economic growth convergence clubs in counties and to examine the influence of initial states and structures on club convergence probability. The study sample covers 2286 counties of China from 1992 to 2010. The results show significant convergence club patterns at the county levels, resulting in the gradual formation of six convergence clubs. The DSOP estimation results show that per capita fixed assets, population density and industrialization have promoted convergence club formation to varying degrees.

Compared with the traditional slow charging loads, random integration of large scale fast charging loads will exert more serious impacts on the security of power network operation. Besides, to maximize social benefits, effective scheduling strategy guiding fast charging behaviors should be formulated rather than simply increasing infrastructure construction investments on the power grid. This paper has analyzed the charging users’ various responses to the elastic charging service fee, introduced the index of charging balance degree to a target region by considering the influence of fast charging loads on power grid. Then, a multi-objective optimization model of the fast charging service fee is constructed, whose service fee can be further optimized by employing fuzzy programming method. Therefore, both users’ satisfaction degree and the equilibrium of charging loads can be maintained simultaneously by guiding EVs to different fast charging stations reasonably. The simulation results demonstrate the effectiveness of proposed dynamic charging service pricing and the proposed fast charging load guidance strategy.

The literature on substance use usually extracts conclusions from data with correlational methods. Our study shows the usefulness of complementing ordered logistic regression (OLR) and fuzzy set qualitative comparative analysis (fsQCA) to assess factors inducing cannabis consumption in a sample of 1,935 teenagers. OLR showed a significant influence of gender (odd ratio (OR) =0.383, p<0.0001), parental monitoring (OR=0.587, p=0.0201); religiousness (OR=0.476, p=0.006); parental tolerance to substance use (OR=42.01, p<0.0001) and having close peers that consume substances (OR=5.60, p<0.0001). FsQCA has allowed fitting linkages between factors from a complementary perspective. (1) Coverage (cov) and consistency (cons) attained by solutions explaining use (cons=0.808, cov=0.357) are clearly lower than by recipes of non-use (cons=0.952, cov=0.869) (2) The interaction of gender, a tolerant family to use and the attitude toward substances by peers is very consistent to explain cannabis use. (3) The most important recipe explaining resistance to cannabis is simply parental disagreement with substance consumption (cons=0.956, cov=0.861) (4) Factors as gender, religiosity, parental monitoring and age show also a relevant impact on attitude toward cannabis use. However, whereas some of them impact symmetrically on use and non-use this does not follow in factors such as parental monitoring or age.

The underlying physical concept of computing out-of-time-ordered correlation (OTOC) is a significant new tool within the framework of quantum field theory, which now-a-days is treated as a measure of random fluctuations. In this paper, by following the canonical quantization technique we demonstrate a computational method to quantify the two different types of Cosmological auto-correlated OTO functions during the epoch when the non-equilibrium features dominates in Primordial Cosmology. In this formulation, two distinct dynamical time scales are involved to define the quantum mechanical operators arising from cosmological perturbation scenario. We have provided detailed explanation regarding the necessity of this new formalism to quantify any random events generated from quantum fluctuations in Primordial Cosmology. We have performed an elaborative computation for the two types of two-point and four-point auto-correlated OTO functions in terms of the cosmological perturbation field variables and its canonically conjugate momenta to quantify random auto-correlations in the non-equilibrium regime. For both the cases we found significantly distinguishable non-chaotic, but random behaviour in the OTO auto-correlations, which was not pointed before in this type of studies. Finally, we have also demonstrated the classical limiting behaviour of the mentioned two types of auto-correlated OTOC functions from the thermally weighted phase space averaged Poisson Brackets, which we found exactly matches with the large time limiting behaviour of the auto-correlations in the super-horizon regime of the cosmological scalar mode fluctuation.

We prove a version of Ekeland Variational Principle (EkVP) in a weighted graph $G$ and its equivalence to Caristi fixed point theorem and to Takahashi minimization principle. The usual completeness and topological notions are replaced with some weaker versions expressed in terms of the graph $G$. The main tool used in the proof is the OSC property for sequences in a graph. Converse results, meaning the completeness of graphs for which one of these principles holds is also considered.