General Scenario Research Articles

EHPE: Skeleton Cues-Based Gaussian Coordinate Encoding for Efficient Human Pose Estimation

Human pose estimation (HPE) has many wide applications such as multimedia processing, behavior understanding and human-computer interaction. Most previous studies have encountered many constraints, such as restricted scenarios and RGB inputs. To mitigate constraints to estimating the human poses in general scenarios, we present an efficient human pose estimation model (i.e., EHPE) with joint direction cues and Gaussian coordinate encoding. Specifically, we propose an anisotropic Gaussian coordinate coding method to describe the skeleton direction cues among adjacent keypoints. To the best of our knowledge, this is the first time that the skeleton direction cues is introduced to the heatmap encoding in HPE task. Then, a multi-loss function is proposed to constrain the output to prevent the overfitting. The Kullback-Leibler divergence is introduced to measure the predication label and its ground truth one. The performance of EHPE is evaluated on two HPE datasets: MS COCO and MPII. Experimental results demonstrate that EHPE can obtain robust results, and it significantly outperforms existing state-of-the-art HPE methods. Lastly, we extend the experiments on infrared images captured by our research group. The experiments achieved the impressive results regardless of insufficient color and texture information.

A quantum fluctuation description of charge qubits

We consider a specific instance of a superconducting circuit, the so-called charge-qubit, consisting of a capacitor and a Josephson junction that we describe by means of the BCS microscopic model in terms of two tunnelling superconducting systems in the strong-coupling quasi-spin formulation. Then, by means of collective observables we derive the Hamiltonian governing the quantum behaviour of the circuit in the limit of a large number N of quasi-spins. Our approach relies on suitable quantum fluctuations, i.e. on collective quasi-spin operators, different from mean-field observables, that retain a quantum character in the large-N limit. These collective operators generate the Heisenberg algebra on the circle and we show that their dynamics reproduces the phenomenological one generated by the charge qubit Hamiltonian obtained by quantizing the macroscopic classical Hamiltonian of the circuit. The microscopic derivation of the emergent, large-N behaviour provides a rigorous setting to investigate more in detail both general quantum circuits and quantum macroscopic scenarios; in particular, in the specific case of charge-qubits, it allows to explicitly obtain the temperature dependence of the critical Josephson current in the strong coupling regime, a result not accessible using standard approximation techniques.

C-ITS Services in Urban Environments: European State of Practice

This paper addresses the state of practice of C-ITS implementation in several cities throughout Europe, and it was carried out under the scope of the C-Roads Platforms. Its goal is to produce an overview of the general scenario of C-ITS development across European urban environments, aiming to better understand the challenges, technological preferences and policy strategies during C-ITS urban deployment. With that purpose, 27 cities were sought through a questionnaire to provide information regarding several aspects, such as city identification and characterization, specifications followed, communication plans and stage of development. In addition to that, the cities were asked to assess the importance and expectations concerning the benefits that would come from the implementation of the C-ITS policies. Results showed that the cities are strongly diverse in terms of road network design, and technological infrastructure and, consequently, experience different policy goals and C-ITS stages of maturity. The outcomes from this paper may support further research studies concerning the strategy behind C-ITS urban deployment and its relation to the city policy goals as well as the benefits of C-ITS systems.

Phoresis kernel theory for passive and active spheres with nonuniform phoretic mobility.

By introducing geometry-based phoresis kernels, we establish a direct connection between the translational and rotational velocities of a phoretic sphere and the distributions of the driving fields or fluxes. The kernels quantify the local contribution of the field or flux to the particle dynamics. The field kernels for both passive and active particles share the same functional form, depending on the position-dependent surface phoretic mobility. For uniform phoretic mobility, the translational field kernel is proportional to the surface normal vector, while the rotational field kernel is zero; thus, a phoretic sphere with uniform phoretic mobility does not rotate. As case studies, we discuss examples of a self-phoretic axisymmetric particle influenced by a globally-driven field gradient, a general scenario for axisymmetric self-phoretic particle and two of its special cases, and a non-axisymmetric active particle.

Evolution of a large Quaternary monogenetic field; the multifaceted volcanism of the Serdán-oriental basin, México

The intermontane Serdán-Oriental basin (SOB), located in the Trans-Mexican Volcanic Belt, records a highly contrasting volcanic field with nearly 166 monogenetic volcanoes, including cones, maars, tuff rings, domes, and lava flows, with basaltic to rhyolitic compositions and from effusive to explosive, and magmatic to phreatomagmatic eruptive styles. Even when this volcanic field has been the focus of several volcanological studies, an evolutive model of its volcanism and its implications has not been reported. This is a geological study of SOB volcanism based on the spatio-temporal evolution and characteristics of its volcanoes. For this, new and published data is integrated, including chronostratigraphic, geochemical, and petrological observations, which were further processed and analyzed by GIS tools. The resulting model indicates that volcanism has been continuous from the middle Pleistocene to the Holocene. Based on parameters such as erupted magma chemistry and volcanic landforms, it can be classified into the following volcanic groups: Group 1 is mafic in composition, forming cones and lava flows during the middle Pleistocene (490 to 190 ka). Group 2 comprises predominantly andesitic volcanism characterized by cones and dome clusters erupted during the middle Pleistocene (250 to 200 ka), partially coeval with Group 1. Group 3 is characterized by rhyolitic volcanism associated with the emplacement of domes in the central part of the SOB during the middle to upper Pleistocene (220 to 24.5 ka). Group 4 includes a predominantly basaltic to andesitic volcanism with minor rhyolitic composition, with a characteristic occurrence of phreatomagmatic and magmatic activity, forming maars and tuff rings, scoria cones, and lava flows during the middle Holocene (12.2 to 6.25 ka). The youngest Group occurs in the upper Holocene (<7.5 ka), and it is marked by mafic volcanism in the form of cones and lava flows, as well as by the emplacement of the voluminous Las Derrumbadas rhyolitic twin domes. Overall, the geochemical data shows a bimodal compositional character with a gap of dacitic magmas, compatible with a general scenario dominated by felsic melt extraction from highly crystalline magma reservoirs. Eruptive rate calculations indicate a general increase with time, which goes from <0.18 km3/ky in the first three groups to 1 and 2.9 km3/ky in groups 4 and 5, respectively. Lastly, density maps and lineaments of the eruptive vents, together with crater elongations, allowed the identification of the spatial trends of the SOB volcanism and a comparison with the existing regional major tectonic structures characterizing the local basement. These findings are relevant to understanding the eruptive nature of this active volcanic field and its highly contrasting and multifaceted volcanism.

Non-relativistic quantum dynamics in Born–Infeld gravity inspired by Eddington spacetime global monopole

In this work, we investigate the quantum dynamics of non-relativistic systems in a Born–Infeld spacetime. We analyze some general scenarios, which concerns the effects of a harmonic oscillator and an inverse square-type potential as well as an Aharonov–Bohm geometric phase. We obtain an analytical solution for the most general case in terms of a confluent Heun function and define the energy spectrum by referring to the ground state, together with its respective eigenfunction. A graphical representation was built so that it was possible to visualize some of the possible energy configurations. For negative values of the Born–Infeld parameter [Formula: see text], we perform a connection with results of quantum dynamics already investigated in the literature for the Ellis–Bronnikov spacetime.

Long-Term Opinion Distributions of an Opinion Formation Model with Averaging Behavior

&#x0D; &#x0D; &#x0D; Sociophysics utilizes mathematical tools from physics to study social phenomena. In particular, interactions between individuals can impact emerging trends in the opinions of a population as a whole. This research focuses on the long-term opinion distributions of a population of individuals who can influence one another through pairwise interactions, where one individual modifies their opinion to be more in line with their neighbor. Interactions are governed by a social network, where friends on the network interact while strangers do not. We introduce a new model for opinion formation with averaging behavior where the opinion of an individual at any time t is an integer between −k and k. For example, an opinion of k could indicate a heavily republican opinion and −k a heavily democratic opinion. As the process evolves in time, interactions between neighbors x and y in the social network result in person x updating her opinion to be one step closer to the opinion of person y. We first consider the scenario where everyone in the social network is friends with everyone else. For k = 1 we compute explicitly the long-term opinion distribution via differential equations. For values of k &gt; 1, we solve for the long-term distribution numerically using Runge-Kutta. We then compute the long-term opinion distribution via simulation, in the more general social network scenario.&#x0D; &#x0D; &#x0D;

Solving NP-Hard Challenges in Logistics and Transportation under General Uncertainty Scenarios Using Fuzzy Simheuristics

In the field of logistics and transportation (L&amp;T), this paper reviews the utilization of simheuristic algorithms to address NP-hard optimization problems under stochastic uncertainty. Then, the paper explores an extension of the simheuristics concept by introducing a fuzzy layer to tackle complex optimization problems involving both stochastic and fuzzy uncertainties. The hybrid approach combines simulation, metaheuristics, and fuzzy logic, offering a feasible methodology to solve large-scale NP-hard problems under general uncertainty scenarios. These scenarios are commonly encountered in L&amp;T optimization challenges, such as the vehicle routing problem or the team orienteering problem, among many others. The proposed methodology allows for modeling various problem components—including travel times, service times, customers’ demands, or the duration of electric batteries—as deterministic, stochastic, or fuzzy items. A cross-problem analysis of several computational experiments is conducted to validate the effectiveness of the fuzzy simheuristic methodology. Being a flexible methodology that allows us to tackle NP-hard challenges under general uncertainty scenarios, fuzzy simheuristics can also be applied in fields other than L&amp;T.

Einstein material balance and modeling of the flow of compressible fluid near the boundary

We consider sewing machinery between nite difference and analytical solutions de ned at different scales: far away and near the source of the perturbation of the flow. One of the essences of the approach is that the coarse problem and the boundary-value problem in the proxy of the source model two different flows. In his remarkable paper, Peaceman proposes a framework for dealing with solutions de ned on different scales for linear time independent problems by introducing the famous Peaceman well block radius. In this article, we consider a novel problem: how to solve this issue for transient flow generated by the compressibility of the fluid. We are proposing a method to glue solution via total fluxes, which are prede ned on coarse grid, and changes in pressure, due to compressibility, in the block containing production (injection) well. It is important to mention that the coarse solution “does not see” the boundary. From an industrial point of view, our report provides a mathematical tool for the analytical interpretation of simulated data for compressible fluid flow around a well in a porous medium. It can be considered a mathematical “shirt” on the Peaceman well-block radius formula for linear (Darcy) transient flow but can be applied in much more general scenarios. In the article, we use the Einstein approach to derive the material balance equation, a key instrument to de ne R0. We will expand the Einstein approach for three regimes of Darcy and non-Darcy flows for compressible fluids (time-dependent): 1. stationary; 2. pseudostationary; 3. boundary dominated. Note that in all known authors literature, the rate of production on the well is time-independent.

Finite-size effect on quantum percolation in topological insulators

We study the finite-size effect on quantum percolation in two-dimensional topological insulators. We demonstrate that the percolation threshold in topological insulators strongly depends on the localization length of the edge states in small clusters due to the finite-size effect. Also, we explain why the percolation threshold in the corresponding classical model determines the lower bound of the quantum percolation threshold in topological insulators. In addition, we extend the percolation model to a more general scenario, where the system is composed of both topological and trivial clusters. We find that the quantum percolation threshold can be less than the classical percolation threshold due to quantum tunneling of the edge states.

Patterns and Actors of Disinformation: Analysis of Debunked Hoaxes in Spain in 2022

This research examines the patterns followed by disinformation in Spain through the fact-checking activities of Maldita.es, the leading fact-checking organisation in Spain. We sought to answer three research questions: 1. What are the predominant topics of the hoaxes debunked by Maldita.es? 2. Who is responsible for the creation and dissemination of these hoaxes? and 3. In what formats and platforms are these hoaxes generally distributed? For this purpose, we conducted a quantitative content analysis of 729 hoaxes fact-checked in 2022 by Maldito Bulo. 40.7% of the debunked hoaxes were related to social issues, while 37.2% focused on political affairs. Regarding those responsible for the creation and dissemination, most of the hoaxes came from unidentified sources, although when the identity is known, the most frequent contributors are social media accounts, alternative and partisan pseudo-media and journalists. These results explore the general disinformation scenario in Spain, using fact-checking as an approximation and discussing its implications.

Production logistics digital twins: Research profiling, application, challenges and opportunities

In the era of Industry 4.0, Production Logistic Digital Twins (PLDTs) have garnered remarkable attention from both academic and industrial communities. This is evident from the growing number of research publications on PLDTs in international scientific journals and conferences. However, given the diversity and complexity of production logistics activities, there is a pressing need for systematic literature review to chart past research and identify potential directions for future endeavors. Therefore, this study primarily focuses on the application of Digital Twins (DTs) in Production Logistics (PL). Firstly, an analysis of PLDTs research profiling is carried out based on general trends, keywords, application scenarios, and basic functions. Secondly, the functional characteristics of PLDTs are examined while summarizing their advantages and limitations across various application scenarios such as transportation, packaging, warehousing, material distribution, and information processing. And the roles played by smart technologies such as Internet of Things (IoT) in PLDTs system are discussed. Finally, possible challenges and future directions of PLDTs in industrial application are presented, accompanied by appropriate classification and extensive recommendations.

Празднование Нового года в Византии

Introduction. Many cultures consider the first day of the new year a holiday which supposes the performance of specific rituals and rites. The traditions of New Year celebrations reflect the nature of this or that civilization, its historical experience, and religious and world-viewing constants. The said is to the full extent actual for the Byzantine civilization. The purpose of the work is to reconstruct the general scenario of official celebrations, to trace its evolution, and to analyse the folk tradition related to it. Methods and materials. The main sources of the given research are liturgical books, treatises on ceremonies, and epistolography. Analysis. In Byzantium, the New Year was celebrated on September 1 at different levels: church, state, and public. Despite its origin from the laity, the Byzantines viewed this holiday primarily as religious as it opened both the new year cycle and the church calendar. By the tenth century, there developed the order of service (akolouthia) for the first day of the new year. The patriarch served special liturgies in St Sophia’s Church and performed a crucession. The emperor was not allowed to participate in the church rituals. In Late Byzantium, the climax of the New Year ritual was the public prayer made in the imperial capital, in the Forum of Constantine, in the presence of the emperor. The ceremonial protocol documented that the ruler must participate in the New Year service. The ordinary people of Byzantium widely celebrated this holiday, spending this day in going to church, paying visits, and exchanging greetings. Conclusions. The enlarging of the programme of palatial ceremonies with the emperor’s appearance in the New Year celebration shows, from the one hand, the strengthening of the secular component of the holiday and, on the other hand, the trend to sacralization of the palatial life. The comparison of the scenario of the New Year celebration that existed in the Age of the Palaiologoi with the official holiday on such a case in the pre-Petrine Russia shows an important Byzantine influence on Russian culture of celebration and church policy.

Artificial intelligence in the service of health and safety at work: Perspectives and challenges from now to 2035 - A prospective study

Artificial intelligence systems are developing very rapidly in all areas. This is particularly true in the case of work, where we are seeing their use in the robotisation of industrial production or the automation of certain functions in services (from chatbots to robotic process automation). In the context of a prospective study devoted to the use of artificial intelligence for occupational risk prevention, a very diverse project group was set up: occupational health practitioners, artificial intelligence specialists, lawyers, futurists, sociologists, and everyday users of artificial intelligence techniques. Using the method of contrasting scenarios, this project group successively documented variables likely to influence the use of artificial intelligence in the service of occupational health and safety, put forward hypotheses on their possible development over the next ten to fifteen years, and constructed scenarios. These relatively general scenarios were then adapted specifically to the subject studied, in particular during seminars devoted to specific uses (possible uses of artificial intelligence tools in epidemiology and accidentology, technologies for securing working environments using artificial intelligence, advanced robotics using artificial intelligence). Based on all the material produced during the study, the study finally resulted in recommendations of the project group on the use of AI in occupational risk prevention proposed for discussion. The subject is indeed of interest to the whole community of practitioners involved in occupational risk prevention whose practices will certainly be affected by these new technological developments.

Live streaming selling strategies of online retailers with spillover effects

This paper investigates online retailers’ optimal strategies in a highly competitive market where they distribute products via regular selling or live streaming selling with spillover effects, and examines the impacts of these strategies on consumer surplus (CS) and social welfare (SW). Using analytical models, we first explore whether and when two competing online retailers to adopt the live streaming sales strategy in an online market with spillover effects. Furthermore, the implications of their optimal strategies on CS and SW are analyzed. Lastly, we relax our assumptions to consider some general scenarios: (1) When the two online retailers engage in sequential pricing, and (2) when some consumers are time-constrained. The main findings are as follows: (1) Online retailers should sometimes sell their products via live streaming, even though it is more likely to send a low quality signal to consumers. Although the positive spillover effects of other competitors’ live streams are strong, retailers may prefer their competitors to adopt the regular selling mode. (2) CS and SW would be significantly improved by the introduction of the live streaming mode when live streams can greatly enhance consumers’ quality beliefs and their spillover effects are relatively strong but not too strong. (3) Pricing sequences do not affect the optimal live streaming sales strategy, while the presence of time-constrained consumers makes online retailers less likely to sell through live streaming.

Analytical solution of the fractional neutron point kinetic equations using the Mittag-Leffler function

A new analytical solution of the fractional point kinetic equations is developed in the present work, which considers one group of delayed neutrons as well as a constant reactivity. One of the main novelties and theoretical contributions of the developed solution is that it does not require approximating the Inverse Laplace transform by numerical means, as other solutions do, and instead it is obtained analytically using the Green and the Mittag-Leffler functions. A set of algorithms and MATLAB codes are developed with the purpose to implement and compute the developed solution in an adequate way, which represents the major computational contribution. Numerical experiments show that the developed solution is very accurate solving short-time dynamics phenomena, being able to reproduce, in a precise way, data that is reported in literature. The development of the proposed analytic solution represents an important contribution to validate numerical methods that are currently used to solve the neutron fractional point kinetic equations. Program SummaryProgram Title: Mittag-Leffler FNPKECPC Library link to program files:https://doi.org/10.17632/v4kfhzw7sf.1Developer's repository link:https://github.com/Cruz-Lopez-Carlos-Antonio/Mittag-Leffler-FNPKE/tree/mainLicensing provisions: Creative Commons by 4.0Programming language: MATLAB (2021a) / Python 3Nature of problem:Fractional Neutron Point Kinetic Equations describe the neutron population in a nuclear reactor, considering the changes on transport and thermohydraulic properties of the system. For such task, a mass balance approach based on fractional and integral derivatives is used, which improves and generalizes the integer case that uses the classical definitions of these mathematical operators. From a physical point of view, this new approach takes into account memory and non-local effects that are omitted in the standard neutron diffusion theory and which are relevant in scenarios where the current neutron density undergoes strongly variations on time. From a mathematical point of view, using fractional derivatives leads to a new and more general type of differential equations of arbitrary order that requires different methods of solution and approximation, and which must include the integer approach as particular case. In such context, the development of analytical solutions is a fundamental problem because it provides a framework to carry out verifications of numerical methods, as well as an insight to perform theoretical comparisons with the classical model. The developed Mittag-Leffler FNPK codes analytically solve the Fractional Neutron Point Kinetic Equations defined in terms of the Caputo's derivatives and subject to classical initial conditions.Solution method:The developed codes are written in MATLAB and Python programming languages, and solve the mentioned fractional differential equation system using a power series expansion as well as the Laplace transform. Such solution considers a single group of precursors of delayed neutrons and it is expressed in terms of the 2-parameter Mittag-Leffler function, being accurately computed considering a small number of terms of the infinite sum. Unlike other approaches, in the present case it is not necessary to use a numerical procedure to find the inverse Laplace transform, because it is analytically found using the Green function. Even when the developed solution is found for a constant reactivity case, the Mittag-Leffler FNPKE codes can extended it to more general scenarios where the reactivity is a function of time or where it depends on the neutron density itself. In these cases, it is necessary to apply a subinterval methodology where the time is divided in small steps, assuming a constant reactivity in each of them. The smaller of the intervals, the more accurate the approximation. With the purpose to overcome the numerical issues related to the computation of the 2-parameter Mittag-Leffler function, the developed codes integrate the most advanced algorithm reported in literature, which is useful also to estimate the high-order derivatives of such function.Additional comments including restrictions and unusual features:The developed codes do not face issues related to arithmetical precision digits, as other solutions do, because it is not expressed in terms of high order polynomials and instead it is written as a linear combination of the Green function. Additionally, several steps can be precomputed without regard the neutron parameters and initial conditions, which represents an important advantage in terms of the computational time.

Coupon promotion and inventory strategies of a supplier considering an e-commerce platform's omnichannel coupons

Omnichannel coupons that are issued by an e-commerce platform and can be used either online or offline have been gaining popularity with the emergence of omnichannel retailing to provide consistent shopping experiences for consumers. This paper investigates the coupon promotion and inventory strategies of a supplier that operates the online-only, store, and BOPS channels considering a platform's omnichannel coupons in the post-pandemic era because consumers are more price-sensitive. The conditions for joint promotional activities where both parties issue coupons are explored. Newsvendor models under six strategies are constructed based on the combination of the two players' coupon promotion strategies to capture the aggregate demand uncertainty. Utilizing the game theory, the optimal decisions of the platform and the supplier are obtained under different strategies. The results indicate that the equilibrium outcome varies from online joint promotion to omnichannel joint promotion that the platform issues omnichannel coupons and the supplier distributes online coupons to only the platform offers omnichannel coupons with the increase in the supplier's loss from returns when consumers' valuation difference is relatively large in a general heterogeneous scenario. Moreover, compared to unilateral promotion, joint promotion allows consumers to receive deeper price discounts and reduces the costs of promotional entities. As the supplier's return loss expands, the platform tends to switch from offering traditional online coupons to issuing omnichannel coupons, resulting in an increase in store inventory.

Shock capturing for a high-order ALE discontinuous Galerkin method with applications to fluid flows in time-dependent domains

In recent decades, the arbitrary Lagrangian–Eulerian (ALE) approach has been one of the most popular choices to deal with the fluid flows having moving boundaries. The ALE finite volume (FV) method is well-known for its capability of shock capturing. Several ALE discontinuous Galerkin (DG) methods are developed to fully explore the advantages of high-order methods, especially in complex flows. The DG scheme is highly efficient and has high resolution in smooth parts of the flow while the FV scheme has advantage on the robustness against shocks. In this paper, we present a novel algorithm to combine both the ALE FV and ALE DG methods into one stable and efficient hybrid approach. The main challenge for a mixed ALE FV method and ALE DG method is to reduce the inconsistency between both discretizations. Of particular concern are the same mesh velocity distribution between DG and FV elements and a continuous mesh velocity at the coupling interfaces. Since the computational efficiency of the proposed algorithm is of major concern, performance aspects will be considered during the construction of the scheme. To investigate the accuracy of the new scheme, several benchmark test cases with prescribed movements are included. Afterwards, the algorithm is applied to more general and complex scenarios to show its ability to cope with complex setups. In our paper, the scheme is implemented into a loosely-coupled fluid–structure interaction (FSI) framework. With a shock-driven cylinder movement in a channel flow and a transonic flow-induced airfoil vibration, we demonstrate our method for FSI applications.

Fourier transformation for acoustic: Principle &amp; applications

A The Fourier transform has a wide range of applications in daily life, including physics, signal processing, acoustics etc. The topic of this article is to demonstrate the principle and applications of the Fourier transform in acoustics through theoretical derivation. The paper first derived the basic formula of the Fourier Transform and the related seven theorems. Then the paper detailed the research of Fourier Transform in underwater acoustic pulse signal detection technology. Finally, the application of Fourier Transform in the defect detection algorithm of MEMS acoustic films was detailed. According to the analysis, the paper demonstrated the primary application of Fourier Transform in underwater acoustic pulse signal detection and defect detection algorithm of MEMS acoustic film. Based on the evaluations, this study demonstrated the general application scenario of Fourier Transform and offered theoretical basis of its application in acoustic field, which promotes its developmental potential in the acoustic field. Overall, these results shed light on guiding further exploration of acoustic research.

Dynamics analysis of a diffusive SIRI epidemic system under logistic source and general incidence rate

This study presents and examines a diffusive SIRI epidemic model incorporating logistic source and a general incidence rate. Differing from existing works, the system incorporates two factors: the general incidence rate and the logistic source. We first consider the well-posedness of the system. Then, utilizing the construction of four Lyapunov functions, we thoroughly examine the global asymptotic stability of equilibria in both specific and general scenarios, assuming all coefficients remain constant. In addition, we establish the basic reproduction number, denoted as R0, and subsequently derive the correlation between R0 and the local basic reproduction number. Furthermore, we provide a detailed discussion of the persistence and extinction of the infective population. In particular, in the case where R0 equals one and certain assumptions are met, we demonstrate the global asymptotic stability of the disease-free equilibrium. Lastly, we substantiate the validity of our theoretical findings through the presentation of five illustrative examples.