A new class of polynomials investigates the numerical solution of the fractional pantograph delay ordinary differential equations. These polynomials are equipped with an auxiliary unknown parameter a, which is obtained using the collocation and least-squares methods. In this study, the numerical solution of the fractional pantograph delay differential equation is displayed in the truncated series form. The upper bound of the solution as well as the error analysis and the rate of convergence theorem are also investigated in this (...) study. In five examples, the numerical results of the present method have been compared with other methods. For the first time, a -polynomials are used in this study to numerically solve delay equations, and accurate approximations have been displayed. (shrink)

Experts often communicate probabilities verbally (e.g., unlikely) rather than numerically (e.g., 25% chance). Although criticism has focused on the vagueness of verbal probabilities, less attention has been given to the potential unintended, biasing effects of verbal probabilities in communicating probabilities to decision-makers. In four experiments (Ns = 201, 439, 435, 696), we showed that probability format (i.e., verbal vs. numeric) influenced participants’ inferences and decisions following a hypothetical financial expert’s forecast. We observed a format effect for low probability forecasts: verbal (...) probabilities were interpreted more pessimistically than numeric equivalents. We attributed the difference to directionality, a linguistic property that biases attention toward an outcome. In the high-probability conditions, the directionality of verbal and numeric probabilities aligned (both were positive), whereas they differed in the low-probability conditions (verbal probabilities were more negative). Participants inferred recommendations congruent with the communicated direction and these inferences mediated the effect of probability format on decisions. (shrink)

In this study, we implemented a new numerical method known as the Chebyshev Pseudospectral method for solving nonlinear delay differential equations having fractional order. The fractional derivative is defined in Caputo manner. The proposed method is simple, effective, and straightforward as compared to other numerical techniques. To check the validity and accuracy of the proposed method, some illustrative examples are solved by using the present scenario. The obtained results have confirmed the greater accuracy than the modified Laguerre wavelet (...) method, the Chebyshev wavelet method, and the modified wavelet-based algorithm. Moreover, based on the novelty and scientific importance, the present method can be extended to solve other nonlinear fractional-order delay differential equations. (shrink)

To solve fractional delay differential equation systems, the Laguerre Wavelets Method is presented and coupled with the steps method in this article. Caputo fractional derivative is used in the proposed technique. The results show that the current procedure is accurate and reliable. Different nonlinear systems have been solved, and the results have been compared to the exact solution and different methods. Furthermore, it is clear from the figures that the LWM error converges quickly when compared to other approaches. When compared (...) with the exact solution to other approaches, it is clear that LWM is more accurate and gets closer to the exact solution faster. Moreover, on the basis of the novelty and scientific importance, the present method can be extended to solve other nonlinear fractional-order delay differential equations. (shrink)

It has become something of a truism that people with Autism Spectrum Disorders (ASD) have difficulties with pragmatics. Granting this, however, it is important to keep in mind that there are numerous kinds of pragmatic ability. One very important divide lies between those pragmatic competences which pertain to non-literal contents – as in, for instance, metaphor, irony and Gricean conversational implicatures – and those which pertain to the literal contents of speech acts. It is against this backdrop that our question (...) arises: Are certain pragmatic tasks more difficult than others for people with ASD? (shrink)

The existing numerous adaptive variants of differential evolution have been improved the search ability of classic DE to certain extent. Nevertheless, those variants of DE do not obtain the promising performance in solving black box problems with unknown features, which is mainly because the adaptive rules of those variants are designed according to their designers’ cognition on the problem features. To enhance the optimization ability of DE in optimizing black box problems with unknown features, a differential evolution with autonomous selection (...) of mutation strategies and control parameters is proposed in this paper, inspired by autonomous decision-making mechanism of reinforcement learning. In ASDE, a historical experience archive with population features is utilized to preserve accumulated historical experience of the combination of mutation strategies and control parameters. Furthermore, the accumulated historical experience can be autonomously mapped into rules repository, and the individuals can choose the combination of mutation strategies and control parameters according to those rules. Additionally, an updating and utilization mechanism of the historical experience is designed to assure that the historical experience can be effectively accumulated and utilized efficiently. Compared with some state-of-the-art intelligence algorithms on 15 functions of CEC2015, 28 functions of CEC2017, and parameter extraction problems of the photovoltaic model, ASDE has the advantages of solution accuracy, convergence speed, and robustness in solving black box problems with unknown features. (shrink)

The process of ‘logical differentiation’ was introduced by Peirce in 1870. Directly analogous to mathematical differentiation, it uses logical terms instead of mathematical variables. Here, this mysterious process receives new interpretations which serve to clarify Peirce’s use of logical terms. I introduce the logical terms, the operation of multiplication, the logical analogy to the binomial theorem, infinitesimal relatives, the concepts of numerical coefficients and the number associated with each term. I also analyse the algebraic development of ‘logical (...) differentiation’ and consider in depth one application of the process. (shrink)

In this paper, we investigate the numerical solution of the coupled fractional massive Thirring equation with the aid of He’s fractional complex transform. This study plays a significant aspect in the field of quantum physics, weakly nonlinear thrilling waves, and nonlinear optics. The main advantage of FCT is that it converts the fractional differential equation into its traditional parts and is also capable to handle the fractional order, whereas the homotopy perturbation method is employed to tackle the nonlinear terms (...) in the coupled fractional massive Thirring equation. An example is illustrated to present the efficiency and validity of the two-scale theory. The solutions are obtained in the form of series with simple and easy computations which confirm that the present approach is good in agreement and is easy to implement for such type of complex systems in science and engineering. (shrink)

In philosophical studies regarding mathematical models of dynamical systems, instability due to sensitive dependence on initial conditions, on the one side, and instability due to sensitive dependence on model structure, on the other, have by now been extensively discussed. Yet there is a third kind of instability, which by contrast has thus far been rather overlooked, that is also a challenge for model predictions about dynamical systems. This is the numerical instability due to the employment of numerical methods (...) involving a discretization process, where discretization is required to solve the differential equations of dynamical systems on a computer. We argue that the criteria for numerical stability, as usually provided by numerical analysis textbooks, are insufficient, and, after mentioning the promising development of backward analysis, we discuss to what extent, in practice, numerical instability can be controlled or avoided. (shrink)

Numerous philosophers accept the differentiation condition, according to which one does not see an object unless one visually differentiates it from its immediate surroundings. This paper, however, sounds a sceptical note. Based on suggestions by Dretske (2007) and Gibson (2002 [1972]), I articulate two ‘principles of occlusion’ and argue that each principle admits of a reading on which it is both plausible and incompatible with the differentiation condition. To resolve the inconsistency, I suggest we abandon the differentiation (...) condition. (shrink)

The dynamics of single populations up to ecosystems, are often described by one or a set of non-linear ordinary differential equations. In this paper we review the use of bifurcation theory to analyse these non-linear dynamical systems. Bifurcation analysis gives regimes in the parameter space with quantitatively different asymptotic dynamic behaviour of the system. In small-scale systems the underlying models for the populations and their interaction are simple Lotka-Volterra models or more elaborated models with more biological detail. The latter ones (...) are more difficult to analyse, especially when the number of populations is large. Therefore for large-scale systems the Lotka-Volterra equations are still popular despite the limited realism. Various approaches are discussed in which the different time-scale of ecological and evolutionary biological processes are considered together. (shrink)

In this article, we investigated a deterministic model of pneumonia-meningitis coinfection. Employing the Atangana–Baleanu fractional derivative operator in the Caputo framework, we analyze a seven-component approach based on ordinary differential equations. Furthermore, the invariant domain, disease-free as well as endemic equilibria, and the validity of the model’s potential results are all investigated. According to controller design evaluation and modelling, the modulation technique devised is effective in diminishing the proportion of incidences in various compartments. A fundamental reproducing value is generated by (...) exploiting the next generation matrix to assess the properties of the equilibrium. The system’s reliability is further evaluated. Sensitivity analysis is used to classify the impact of each component on the spread or prevention of illness. Using simulation studies, the impacts of providing therapy have been determined. Additionally, modelling the appropriate configuration demonstrated that lowering the fractional order from 1 necessitates a rapid initiation of the specified control technique at the largest intensity achievable and retaining it for the bulk of the pandemic’s duration. (shrink)

In his essay Thinking Colours and/or Machines Kittler hints at a key point in the emergence of modern European culture: the point at which ‘letters and numbers no longer coincide’. In this essay - first published in 2003 as Zahl und Ziffer - Kittler traces the split between numerals and numbers in sweeping historical detail. This is part of a much larger project, the aim of which is to think about technology, history and culture anew by considering the ways in (...) which ‘letters, numbers, images and tones’ have been differentiated and re-integrated by developing notation systems and media technologies. In this present essay, Kittler is concerned specifically with the question of number. His argument is that numbers and numerals have not always stood apart. In Old Hebrew and even nursery rhymes, for example, numbers are in fact words. This might seem like a banal observation, but for Kittler it is crucial as historically, mathematics proper only developed ‘in cultures in which numbers are present as numerals’, a development which entailed the transformation of numbers from signifiers into signifieds and which rested on the emergence of storage and transmission media that Kittler calls ‘the media of mathematics’. This connection between media and mathematics is explored through a wide range of philosophical sources: Plato, Philolaus, Aristotle and Aquinas, to name but a few. Kittler is fascinated by the inscription technologies that make mathematics possible, and which at the same time structure cultural forms as well as our bodily experience of them. As he puts it in a programmatic aside, ‘media studies only make sense’ if they focus on how ‘media make senses.’ Hence his focus on the Greek phonetic alphabet: for Kittler, its superiority has less to do with its ability to reproduce the spoken words of any language, than with the fact that at one point it was used to handle language, music, and mathematics - that is, one and the same set of signs was used to encode letters, tones and numbers. This, however, was not an abstract undertaking but developed in constant feedback with specific instruments or media, especially the lyre and the bow. It was here that fundamental concepts such as logoi were first developed that were subsequently distorted, misunderstood and deprived of their musico-technical origins by philosophers such as Aristotle. Kittler’s essay is thus also part of a larger cultural project, indebted in particular to Martin Heidegger, whose aim it is to ferret out the different, as yet unrevealed beginning of occidental culture. Moreover, while it was necessary for the evolution of modern mathematics that numbers receive a notation system of their own that will allow for ratios and decimals, among others, it is obvious that Kittler sees the computer as a return of universal alphabet that operates in constant feedback with a medium that shapes our senses: ‘In the Greek alphabet our senses were present - and thanks to Turing they are so once again.’. (shrink)

Bound-constrained optimization has wide applications in science and engineering. In the last two decades, various evolutionary algorithms were developed under the umbrella of evolutionary computation for solving various bound-constrained benchmark functions and various real-world problems. In general, the developed evolutionary algorithms belong to nature-inspired algorithms and swarm intelligence paradigms. Differential evolutionary algorithm is one of the most popular and well-known EAs and has secured top ranks in most of the EA competitions in the special session of the IEEE Congress on (...) Evolutionary Computation. In this paper, a customized differential evolutionary algorithm is suggested and applied on twenty-nine large-scale bound-constrained benchmark functions. The suggested C-DE algorithm has obtained promising numerical results in its 51 independent runs of simulations. Most of the 2013 IEEE-CEC benchmark functions are tackled efficiently in terms of proximity and diversity. (shrink)

We concur with Cohen Kadosh & Walsh (CK&W) that representation of numbers in the parietal cortex is format dependent. In addition, we suggest that all formats do not automatically, and equally, access analog magnitude representation in the intraparietal sulcus (IPS). Understanding how development, learning, and context lead to differential access of analog magnitude representation is a key question for future research.

An important task in mathematical sciences is to make quantitative predictions, which is often done via the solution of differential equations. In this paper, we investigate why, to perform this task, scientists sometimes choose to use numerical methods instead of analytical solutions. Via several examples, we argue that the choice for numerical methods can be explained by the fact that, while making quantitative predictions seems at first glance to be facilitated by analytical solutions, this is actually often much (...) easier with numerical methods. Thus we challenge the widely presumed superiority of analytical solutions over numerical methods. (shrink)

Much research effort has been directed in different physiological contexts towards describing realistic behaviors with differential equations. One observes obviously that more state-variables give the model more accuracy. Unfortunately, the computational cost involved is higher. A new algorithm is presented for simulating a model described by a system of differential equations in which efficiency may not be altered by its size. In order to do this, the method is based on a polynomial description of the state-variables' evolution and on a (...) computation distributed control. Evaluations and results performed with classical models like Fitzhugh Nagumo or Hodgkin Huxley, allow validation of the method and exhibits its potential to decrease the computational costs. (shrink)

In Chinese philosophy, although the concept of qi has numerous meanings, it is not completely without order or chaotic. Generally speaking, qi has several different levels of meanings, such as in philosophy, physics, physiology, psychology, ethics, and so on. On the philosophical level, qi is similar to air, and it is essentially similar to the matter-energy or field in physics, which refers to the origin or an element of all things in the world. It is from this point that the (...) meanings of qi in physiology, psychology, ethics as well as aesthetics are derived. This paper analyzes the meanings of qi on five levels and seeks to clarify misunderstandings about qi, such as its alleged pan-vitalistic, conscious and pan-ethical characters. (shrink)

Deleuze’s differential ontology is a sustained attempt to think and affirm difference as opposed to the unity of identity he insists philosophical thought has tended to privilege. However, by distinguishing between three senses of identity, termed identity of the identical, same, and common, I show that, while Deleuze’s differential ontology offers a powerful critique of identity in the senses of the identical and same, at numerous points in his analysis, such as the virtual-actual movement, the transcendental conditions defining different forms (...) of thinking, and the relationship between the forms of thinking, it appears Deleuze’s affirmation of difference depends on identity in the sense of the common. Rather than using these instances to offer a critique of Deleuze’s differential ontology, I follow his exhortation to read a philosopher creatively and suggest that distinguishing between three senses of identity reveals the complexity of the difference-identity relationship and acts as a stimulus to rethinking this relationship. (shrink)

The numerous researches devoted to 'jaundice' during the Second World War have brought to light the existence of an infectious type of hepatic jaundice or 'homologous serum jaundice' following parenteral injection of vaccines containing human serum and blood transfusions, which were carried out on a large scale at the time. This type of serum jaundice was then gradually differentiated from 'catarrhal', contagious or epidemic jaundice by clinical trials along with large series of animal studies. Finally, the epidemiological, clinical and biological (...) data obtained made it possible to establish, between 1944 and 1954, the viral etiology of these two types of jaundice: the A virus, present in the patients' blood and stools, was considered to be the agent responsible for epidemic hepatitis; the B virus, present primarily in the blood, was held to be responsible for serum hepatitis. (shrink)

Solvency assessment is the core content of insurance supervision. In this paper, from the perspective of capital flow, the insurance company’s capital flow is regarded as a dynamic system, the stochastic differential equations model is established to describe its flow characteristics, and the existence of positive equilibrium point of the system is proved, as well as the conditions of stability at equilibrium point, that is, the requirements of the insurance company’s solvency. Furthermore, by using the numerical simulation method, we (...) get the strategy of insurance companies to deal with the solvency shortage when facing the change of external environment, and the strategy of insurance company to deal with solvency shortage is obtained. (shrink)

In this paper, DSEK model with fractional derivatives of the Atangana-Baleanu Caputo is proposed. This paper gives a brief overview of the ABC fractional derivative and its attributes. Fixed point theory has been used to establish the uniqueness and existence of solutions for the fractional DSEK model. According to this theory, we will define two operators based on Lipschitzian and prove that they are contraction mapping and relatively compact. Ulam-Hyers stability theorem is implemented to prove the fractional DSEK model’s stability (...) in Banach space. Also, fractional Euler’s numerical method is derived for initial value problems with ABC fractional derivative and implemented on fractional DSEK model. The symmetric properties contribute to determining the appropriate method for finding the correct solution to fractional differential equations. The numerical solutions generated using fractional Euler’s method have been plotted for different values of α where α ∈ 0,1 and different step sizes h. Result discussion will be given, describing the changes that occur due to the step size h. (shrink)

During mouse early development cell adhesion molecules are indispensable for the embryo organisation. A family of molecules probably involved in development is the transmembrane glycoprotein CD44 family, which exists in multiple isoforms. These are generated by alternative splicing of the pre‐mRNA, resulting in the enlargement of the extracellular part of the molecule. The standard form of CD44 is widely expressed in adult tissues and in embryos from day 9.5 post coitum onwards, while the numerous variant isoforms exhibit highly specialised patterns (...) of expression that are already in the egg cylinder at day 6.5 of development. In lymphohemopoiesis, specific variant isoforms also emerge at decisive differentiation stages. Although specific ligands for the variant region still await isolation, the highly organised expression of CD44 variant isoforms suggests they have a pivotal role in cellular interactions during early development, pattern formation and hemopoiesis. (shrink)

In this article, the main definitions and differentiation concepts of neutrosophic fuzzy environment will be reviewed. This article will introduce an analytical methodology for solving the second-order linear ordinary differential problem with neutrosophic fuzzy boundary values, this analysis will be under generalized Hukuhara differentiability to show the analytical solutions from a different point of view for the uncertain system, some of these solutions may be decreasing in uncertainty or maybe reflecting the behavior of some real-world systems better. Some applications (...) and numeral examples will be solved to show the behavior of the solution. (shrink)

The differentiation of T Lymphocytes within the thymus is an important biological phenomenon during wich these cell acquire their functions to further control the immune system. Numerous experiments under various conditions have been devised to understand the different mechanisms involved in this complex process. Nevertheless, interpretation of these experiments lead to still contradictory debatable hypotheses. Modelisation of this process through classical simulation methods cannot be envisaged because they are not adapted to modifications of the model structure, which is the (...) point of interest. For these reasons, we proposed a new approach of automatic search for model. The program consists of four independent connected modules : The generator produces model, based on the rationale of formal grammars. Protocol and experimental data are stored in a set of experiments. The simulator using a protocol and a model provides simulated results. Finally, the supervisor by comparing simulated results and experimental data, adapts the model parameters to increase their fit and either chooses a new experiment to explore, or modifies the model structure. Change of the model structure is performed among still unexplored models according to their promise level, which is iteratively evaluated relatively to previously explored models through a proposed model distance. The generator is written in Prolog and the other modules in C++. The architecture of the program allows us to modify or complete a module without changing anything in the other modules. As a consequence, the proposed modeling approach conceived to study T lymphocyte differentiation within the thymus remains independent of this biological phenomenon and can be applied to other biological problems. (shrink)

I describe two approaches to modelling the universe, the one having its origin in topos theory and differential geometry, the other in set theory. The first is synthetic differential geometry. Traditionally, there have been two methods of deriving the theorems of geometry: the analytic and the synthetic. While the analytical method is based on the introduction of numerical coordinates, and so on the theory of real numbers, the idea behind the synthetic approach is to furnish the subject of geometry (...) with a purely geometric foundation in which the theorems are then deduced by purely logical means from an initial body of postulates. The most familiar examples of the synthetic geometry are classical Euclidean geometry and the synthetic projective geometry introduced by Desargues in the 17th century and revived and developed by Carnot, Poncelet, Steiner and others during the 19th century. The power of analytic geometry derives very largely from the fact that it permits the methods of the calculus, and, more generally, of mathematical analysis, to be introduced into geometry, leading in particular to differential geometry (a term, by the way, introduced in 1894 by the Italian geometer Luigi Bianchi). That being the case, the idea of a “synthetic” differential geometry seems elusive: how can differential geometry be placed on a “purely geometric” or “axiomatic” foundation when the apparatus of the calculus seems inextricably involved? To my knowledge there have been two attempts to develop a synthetic differential geometry. The first was initiated by Herbert Busemann in the 1940s, building on earlier work of Paul Finsler. Here the idea was to build a differential geometry that, in its author’s words, “requires no derivatives”: the basic objects in Busemann’s approach are not differentiable manifolds, but metric spaces of a certain type in which the notion of a geodesic can be defined in an intrinsic manner. I shall not have anything more to say about this approach. The second approach, that with which I shall be concerned here, was originally proposed in the 1960s by F.. (shrink)

In this paper, some novel analytical and numerical techniques are introduced for solving and analyzing nonlinear second-order ordinary differential equations that are associated to some strongly nonlinear oscillators such as a quadratically damped pendulum equation. Two different analytical approximations are obtained: for the first approximation, the ansatz method with the help of Chebyshev approximate polynomial is employed to derive an approximation in the form of trigonometric functions. For the second analytical approximation, a novel hybrid homotopy with Krylov–Bogoliubov–Mitropolsky method is (...) introduced for the first time for analyzing the evolution equation. For the numerical approximation, both the finite difference method and Galerkin method are presented for analyzing the strong nonlinear quadratically damped pendulum equation that arises in real life, such as nonlinear phenomena in plasma physics, engineering, and so on. Several examples are discussed and compared to the Runge–Kutta numerical approximation to investigate and examine the accuracy of the obtained approximations. Moreover, the accuracy of all obtained approximations is checked by estimating the maximum residual and distance errors. (shrink)

Central to the differentiation and patterning of the Drosophila oocyte is the asymmetric intracellular localization of numerous mRNA and protein molecules involved in developmental signalling. Recent advances have identified some of the molecules mediating oocyte differentiation, specification of the anterior pole of the embryo, and determination of the embryonic germ line. This work is considered in the context of the classical model of the germ plasm as a cytoplasmic determinant for germ cell formation.

An effective numerical scheme based on Euler wavelets is proposed for numerically solving a class of neutral delay differential equations. The technique explores the numerical solution via Euler wavelet truncated series generated by a set of functions and matrix inversion of some collocation points. Based on the operational matrix, the neutral delay differential equations are reduced to a system of algebraic equations, which is solved through a numerical algorithm. The effectiveness and efficiency of the technique have been (...) illustrated by several examples of neutral delay differential equations. The main advantages and key role of using the Euler wavelets in this work lie in the performance, accuracy, and computational cost of the proposed technique. (shrink)

Our research focuses on the perception of difference in the evaluations of positive and negative options. The literature provides evidence for two opposite effects: on the one hand, negative objects are said to be more differentiated, on the other, people are shown to see greater differences between positive options. In our study, we investigated the perception of difference between fictitious political candidates, hypothesizing greater differences among the evaluations of favorable candidates. Additionally, we analyzed how positive and negative information affect candidate (...) evaluation, predicting further asymmetries. In three experiments, participants evaluated various candidate profiles presented in a numeric and narrative manner. The evaluation tasks were designed as individual or joint assessments. In all three studies, we found more differentiation between positive than negative options. Our research suggests that after exceeding a certain, relatively small level of negativity, people do not see any further increase in negativity. The increase in positivity, on the other hand, is more gradual, with greater differentiation among positive options. Our findings are discussed in light of cognitive-experiential self-theory and density hypothesis. (shrink)

Sporulation in the mold Neurospora crussa can proceed along three very different pathways, leading to the production of three types of spores. Two asexual sporulation pathways that lead to the formation of macroconidia and microconidia involve budding from hyphae by two different mechanisms. A much more complex sexual reproductive pathway involves the formation of a fruiting body called a perithecium, in which meiosis takes place and ascospores are formed in sac‐like cells called asci. Numerous mutations exist that affect these developmental (...) pathways, and genes have been isolated that are expressed preferentially during sporulation. The Neurospora sporulation pathways offer a simple system with which to study mechanisms and regulation of development that are usually obscured by complex cell‐cell interactions involved in animal and plant development. (shrink)

In this paper, we present an intensive investigation of the finite volume method compared to the finite difference methods. In order to show the main difference in the way of approaching the solution, we take the Burgers equation and the Buckley–Leverett equation as examples to simulate the previously mentioned methods. On the one hand, we simulate the results of the finite difference methods using the schemes of Lax–Friedrichs and Lax–Wendroff. On the other hand, we apply Godunov’s scheme to simulate the (...) results of the finite volume method. Moreover, we show how starting with a variational formulation of the problem, the finite element technique provides piecewise formulations of functions defined by a collection of grid data points, while the finite difference technique begins with a differential formulation of the problem and continues to discretize the derivatives. Finally, some graphical and numerical comparisons are provided to illustrate and corroborate the differences between these two main methods. (shrink)

In this article, we revisit the classic comparison between Bertrand and Cournot competition in the presence of a cartel of firms that faces outsiders acting individually. This competition setting enables to deal with both non-cooperative and cooperative oligopoly games. We concentrate on industries consisting of symmetrically differentiated products where firms operate at a constant and identical marginal cost. First, while the standard Bertrand–Cournot rankings still hold for Nash equilibrium prices, we show that the results may be altered for Nash equilibrium (...) quantities and profits. Second, we define cooperative Bertrand and Cournot oligopoly games with transferable utility on the basis of their non-cooperative foundation. We establish that the core of a cooperative Cournot oligopoly game is strictly included in the core of a cooperative Bertrand oligopoly game when the number of firms is lower or equal to 25. Moreover, we focus on the aggregate-monotonic core, a subset of the core, that has the advantage to select point solutions satisfying both core selection and aggregate monotonicity properties. We succeed in comparing the aggregate-monotonic cores between Bertrand and Cournot competition regardless of the number of firms. Finally, we study a class of three-firm oligopolies with asymmetric costs in which the core inclusion property mentioned above still holds. We also provide numerical examples to illustrate the difficulty to generalize this result to an arbitrary number of firms because of negative equilibrium quantities. (shrink)

This article considers the government, opinion leaders, and Internet users to be a system for correcting false information, and it considers the problem of correcting false information that arises in the aftermath of major emergencies. We use optimal control theory and differential game theory to construct differential game models of decentralized decision-making, centralized decision-making, and subsidized decision-making. The solutions to these models and their numerical simulations show that the government, opinion leaders, and Internet users exercise cost-subsidized decision-making instead of (...) decentralized decision-making. The equilibrium strategies, local optimal benefits, and overall optimal benefits of the system achieve Pareto improvement. Given the goal of maximizing the benefits to the system under centralized decision-making, the equilibrium results are Pareto-optimal. The research here provides a theoretical basis for dealing with the mechanism of correcting false information arising from major emergencies, and our conclusions provide methodological support for the government to effectively deal with such scenarios. (shrink)

In this paper, we consider the iterative algorithm for a boundary value problem of n -order fractional differential equation with mixed integral and multipoint boundary conditions. Using an iterative technique, we derive an existence result of the uniqueness of the positive solution, then construct the iterative scheme to approximate the positive solution of the equation, and further establish some numerical results on the estimation of the convergence rate and the approximation error.

Measuring psychological attributes, such as motivation, typically involves rating scales, assuming that an attribute can be ordered, and that ratings represent this order. Previously, only the first assumption had been tested, albeit limited. First, we checked the ordinal structure of motivation, looking at whether people can establish transitive relations between motivation levels in pairwise comparisons; and we found different ordering patterns: strict transitive, weak transitive, changing order, and intransitivity. The rate of intransitivity was similar to that found previously and was (...) somewhat higher than we obtained when we asked participants to compare definitely quantitative attributes. Second, we checked if specific ordering patterns were related to individual interpretations of the statements that deviated from expected motivation types. Indeed, about a third of participants miscategorized statements, and these deviant interpretations were related to intransitivity as well as weak transitivity. Third, we checked whether Likert ratings represent the order of motives obtained from pairwise comparisons. We found rather homomorphic representation: ratings correlated with the order, but they did not differentiate between different ordering patterns and hierarchies of motives. We conclude that the Likert rating scale provides less information about respondents than pairwise ordering. The findings question the mainstream practice of using rating scales without testing underlying assumptions. (shrink)

This paper proposes a Cournot game organized by three competing firms adopting bounded rationality. According to the marginal profit in the past time step, each firm tries to update its production using local knowledge. In this game, a firm’s preference is represented by a utility function that is derived from a constant elasticity of substitution production function. The game is modeled by a 3-dimensional discrete dynamical system. The equilibria of the system are numerically studied to detect their complex characteristics due (...) to difficulty to get an explicit form for those equilibria. For the proposed utility function, some cases with different value parameters are considered. Numerical simulations are used to provide an experimental evidence for the complex behavior of the evolution of the system. The obtained results show that the system loses its stability due to different types of bifurcations. (shrink)

We numerically solve the functional differential equations (FDEs) of 2-particle electrodynamics, using the full electrodynamic force obtained from the retarded Lienard–Wiechert potentials and the Lorentz force law. In contrast, the usual formulation uses only the Coulomb force (scalar potential), reducing the electrodynamic 2-body problem to a system of ordinary differential equations (ODEs). The ODE formulation is mathematically suspect since FDEs and ODEs are known to be incompatible; however, the Coulomb approximation to the full electrodynamic force has been believed to be (...) adequate for physics. We can now test this long-standing belief by comparing the FDE solution with the ODE solution, in the historically interesting case of the classical hydrogen atom. The solutions differ. A key qualitative difference is that the full force involves a ‘delay’ torque. Our existing code is inadequate to calculate the detailed interaction of the delay torque with radiative damping. However, a symbolic calculation provides conditions under which the delay torque approximately balances (3rd order) radiative damping. Thus, further investigations are required, and it was prematurely concluded that radiative damping makes the classical hydrogen atom unstable. Solutions of FDEs naturally exhibit an infinite spectrum of discrete frequencies. The conclusion is that (a) the Coulomb force is not a valid approximation to the full electrodynamic force, so that (b) the n-body interaction needs to be reformulated in various current contexts such as molecular dynamics. (shrink)

Introduction Numerous guidelines and policies for ethical research practice have evolved over time, how this translates to global health practice in resource-constrained settings is unclear. The purpose of this paper is to describe how the concept of ancillary care has evolved over time and how it is included in the ethics guidelines and policy documents that guide the conduct of research in the global south with both an international focus and providing a specific example of Malawi, where the first author (...) lives and works, as a case study. Methods Discourse analysis was conducted on 34 international ethics guidelines and policy documents. Documents were purposively selected if they contained a set of key terms that reflect the concept of ancillary care. Following a process of inductive discourse analysis, five key interrelated text phrases relating to ancillary care were extracted from the documents. The evolution of these phrases over time was explored as they represented the development of the concept of ancillary care as a component of ethical health research guidance and practice. Results We found key interrelated phrases that represent discourses regarding the evolution of ancillary care including participant protection; provide care as appropriate; supererogation; patient needs prevail over science; and ancillary care as an obligation. Arguments for the provision of ancillary care were characterised by safeguarding the safety, health rights and well-being of study participants. However, despite the evolution of discourse around ethical obligations to provide ancillary care, this is rarely made explicit within guidance documents, leaving interpretive space for differential application in practice. Conclusion While there have been major changes to the ethics guidance that reflect significant evolution in the ethical conduct of research, the specific vocabulary or language used to explain the ethics of researchers' ancillary care obligations to the health needs of their research participants, lacks clarity and consistency. As a result, the concept of ancillary care continues to be under-represented in local ethical guidelines and regulations, with no clear directives for country-level research ethics committees to apply in regulating ancillary care responsibilities. (shrink)

The directionality of space-number association (SNA) is shaped by cultural experiences. It usually follows the culturally dominant reading direction. Smaller numbers are generally associated with the starting side for reading (left side in Western cultures), while larger numbers are associated with the right endpoint side. However, SNAs consistent with cultural reading directions are present before children can actually read and write. Therefore, these SNAs cannot only be shaped by the direction of children’s own reading/writing behavior. We propose six distinct processes (...) – one biological and five cultural/educational – underlying directional SNAs before formal reading acquisition: (i) Brain lateralization, (ii) Monitoring adult reading behavior, (iii) Pretend reading and writing, and rudimentary reading and writing skills, (iv) Dominant attentional directional preferences in a society, not directly related to reading direction, (v) Direct spatial-numerical learning, (vi) Other spatial-directional processes independent of reading direction. In this mini-review, we will differentiate between these processes, elaborate when in development they might emerge, discuss how they may create the SNAs observed in preliterate children and propose how they can be studied in the future. (shrink)

The numerical study of a glycolytic model formed by a system of three delay differential equations reveals a multiplicity of stable coexisting states: birhythmicity, trirhythmicity, hard excitation and quasiperiodic with chaotic regimes. For different initial functions in the phase space one may observe the coexistence of two different quasiperiodic motions, the existence of a stable steady state with a stable torus, and the existence of a strange attractor with different stable regimes (chaos with torus, chaos with bursting motion, and (...) chaos with different periodic regimes). For a single range of the control parameter values our system may exhibit different bifurcation diagrams: in one case a Feigenbaum route to chaos coexists with a finite number of successive periodic bifurcations, in other conditions it is possible to observe the coexistence of two quasiperiodicity routes to chaos. These studies were obtained both at constant input flux and under forcing conditions. (shrink)

Numerous studies have shown that men experience relatively greater levels of jealousy in response to the sexual aspects of an infidelity (relative to women), whereas women experience relatively greater levels of jealousy in response to the emotional aspects of an infidelity (relative to men). The traditional explanation for this relationship suggests that men experience this greater level of jealousy due to threats of a loss of paternal certainty. In this article, we present three studies that demonstrate that men’s differentially greater (...) jealousy occurs in response to situations that threaten paternity opportunities. These results suggest that a loss of perceived paternity opportunities is the ultimate origin of men’s increased jealousy in response to sexual infidelity. (shrink)

Numerous studies indicate that racial minorities are both more likely to be executed for murder and that those who murder them are less likely to be executed than if they murder whites. Death penalty opponents have long attempted to use these studies to argue for a moratorium on capital punishment. Whatever the merits of such arguments, they overlook the fact that such discrimination alters the costs of murder; racial discrimination imposes higher costs on minorities for murdering through tougher sentences, and (...) it imposes lower costs on whites for murdering minorities by dispensing weaker sentences. These cost differentials constitute an injustice not simply to actual minority defendants in capital cases, nor simply to the actual minority victims of murder, but to all members of minority communities. I here offer two arguments for a moratorium on capital punishment: The first draws upon evidence of racial discrimination against minority defendants in capital cases, and claims that such discrimination modifies the costs of murder in such a way that minority individuals do not enjoy equal status under the law. The second draws upon the evidence regarding racial discrimination in relation to the race of victims, and claims that such discrimination modifies the costs of murder in such a way that minority individuals do not enjoy the equal protection of the law. Thus, by not assigning equal costs to murder, the American criminal justice system fails to provide racial minorities the equality under the law and discounts the value of their lives and liberties. A moratorium is the least unjust response to such a social injustice. I also reply to the criticism that a moratorium prevents us from executing deserving murderers. (shrink)

Terminally differentiating stratified squamous epithelial cells assemble a specialized protective barrier structure on their periphery termed the cornified cell envelope (CE). It is composed of numerous structural proteins that become cross‐linked by several transglutaminase enzymes into an insoluble macromolecular assembly. Several proteins are involved in the initial stages of CE assembly, but only certain proteins from a choice of more than 20 different proteins are used in the final stages of CE reinforcement, apparently to meet tissue‐specific requirements. In addition, a (...) variable selection of proteins may be upregulated in response to genetic defects of one of the CE proteins or tissue injury, in an effort to maintain an effective barrier. Additionally, in the epidermis and hair fiber cuticle, a layer of lipids is covalently attached to the proteins, which provides essential water barrier properties. Here we describe our current understanding of CE structure, a possible mechanism of its assembly, and various disorders that cause a defective barrier. BioEssays 24:789–800, 2002. Published 2002 Wiley Periodicals, Inc. (shrink)

AI has numerous applications and in various fields, including the military domain. The increase in the degree of autonomy in some decision-making systems leads to discussions on the possible future use of lethal autonomous weapons systems (LAWS). A central issue in these discussions is the assignment of moral responsibility for some AI-based outcomes. Several authors claim that the high autonomous capability of such systems leads to a so-called “responsibility gap.” In recent years, there has been a surge in philosophical literature (...) around the concept of responsibility gaps and different solutions have been devised to close or bridge these gaps. In order to move forward in the research around LAWS and the problem of responsibility, it is important to increase our understanding of the different perspectives and discussions in this debate. This paper attempts to do so by disentangling the various arguments and providing a critical overview. After giving a brief outline of the state of the technology of LAWS, I will review the debates over responsibility gaps using three differentiators: those who believe in the existence of responsibility gaps versus those who do not, those who hold that responsibility gaps constitute a new moral problem versus those who argue they do not, and those who claim that solutions can be successful as opposed to those who believe that it is an unsolvable problem. (shrink)

Vesely (experimental physics, U. of Vienna, Austria) provides the basic numerical and computational techniques, followed by an explanation of specific problems of computational physics. Appendices address properties of computing machines and an outline of the technique of Fast Fourier Transformation. The first edition, published by Plenum Press, Ne.

Numerous sex differences in obsessive-compulsive disorder (OCD) instantiations are likely universal, as the associated evolutionary threats and concerns onto which they map were differentially important to the two sexes. Hence, although some ritualized behaviors or thoughts are indeed culture-specific, others are both culturally and temporally invariant as they are rooted in universal Darwinian etiologies (e.g., the sex differences in OCD symptomatology posited here). (Published Online February 8 2007).

Numerous liver specific genes are transcriptionally activated by the binding to their promoter or enhancer of Hepatic Nuclear Factor 1 (HNF1). HNF1 contains a variant homeo‐domain and binds to DNA as either a homod‐imer or a heterodimer with the vHNF1 protein. Surprisingly, HNF1 is not restricted to hepatocytes but is expressed in epithelial cells of several endoderm derived organs and in mesoderm derived kidney tubules. Hence, HNF1 alone can not account for the differentiated state of the hepatic cells. In fact, (...) several other liver‐enriched transcription factors have been cloned. The hepatic phenotype could result from the combinatorial. expression of these regulators. Possible involvement of these trans‐acting factors in liver organogenesis and hepatic differentiation is discussed. (shrink)