Boyd-Wong type contractions in generalized parametric bipolar metric space.

In this manuscript, we introduce a new notion of generalized parametric bipolar metric space as a generalization of generalized parametric space and bipolar metric space. We also introduce Boyd-Wong type contractions for covariant and contravariant mappings to prove the fixed point results in the newly defined space. Some examples are also provided to illustrate the main results. Some corollaries are given of our results which shows the existence of fixed point for Banach type covariant and contravariant contractions. We solve integral and fractional differential equations with the help of proved results.

Exploring dynamics of plant-herbivore interactions: bifurcation analysis and chaos control with Holling type-II functional response.

In this study, we examine the plant-herbivore discrete model of apple twig borer and grape vine interaction, with a particular emphasis on the extended weak-predator response to Holling type-II response. We explore the dynamical and qualitative analysis of this model and investigate the conditions for stability and bifurcation. Our study demonstrates the presence of the Neimark-Sacker bifurcation at the interior equilibrium and the transcritical bifurcation at the trivial equilibrium, both of which have biological feasibility. To avoid unpredictable outcomes due to bifurcation, we employ chaos control methods. Furthermore, to support our theoretical and mathematical findings, we develop numerical simulation techniques with examples. In summary, our research enhances the comprehension of the dynamics pertaining to interactions between plants and herbivores in the context of discrete-time population models.

Nitrogen dioxide as proxy indicator of air pollution from fossil fuel burning in New Delhi during lockdown phases of COVID-19 pandemic period: impact on weather as revealed by Sentinel-5 precursor (5p) spectrometer sensor.

There has been a long-lasting impact of the lockdown imposed due to COVID-19 on several fronts. One such front is climate which has seen several implications. The consequences of climate change owing to this lockdown need to be explored taking into consideration various climatic indicators. Further impact on a local and global level would help the policymakers in drafting effective rules for handling challenges of climate change. For in-depth understanding, a temporal study is being conducted in a phased manner in the New Delhi region taking NO2 concentration and utilizing statistical methods to elaborate the quality of air during the lockdown and compared with a pre-lockdown period. In situ mean values of the NO2 concentration were taken for four different dates, viz. 4th February, 4th March, 4th April, and 25th April 2020. These concentrations were then compared with the Sentinel (5p) data across 36 locations in New Delhi which are found to be promising. The results indicated that the air quality has been improved maximum in Eastern Delhi and the NO2 concentrations were reduced by one-fourth than the pre-lockdown period, and thus, reduced activities due to lockdown have had a significant impact. The result also indicates the preciseness of Sentinel (5p) for NO2 concentrations.

An Intelligent Platform for Software Component Mining and Retrieval.

The development of robotic applications necessitates the availability of useful, adaptable, and accessible programming frameworks. Robotic, IoT, and sensor-based systems open up new possibilities for the development of innovative applications, taking advantage of existing and new technologies. Despite much progress, the development of these applications remains a complex, time-consuming, and demanding activity. Development of these applications requires wide utilization of software components. In this paper, we propose a platform that efficiently searches and recommends code components for reuse. To locate and rank the source code snippets, our approach uses a machine learning approach to train the schema. Our platform uses trained schema to rank code snippets in the top k results. This platform facilitates the process of reuse by recommending suitable components for a given query. The platform provides a user-friendly interface where developers can enter queries (specifications) for code search. The evaluation shows that our platform effectively ranks the source code snippets and outperforms existing baselines. A survey is also conducted to affirm the viability of the proposed methodology.

A Comparison Study of Predator-Prey Model in Deterministic and Stochastic Environments with the Impacts of Fear and Habitat Complexity.

In theoretical ecology, recent field experiments on terrestrial vertebrates observe that the predator-prey interaction can not only be curtailed by direct consumption but also governed by some indirect effects such as the fear of predator which may reduce the reproduction rate of prey individuals. Based on this fact, we have developed and explored the predator-prey interaction with the influence of both cost and benefit of fear effect (felt by prey). A Holling type III functional response with the effect of habitat complexity has been taken to consume the prey biomass. Positivity and boundedness of the studied system prove that the model is well-behaved. The uniform persistence of the studied system is derived analytically under some parametric restrictions. The feasibility conditions and stability criteria of each equilibrium points have been discussed. Next, we have exhibited the existence of Hopf-bifurcation around the interior equilibrium point. Our mathematical analyses show that habitat complexity and fear effect both have a great impact on the persistence of the predator biomass. Furthermore, we have investigated the effect of breeding delay parameter such that the system loses its stability behaviour and enters into a limit cycle oscillations through Hopf-bifurcation. Numerical simulations are illustrated to verify our analytical outcomes. Numerically, we have perturbed the death rates of prey and predator species with Gaussian white noise terms due to the effects of environmental fluctuations.

A Dynamically Consistent Nonstandard Difference Scheme for a Discrete-Time Immunogenic Tumors Model.

This manuscript deals with the qualitative study of certain properties of an immunogenic tumors model. Mainly, we obtain a dynamically consistent discrete-time immunogenic tumors model using a nonstandard difference scheme. The existence of fixed points and their stability are discussed. It is shown that a continuous system experiences Hopf bifurcation at one and only one positive fixed point, whereas its discrete-time counterpart experiences Neimark-Sacker bifurcation at one and only one positive fixed point. It is shown that there is no chance of period-doubling bifurcation in our discrete-time system. Additionally, numerical simulations are carried out in support of our theoretical discussion.

Entropy generation from convective-radiative moving exponential porous fins with variable thermal conductivity and internal heat generations.

The performance and thermal properties of convective-radiative rectangular and moving exponential porous fins with variable thermal conductivity together with internal heat generation are investigated. The second law of thermodynamics is used to investigate entropy generation in the proposed fins. The model is numerically solved using shooting technique. It is observed that the entropy generation depends on porosity parameter, temperature ratio, temperature distribution, thermal conductivity and fins structure. It is noted that entropy generation for a decay exponential fin is higher than that of a rectangular fin which is greater than that of a growing exponential fin. Moreover, entropy generation decreases as thermal conductivity increases. The results also reveal that entropy generation is maximum at the fin's base and the average entropy production depends on porosity parameters and temperature ratio. It is further reveal that the temperature ratio has a smaller amount of influence on entropy as compared to porosity parameter. It is concluded that when the temperature ratio is increases from 1.1 to 1.9, the entropy generation number is also increase by [Formula: see text] approximately. However, increasing porosity from 1 to 80 gives 14-fold increase in average entropy generation.

On the Supervision of a Saturated SIR Epidemic Model with Four Joint Control Actions for a Drastic Reduction in the Infection and the Susceptibility through Time.

This paper presents and studies a new epidemic SIR (Susceptible-Infectious-Recovered) model with susceptible recruitment and eventual joint vaccination efforts for both newborn and susceptible individuals. Furthermore, saturation effects in the infection incidence terms are eventually assumed for both the infectious and the susceptible subpopulations. The vaccination action on newborn individuals is assumed to be applied to a fraction of them while that on the susceptible general population is of linear feedback type reinforced with impulsive vaccination actions (in practice, very strong and massive vaccination controls) at certain time points, based on information on the current levels of the susceptible subpopulation. Apart from the above vaccination controls, it is also assumed that the average of contagion contacts can be controlled via intervention measures, such as confinements or isolation measures, social distance rules, use of masks, mobility constraints, etc. The main objectives of the paper are the achievement of a strictly decreasing infection for all time periods and that of the susceptible individuals over the initial period if they exceed the disease-free equilibrium value. The monitoring mechanism is the combined activation of intervention measures to reduce the contagion contacts together with the impulsive vaccination to reduce susceptibility. The susceptibility and recovery levels of the disease-free equilibrium point are suitably prefixed by the design of the regular feedback vaccination on the susceptible subpopulation.

Model-based ensembles: Lessons learned from retrospective analysis of COVID-19 infection forecasts across 10 countries.

Mathematical models of different types and data intensities are highly used by researchers, epidemiologists, and national authorities to explore the inherently unpredictable progression of COVID-19, including the effects of different non-pharmaceutical interventions. Regardless of model complexity, forecasts of future COVID-19 infections, deaths and hospitalization are associated with large uncertainties, and critically depend on the quality of the training data, and in particular how well the recorded national or regional numbers of infections, deaths and recoveries reflect the the actual situation. In turn, this depends on, e.g., local test and abatement strategies, treatment capacities and available technologies. Other influencing factors including temperature and humidity, which are suggested by several authors to affect the spread of COVID-19 in some countries, are generally only considered by the most complex models and further serve to inflate the uncertainty. Here we use comparative and retrospective analyses to illuminate the aggregated effect of these systematic biases on ensemble-based model forecasts. We compare the actual progression of active infections across ten of the most affected countries in the world until late November 2020 with "re-forecasts" produced by two of the most commonly used model types: (i) a compartment-type, susceptible-infected-removed (SIR) model; and (ii) a statistical (Holt-Winters) time series model. We specifically examine the sensitivity of the model parameters, estimated systematically from different subsets of the data and thereby different time windows, to illustrate the associated implications for short- to medium-term forecasting and for probabilistic projections based on (single) model ensembles as inspired by, e.g., weather forecasting and climate research. Our findings portray considerable variations in forecasting skill in between the ten countries and demonstrate that individual model predictions are highly sensitive to parameter assumptions. Significant skill is generally only confirmed for short-term forecasts (up to a few weeks) with some variation across locations and periods.

Qualitative analysis of a discrete-time phytoplankton-zooplankton model with Holling type-II response and toxicity.

The interaction among phytoplankton and zooplankton is one of the most important processes in ecology. Discrete-time mathematical models are commonly used for describing the dynamical properties of phytoplankton and zooplankton interaction with nonoverlapping generations. In such type of generations a new age group swaps the older group after regular intervals of time. Keeping in observation the dynamical reliability for continuous-time mathematical models, we convert a continuous-time phytoplankton-zooplankton model into its discrete-time counterpart by applying a dynamically consistent nonstandard difference scheme. Moreover, we discuss boundedness conditions for every solution and prove the existence of a unique positive equilibrium point. We discuss the local stability of obtained system about all its equilibrium points and show the existence of Neimark-Sacker bifurcation about unique positive equilibrium under some mathematical conditions. To control the Neimark-Sacker bifurcation, we apply a generalized hybrid control technique. For explanation of our theoretical results and to compare the dynamics of obtained discrete-time model with its continuous counterpart, we provide some motivating numerical examples. Moreover, from numerical study we can see that the obtained system and its continuous-time counterpart are stable for the same values of parameters, and they are unstable for the same parametric values. Hence the dynamical consistency of our obtained system can be seen from numerical study. Finally, we compare the modified hybrid method with old hybrid method at the end of the paper.

Highlighting the compound risk of COVID-19 and environmental pollutants using geospatial technology.

The new COVID-19 coronavirus disease has emerged as a global threat and not just to human health but also the global economy. Due to the pandemic, most countries affected have therefore imposed periods of full or partial lockdowns to restrict community transmission. This has had the welcome but unexpected side effect that existing levels of atmospheric pollutants, particularly in cities, have temporarily declined. As found by several authors, air quality can inherently exacerbate the risks linked to respiratory diseases, including COVID-19. In this study, we explore patterns of air pollution for ten of the most affected countries in the world, in the context of the 2020 development of the COVID-19 pandemic. We find that the concentrations of some of the principal atmospheric pollutants were temporarily reduced during the extensive lockdowns in the spring. Secondly, we show that the seasonality of the atmospheric pollutants is not significantly affected by these temporary changes, indicating that observed variations in COVID-19 conditions are likely to be linked to air quality. On this background, we confirm that air pollution may be a good predictor for the local and national severity of COVID-19 infections.

On a Discrete SEIR Epidemic Model with Two-Doses Delayed Feedback Vaccination Control on the Susceptible.

A new discrete susceptible-exposed-infectious-recovered (SEIR) epidemic model is presented subject to a feedback vaccination effort involving two doses. Both vaccination doses, which are subject to a non-necessarily identical effectiveness, are administrated by respecting a certain mutual delay interval, and their immunity effect is registered after a certain delay since the second dose. The delays and the efficacies of the doses are parameters, which can be fixed in the model for each concrete experimentation. The disease-free equilibrium point is characterized as well as its stability properties, while it is seen that no endemic equilibrium point exists. The exposed subpopulation is supposed to be infective eventually, under a distinct transmission rate of that of the infectious subpopulation. Some simulation examples are presented by using disease parameterizations of the COVID-19 pandemic under vaccination efforts requiring two doses.

A Modelization of the Propagation of COVID-19 in Regions of Spain and Italy with Evaluation of the Transmission Rates Related to the Intervention Measures.

Two discrete mathematical SIR models (Susceptible-Infectious-Recovered) are proposed for modelling the propagation of the SARS-CoV-2 (COVID-19) through Spain and Italy. One of the proposed models is delay-free while the other one considers a delay in the propagation of the infection. The objective is to estimate the transmission, also known as infectivity rate, through time taking into account the infection evolution data supplied by the official health care systems in both countries. Such a parameter is estimated through time at different regional levels and it is seen to be strongly dependent on the intervention measures such as the total (except essential activities) or partial levels of lockdown. Typically, the infectivity rate evolves towards a minimum value under total lockdown and it increases again when the confinement measures are partially or totally removed.

On the Entropy of Events under Eventually Global Inflated or Deflated Probability Constraints. Application to the Supervision of Epidemic Models under Vaccination Controls.

This paper extends the formulation of the Shannon entropy under probabilistic uncertainties which are basically established in terms or relative errors related to the theoretical nominal set of events. Those uncertainties can eventually translate into globally inflated or deflated probabilistic constraints. In the first case, the global probability of all the events exceeds unity while in the second one lies below unity. A simple interpretation is that the whole set of events losses completeness and that some events of negative probability might be incorporated to keep the completeness of an extended set of events. The proposed formalism is flexible enough to evaluate the need to introduce compensatory probability events or not depending on each particular application. In particular, such a design flexibility is emphasized through an application which is given related to epidemic models under vaccination and treatment controls. Switching rules are proposed to choose through time the active model, among a predefined set of models organized in a parallel structure, which better describes the registered epidemic evolution data. The supervisory monitoring is performed in the sense that the tested accumulated entropy of the absolute error of the model versus the observed data is minimized at each supervision time-interval occurring in-between each two consecutive switching time instants. The active model generates the (vaccination/treatment) controls to be injected to the monitored population. In this application, it is not proposed to introduce a compensatory event to complete the global probability to unity but instead, the estimated probabilities are re-adjusted to design the control gains.

On the Use of Entropy Issues to Evaluate and Control the Transients in Some Epidemic Models.

This paper studies the representation of a general epidemic model by means of a first-order differential equation with a time-varying log-normal type coefficient. Then the generalization of the first-order differential system to epidemic models with more subpopulations is focused on by introducing the inter-subpopulations dynamics couplings and the control interventions information through the mentioned time-varying coefficient which drives the basic differential equation model. It is considered a relevant tool the control intervention of the infection along its transient to fight more efficiently against a potential initial exploding transmission. The study is based on the fact that the disease-free and endemic equilibrium points and their stability properties depend on the concrete parameterization while they admit a certain design monitoring by the choice of the control and treatment gains and the use of feedback information in the corresponding control interventions. Therefore, special attention is paid to the evolution transients of the infection curve, rather than to the equilibrium points, in terms of the time instants of its first relative maximum towards its previous inflection time instant. Such relevant time instants are evaluated via the calculation of an "ad hoc" Shannon's entropy. Analytical and numerical examples are included in the study in order to evaluate the study and its conclusions.

Some fixed point theorems for mappings satisfying rational inequality in modular metric spaces with applications.

We prove some theorems on the existence and uniqueness of fixed point for Reich-type contraction mappings and Geraghty-type mappings satisfying rational inequalities in modular metric spaces. Our results include the results of [1] and [2] as special cases. Furthermore, we apply our main results in proving the existence and uniqueness of solution of nonlinear Barbashin-type integrodifferential equation satisfying a given initial value problem in modular metric space X ω .

ANN-Based Airflow Control for an Oscillating Water Column Using Surface Elevation Measurements.

Oscillating water column (OWC) plants face power generation limitations due to the stalling phenomenon. This behavior can be avoided by an airflow control strategy that can anticipate the incoming peak waves and reduce its airflow velocity within the turbine duct. In this sense, this work aims to use the power of artificial neural networks (ANN) to recognize the different incoming waves in order to distinguish the strong waves that provoke the stalling behavior and generate a suitable airflow speed reference for the airflow control scheme. The ANN is, therefore, trained using real surface elevation measurements of the waves. The ANN-based airflow control will control an air valve in the capture chamber to adjust the airflow speed as required. A comparative study has been carried out to compare the ANN-based airflow control to the uncontrolled OWC system in different sea conditions. Also, another study has been carried out using real measured wave input data and generated power of the NEREIDA wave power plant. Results show the effectiveness of the proposed ANN airflow control against the uncontrolled case ensuring power generation improvement.

Short-Term Statistical Forecasts of COVID-19 Infections in India.

COVID-19 cases in India have been steadily increasing since January 30, 2020 and have led to a government-imposed lockdown across the country to curtail community transmission with significant impacts on societal systems. Forecasts using mathematical-epidemiological models have played and continue to play an important role in assessing the probability of COVID-19 infection under specific conditions and are urgently needed to prepare health systems for coping with this pandemic. In many instances, however, access to dedicated and updated information, in particular at regional administrative levels, is surprisingly scarce considering its evident importance and provides a hindrance for the implementation of sustainable coping strategies. Here we demonstrate the performance of an easily transferable statistical model based on the classic Holt-Winters method as means of providing COVID-19 forecasts for India at different administrative levels. Based on daily time series of accumulated infections, active infections and deaths, we use our statistical model to provide 48-days forecasts (28 September to 15 November 2020) of these quantities in India, assuming little or no change in national coping strategies. Using these results alongside a complementary SIR model, we find that one-third of the Indian population could eventually be infected by COVID-19, and that a complete recovery from COVID-19 will happen only after an estimated 450 days from January 2020. Further, our SIR model suggests that the pandemic is likely to peak in India during the first week of November 2020.

On the Design of Hyperstable Feedback Controllers for a Class of Parameterized Nonlinearities. Two Application Examples for Controlling Epidemic Models.

This paper studies the hyperstability and the asymptotic hyperstability of a single-input single-output controlled dynamic system whose feed-forward input-output dynamics is nonlinear and eventually time-varying consisting of a linear nominal part, a linear incremental perturbed part and a nonlinear and eventually time-varying one. The nominal linear part is described by a positive real transfer function while the linear perturbation is defined by a stable transfer function. The nonlinear and time-varying disturbance is, in general, unstructured but it is upper-bounded by the combination of three additive absolute terms depending on the input, output and input-output product, respectively. The non-linear time-varying feedback controller is any member belonging to a general class which satisfies an integral Popov's-type inequality. This problem statement allows the study of the conditions guaranteeing the robust stability properties under a variety of the controllers designed for the controlled system and controller disturbances. In this way, set of robust hyperstability and asymptotic hyperstability of the closed-loop system are given based on the fact that the input-output energy of the feed-forward controlled system is positive and bounded for all time and any given initial conditions and controls satisfying Popov's inequality. The importance of those hyperstability and asymptotic hyperstability properties rely on the fact that they are related to global closed-loop stability, or respectively, global closed-loop asymptotic stability of the same uncontrolled feed-forward dynamics subject to a great number of controllers under the only condition that that they satisfy such a Popov's-type inequality. It is well-known the relevance of vaccination and treatment controls for Public Health Management at the levels of prevention and healing. Therefore, two application examples concerning the linearization of known epidemic models and their appropriate vaccination and/or treatment controls on the susceptible and infectious, respectively, are discussed in detail with the main objective in mind of being able of achieving a fast convergence of the state- trajectory solutions to the disease- free equilibrium points under a wide class of control laws under deviations of the equilibrium amounts of such populations.

An equivalent condition to the Jensen inequality for the generalized Sugeno integral.

For the classical Jensen inequality of convex functions, i.e., [Formula: see text] an equivalent condition is proved in the framework of the generalized Sugeno integral. Also, the necessary and sufficient conditions for the validity of the discrete form of the Jensen inequality for the generalized Sugeno integral are given.