This paper presents the nonlinear dynamic analysis of energy-based models arisen from the applied systems characterized by the energy transport in the presence of fractional order derivative and time delay. The studied model is the fractional version of Bianca-Ferrara-Dalgaard-Strulik model of economy which is viewed as a transport network for energy in which the law of motion of capital occurs. By considering the time delay as bifurcation parameter, a proof to investigate the existence of Hopf bifurcation (...) and the phase lock solutions using the Poincare-Linstedt and the harmonic balance methods is given. At definite values of time delay, period-doubling bifurcations followed up by the consequences of chaotic states are detected. Simulation results assure that the BFDS model can generate new chaotic attractors beyond half order derivatives through the effect of the time delay on that system. In accordance with the literatures related to the problem of chaos, the concluded results confirm the proposed theorem by El-Borhamy in which the time delay possesses the ability to change the dynamic state of nonlinear systems from regular to chaotic within the fractional order derivative domain. (shrink)

Consensus of fractional-order multiagent systems with single integral has been wildly studied. However, the dynamics with multiple integral also exist in FOMASs, and they are rarely studied at present. In this paper, consensus problems for multi-integral fractional-order multiagent systems with nonuniform time-delays are addressed. The consensus conditions for MIFOMASs are obtained by a novel frequency-domain method which properly eliminates consensus problems of the systems associated with nonuniform time-delays. Besides, the method revealed in this paper is applicable to classical (...) high-order multiagent systems which is a special case of MIFOMASs. Finally, several numerical simulations with different parameters are performed to validate the correctness of the results. (shrink)

Behavioral science has long been puzzled by the experience of temptation, the resulting impulsiveness, and the variably successful control of this impulsiveness. In conventional theories, a governing faculty like the ego evaluates future choices consistently over time, discounting their value for delay exponentially, that is, by a constant rate; impulses arise when this ego is confronted by a conditioned appetite. Breakdown of Will presents evidence that contradicts this model. Both people and nonhuman animals spontaneously discount the value of expected (...) events in a curve where value is divided approximately by expected delay, a hyperbolic form that is more bowed than the rational, exponential curve. With hyperbolic discounting, options that pay off quickly will be temporarily preferred to richer but slower-paying alternatives, a phenomenon that, over periods from minutes to days, can account for impulsive behaviors, and over periods of fractional seconds can account for involuntary behaviors. Contradictory reward-getting processes can in effect bargain with each other, and stable preferences can be established by the perception of recurrent choices as test cases in recurrent intertemporal prisoner's dilemmas. The resulting motivational pattern resembles traditional descriptions of the will, as well as of compulsive phenomena that can now be seen as side-effects of will: over-concern with precedent, intractable but circumscribed failures of self-control, a motivated unconscious, and an inability to exploit emotional rewards. Hyperbolic curves also suggest a means of reducing classical conditioning to motivated choice, the last necessary step for modeling many involuntary processes like emotion and appetite as reward-seeking behaviors; such modeling, in turn, provides a rationale for empathic reward and the “construction” of reality. Key Words: altruism ; appetite; behavioral economics; classical conditioning; compulsions; dynamic inconsistency; emotions; empathy; freedom of will; hyperbolic discounting; impulsiveness; intertemporal bargaining; self-control; social construction; volition; weakness of will. (shrink)

This book is an introduction to French phenomenology in the post 1945 period. Whilst many of phenomenology's greatest thinkers - Husserl, Heidegger, Sartre and Merleau-Ponty - wrote before this period, Steven DeLay introduces and assesses the creative and important turn phenomenology took after these figures. He presents a clear and rigorous introduction to the work of relatively unfamiliar and underexplored philosophers, including Jean-Louis Chrétien, Michel Henry, Jean-Yves Lacoste, Jean-Luc Marion and others. -/- After an introduction setting out (...) the crucial Husserlian and Heideggerian background to French phenomenology, DeLay explores Emmanuel Levinas’s ethics as first philosophy, Henry’s material phenomenology, Marion’s phenomenology of givenness, Lacoste’s phenomenology of liturgical man, Chrétien’s phenomenology of the call, Claude Romano’s evential hermeneutics, and Emmanuel Falque’s phenomenology of the borderlands. Starting with the reception of Husserl and Heidegger in France, DeLay explains how this phenomenological thought challenges boundaries between philosophy and theology. Taking stock of its promise in light of the legacy it has transformed, DeLay concludes with a summary of the field’s relevance to theology and analytic philosophy, and indicates what the future holds for phenomenology. -/- Phenomenology in France: A Philosophical and Theological Introduction is an excellent resource for all students and scholars of phenomenology and continental philosophy, and will also be useful to those in related disciplines such as theology, literature and French studies. (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)

In this paper, we deal with an alternative analytical analysis of fractional-order partial differential equations with proportional delay, achieved by applying Yang decomposition method, where the fractional derivative is taken in Caputo sense. The suggested series results are discovered to quickly converge to an exact solution. The computation of three test problems of fractional-order with proportional delay partial differential equations was presented to confirm the validity and efficiency of suggested method. The system appears to be (...) a very dependable, effective, and powerful method for solving a variety of physical problems that arise in engineering and science. (shrink)

This book is an introduction to French phenomenology in the post-1945 period. While many of phenomenology's greatest thinkers--Husserl, Heidegger, Sartre and Merleau-Ponty--wrote before this period, Steven DeLay introduces and assesses the creative and important turn phenomenology took after these figures. He presents a clear and rigorous introduction to the work of relatively unfamiliar and underexplored philosophers, including Jean-Louis Chrétien, Michel Henry, Jean-Yves Lacoste, Jean-Luc Marion and others. After an introduction setting out the crucial Husserlian and Heideggerian background (...) to French phenomenology, DeLay explores Emmanuel Levinas's ethics as first philosophy, Henry's material phenomenology, Marion's phenomenology of givenness, Lacoste's phenomenology of liturgical man, Chrétien's phenomenology of the call, Claude Romano's evential hermeneutics, and Emmanuel Falque's phenomenology of the borderlands. Starting with the reception of Husserl and Heidegger in France, DeLay explains how this phenomenological thought challenges boundaries between philosophy and theology. Taking stock of its promise in light of the legacy it has transformed, DeLay concludes with a summary of the field's relevance to theology and analytic philosophy, and indicates what the future holds for phenomenology. Phenomenology in France: A Philosophical and Theological Introduction is an excellent resource for all students and scholars of phenomenology and continental philosophy, and will also be useful to those in related disciplines such as theology, literature, and French studies. (shrink)

Short-term or working memory provides temporary storage of information in the brain after an experience and is associated with conscious awareness. Neurons sensitive to the multiple stimulus attributes comprising an experience are distributed within many brain regions. Such distributed cell assemblies, activated by an event, are the most plausible system to represent the WM of that event. Studies with a variety of imaging technologies have implicated widespread brain regions in the mediation of WM for different categories of information. Each kind (...) of WM may thus be expected to involve many brain regions rather than a local, uniquely dedicated set of cells. Neurons in a distributed “cell assembly” may be self-selected by their temporally coherent activations. The process by which this fragmented representation of the recent past is reassembled to accomplish essentially automatic and reliable recognition of a recurrent event constitutes an important problem. One plausible mechanism to achieve the identification of past with previous events would require that the representational system mediating WM must coexist in spatial extent and somehow overlap in temporal activation with cell ensembles registering input from subsequent events. The detection of such a postulated mechanism required an experimental approach which would focus upon spatial patterns of coherent activation while information about different events was stored in WM and retrieved, rather than focusing upon the temporal sequences of activation in localized regions of interest. For this purpose, the familiar delayed matching from sample task was modified. A series of information-free flashes, or “noncontingent probes,” was presented before an initial series of visual information items, the Priming Sample, which were to be held in WM during a Delay Period. A second series of visual information items were then presented, the Matching Sample. The task required detection of any item in the second series which had beenabsentfrom the initial series. Thirty such trials with a particular category of visual information constituted a single task. Several DMS tasks with this standardized design, but with different categories of visual information, were presented within each test session. The information categories included letters of the alphabet, single digit numbers, or faces from a school yearbook. Event-related potentials , were computed from 21 standardized electrode placements, separately for information-free probes and for information items in each interval of the trials within a task. Because each electrode is particularly sensitive to coherent activation of neurons in the immediately underlying brain regions, topographic maps were constructed and interpolated across the surface of the scalp. The momentary fluctuations of the resulting voltage “landscapes” throughout the task were then subjected to quantitative analysis. Distinctive landscapes sometimes persisted for prolonged periods, implying sustained engagement of very large populations of neurons. “Difference landscapes” were constructed by subtraction of topographic maps evoked by noncontingent probes during the Delay Period from maps of probe ERPs before the presentation of the initial information in the Priming Sample. Such probe difference landscapes displayed recurrent high similarity to momentary landscapes elicited during subsequent presentation of the information items in the Matching Sample. It seemed as if the distributed cell assembly continuously engaged by mediation of WM of the diverse attributes of the initial stimuli was being dynamically compared to the ensembles engaged by registration of the subsequent stimuli. Spatial Principal Component Analysis was applied to the sequences of momentary voltage landscapes observed throughout trials of each task. This method sought a small number of spatial patterns with which these large sets of inhomogeneous spatial distributions of voltage could be reconstructed. This is the spatial analog of the reconstruction of local ERPs by temporal principal components, as often described previously. Five Spatial Principal Components were found which accounted for about 90% of the total variance of voltage across the surface of the scalp throughout every task. Theloadings,or distinguishing topographic features, of these SPCs, were highly similar during every cognitive task for every subject. However,factor scores,or relative average contribution to the overall voltage distributions, of the different SPCs varied substantially among subjects between the tasks and momentarily within successive intervals of each task. These five SPCs may reflect coherent activation of huge distributed ensembles of neurons which comprise independent but interacting functional brain subsystems. These subsystems may correspond to basic resources available to individuals for allocation to mediate conscious evaluation of information during cognitive activity, providing a filter to bind together fractionated representations of the past to evaluate the present. (shrink)

In this paper, the stability and stabilization issues for a class of delayed neural networks with time-varying hybrid impulses are investigated. The hybrid effect of two types of impulses including both stabilizing and destabilizing impulses is considered simultaneously in the analysis of systems. To characterize the occurrence features of impulses, the concepts of average impulse interval and average impulse strength are employed. Based on the analysis of stability, a pinning impulsive controller which can ensure the global exponential stability of the (...) studied neural networks is designed by pinning a small fraction of neurons. Finally, two numerical examples are given to illustrate the effectiveness of the proposed control schemes for delayed neural networks with hybrid impulses. (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)

Consensus of fractional-order multiagent systems with single integral has been wildly studied. However, the dynamics with multiple integral also exist in FOMASs, and they are rarely studied at present. In this paper, consensus problems for multi-integral fractional-order multiagent systems with nonuniform time-delays are addressed. The consensus conditions for MIFOMASs are obtained by a novel frequency-domain method which properly eliminates consensus problems of the systems associated with nonuniform time-delays. Besides, the method revealed in this paper is applicable to classical (...) high-order multiagent systems which is a special case of MIFOMASs. Finally, several numerical simulations with different parameters are performed to validate the correctness of the results. (shrink)

Delay discounting is a common phenomenon in daily life, which refers to the subjective value of a future reward decreasing as a function of time. Previous studies have identified several cortical regions involved in delay discounting, but the neural network constructed by the cortical regions of delay discounting is less clear. In this study, we employed resting-state functional magnetic resonance imaging (RS-fMRI) to measure the spontaneous neural activity in a large sample of healthy young adults and used (...) the Monetary Choice Questionnaire to directly measure participants’ level of delay discounting. To identify the neural network of delay discounting at rest, we used an individual difference approach to explore brain regions whose spontaneous activities were related to delay discounting across the whole brain. Then, these brain regions served as seeds to identify the neural network of delay discounting. We found that the fractional amplitude of low-frequency fluctuations (fALFF) of the left insula were positively correlated to delay discounting. More importantly, its connectivity to the anterior cingulate cortex was read out for participants’ behavioral performance in the task of delay discounting. In short, our study provides empirical evidence that insula-anterior cingulate cortex connectivity may serve as a part of the neural network for delay discounting. (shrink)

We study the dynamical behavior of multiple quasi-synchronization of a type of fractional-order coupled neural networks with delay and uncertain parameters. By utilizing the pinned pulse control strategy technique, we establish a new pulse controller, which realizes the multiple quasisynchronization of the system. Furthermore, we derive some new criteria of multiple quasisynchronization by using the comparison principle and mathematical analysis. Eventually, simulations are carried out with two examples to explicate the effectiveness of the conclusions.

In the traditional frame of classical electrodynamics, a hydrogen atom would emit electromagnetic waves and thus constantly lose energy, resulting in the fall of the electron on the proton over a finite period of time. The corresponding results were derived under the assumption of the instantaneous interaction between the proton and the electron. In 2004, Raju published a paper where he removed the assumption of the instantaneous interaction and studied the role of a time delay in the classical (...) hydrogen atom. He introduced a model of this effect that can be solved analytically. He calculated the radius rsel of a selected orbit, for which this effect and the radiation reaction force would cancel each other with respect to the tangential acceleration. It turned out that rsel is by an order of magnitude smaller than the Bohr radius. In the present paper we use Raju’s model for the corresponding gravitational situation. In frames of Newton’s gravity, we calculate analytically the radius and the energy Esel of a selected orbit, for which the retardation effect and the radiation reaction force would cancel each other out with respect to the tangential acceleration. Then we compare our outcome with some results of Kaplan’s solution for the two-body gravitational problem based on the Schwarzschild’s field. We show that Esel is very close to the minimum energy of bound states obtained by Kaplan in Einstein’s gravity. We emphasize that the selected orbit from the present paper represents the second only physical situation where the radiation reaction force is zero, but the radiation-caused energy loss is not zero. (shrink)

Clinical experience suggests that adult survivors of childhood trauma arrive at their memories in a number of ways, with varying degrees of associated distress and uncertainty and, in some cases, after memory lapses of varying duration and extent. Among those patients who enter psychotherapy as a result of early abuse, three general patterns of traumatic recall are identified: relatively continuous and complete recall of childhood abuse experiences coupled with changing interpretations of these experiences, partial amnesia for abuse events, accompanied by (...) a mixture of delayed recall and delayed understanding, and delayed recall following a period of profound and pervasive amnesia. These patterns are represented by three composite clinical vignettes. Variations among them suggest that the phenomena underlying traumatic recall are continuous not dichotomous. Future research into the nature of traumatic memory should be informed by clinical observation. (shrink)

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)

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)

In this paper, we put forward a time-delay ecological competition system with food restriction and diffusion terms under Neumann boundary conditions. For the case without delay, the conditions for local asymptotic stability and Turing instability are constructed. For the case with delay, the existence of Hopf bifurcation is demonstrated by analyzing the root distribution of the corresponding characteristic equations. Furthermore, by using the normal form theory and the center manifold reduction of partial functional differential equations, explicit formulas (...) are obtained to determine the direction of bifurcations and the stability of bifurcating periodic solutions. Finally, some simulation examples are provided to substantiate our analysis. (shrink)

Recent studies on the effects of mandatory online teaching, resulting from the COVID-19 pandemic, have widely reported low levels of satisfaction, unwillingness to continue online teaching, and negative impacts on the psychological well-being of teachers. Emerging research has highlighted the potential role of psychological need thwarting, in terms of autonomy, competence, and relatedness thwarting, resulting from online teaching. The aim of this study was to evaluate the immediate and delayed effects of PNT of online teaching on teachers’ well-being, intention to (...) continue online teaching, and job satisfaction. Moreover, data collected from both cross-sectional and longitudinal surveys allowed for a systematic validation of an important instrument in the field of teacher psychology, the Psychological Need Thwarting Scale of Online Teaching, in terms of longitudinal reliability and validity. The data reveal the usefulness of the construct of PNT in terms predicting and explaining teachers’ willingness to continue using online teaching as well as the degree of burnout after a period of 2 months, such that PNT is positively associated with burnout and negatively associated with willingness to continue online teaching. As such, the PNTSOT is recommended for future research evaluating the long-term psychological, affective, and intentional outcomes stemming from teachers’ PNT. Moreover, based on our findings that the impact from PNT of online teaching is persistent and long-term, we suggest that school leaders provide flexible and sustained professional development, model respectful and adaptive leadership, and create opportunities for mastery for the development of community of practice that can mitigate the thwarting of teachers’ autonomy, competence, and relatedness during times of uncertainty. Additionally, in terms of the psychometric properties of the PNTSOT instrument, our empirical findings demonstrate internal reliability, test–retest reliability, measurement invariance, and criterion validity based on cross-sectional and longitudinal data. (shrink)

In this paper, the nonsmooth compound transmission control protocol with the gentle random early detection system with the state-dependent round-trip delay is investigated in detail. Uniqueness of the positive equilibrium is proved firstly. Then, the closed approximate periodic solutions in this state-dependent delayed nonsmooth compound TCP with the GRED model are obtained by employing the harmonic balance and alternating frequency/time domain method. Then, we compare the results generated by numerical simulations with those of the closed approximate expressions obtained by (...) HB-AFT. It indicates that HB-AFT is simple, correct, and powerful for state-dependent delayed nonsmooth dynamical systems. Finally, we find the complicated dynamic: chaos. It is a grazing chaos with a hybrid property, i.e., where usually w oscillates at a very low frequency and q oscillates at a very high frequency. And, the route to chaos is a very rare route, i.e., the instantaneous and local transition of stable equilibrium to chaos. So, to the end of stability and good performance, we should adjust the parameters carefully to avoid the periodic and chaotic oscillations. (shrink)

In this paper, a finance system with delay is considered. By analyzing the corresponding characteristic equations, the local stability of equilibrium is established. The existence of Hopf bifurcations at the equilibrium is also discussed. Furthermore, formulas for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by applying the normal form method and center manifold theorem. Finally, numerical simulation results are presented to validate the theoretical analysis. Numerical simulation results show that (...) class='Hi'>delay can lead a stable system into a chaotic state. (shrink)

In this paper, we propose a time-delayed predator-prey model with Holling-type II functional response, which incorporates the gestation period and the cost of fear into prey reproduction. The dynamical behavior of this system is both analytically and numerically investigated from the viewpoint of stability, permanence, and bifurcation. We found that there are stability switches, and Hopf bifurcations occur when the delay τ passes through a sequence of critical values. The explicit formulae which determine the direction, stability, and other (...) properties of the bifurcating periodic solutions are given by using the normal form theory and center manifold theorem. We perform extensive numerical simulations to explore the impact of some important parameters on the dynamics of the system. Numerical simulations show that high levels of fear have a stabilizing effect while relatively low levels of fear have a destabilizing effect on the predator-prey interactions which lead to limit-cycle oscillations. We also found that the model with or without a delay-dependent factor can have a significantly different dynamics. Thus, ignoring the delay or not including the delay-dependent factor might result in inaccurate modelling predictions. (shrink)

ABSTRACTPrevious research has shown that, in comparison to neutral stimuli, false memories for high arousing negative stimuli are greater after very fast presentation and limited attention at study. However, full compared to limited attention conditions still produce comparably more false memories for all stimuli types. Research has also shown that emotional stimuli benefit from a period of consolidation. What effect would such consolidation have on false memory formation even when attention is limited at study? The aim of the present (...) study was to investigate the effect of fast presentation on false memory production for negatively-arousing and neutral items over time using the DRM paradigm. Sixty-eight participants studied Negative and neutral DRM lists with fast or slow presentation conditions. Half completed a recognition test immediately and half completed a recognition test after one-week. Results revealed that, for fast presentation, negative critical lures increased after one week and were comparab... (shrink)

Spontaneous eye blink rate has been linked to attention and memory, specifically working memory. sEBR is also related to striatal dopamine activity with schizophrenia and Parkinson’s disease showing increases and decreases, respectively, in sEBR. A weakness of past studies of sEBR and WM is that correlations have been reported using blink rates taken at baseline either before or after performance of the tasks used to assess WM. The goal of the present study was to understand how fluctuations in sEBR during (...) different phases of a visual WM task predict task accuracy. In two experiments, with recordings of sEBR collected inside and outside of a magnetic resonance imaging bore, we observed sEBR to be positively correlated with WM task accuracy during the WM delay period. We also found task-related modulation of sEBR, including higher sEBR during the delay period compared to rest, and lower sEBR during task phases that place demands on visual attention. These results provide further evidence that sEBR could be an important predictor of WM task performance with the changes during the delay period suggesting a role in WM maintenance. The relationship of sEBR to DA activity and WM maintenance is discussed. (shrink)

In many real-world gambles, a non-trivial amount of time passes before the uncertainty is resolved but after a choice is made. An individual may have a preference between gambles with identical probability distributions over final outcomes if they differ in the timing of resolution of uncertainty. In this domain, utility consists not only of the consumption of outcomes, but also the psychological utility induced by an unresolved gamble. We term this utility anxiety. Since a reflective decision maker may want to (...) include anxiety explicitly in analysis of unresolved lotteries, a multiple-outcome model for evaluating lotteries with delayed resolution of uncertainty is developed. The result is a rank-dependent utility representation (e.g., Quiggin, 1982), in which period weighting functions are related iteratively. Substitution rules are proposed for evaluating compound temporal lotteries. The representation is appealing for a number of reasons. First, probability weights can be interpreted as the cognitive attention allocated to certain outcomes. Second, the model disaggregates strength of preference from temporal risk aversion and thus provides some insight into the old debate about the relationship between von Neumann–Morgenstern utility functions and strength of preference value functions. (shrink)

Due to the inevitable delay phenomenon in the process of signal conversion and transmission, time delay is bound to occur between neurons. Therefore, it is necessary to introduce the concept of time delay into the membrane computing models. Spiking neural P systems, as an attractive type of neural-like P systems in membrane computing, are widely followed. Inspired by the phenomenon of time delay, in our work, a new variant of spiking neural P systems called delayed spiking (...) neural P systems is proposed. Compared with normal spiking neural P systems, the proposed systems achieve time control by setting the schedule on spiking rules and forgetting rules, and the schedule is also used to realize the system delay. A schedule indicates the time difference between receiving and outputting spikes, and it also makes the system work in a certain time, which means that a rule can only be used within a specified time range. We specify that each rule is performed only in the continuous schedule, during which the neuron is locked and cannot send or receive spikes. If the neuron is not available at a given time, it will not receive or send spikes due to the lack of a schedule for this period of time. Moreover, the universality of DSN P systems in both generating and accepting modes is proved. And a universal DSN P system having 81 neurons for computing functions is also proved. (shrink)

The number of elements in a small set of items is appraised in a fast and exact manner, a phenomenon called subitizing. In contrast, humans provide imprecise responses when comparing larger numerosities, with decreasing precision as the number of elements increases. Estimation is thought to rely on a dedicated system for the approximate representation of numerosity. While previous behavioral and neuroimaging studies associate subitizing to a domain-general system related to object tracking and identification, the nature of small numerosity processing is (...) still debated. We investigated the neural processing of numerosity across subitizing and estimation ranges by examining electrophysiological activity during the memory retention period in a delayed numerical match-to-sample task. We also assessed potential differences in the neural signature of numerical magnitude in a fully non-symbolic or cross-format comparison. In line with behavioral performance, we observed modulation of parietal-occipital neural activity as a function of numerosity that differed in two ranges, with distinctive neural signatures of small numerosities showing clear similarities with those observed in visuospatial working memory tasks. We also found differences in neural activity related to numerical information in anticipation of single vs. cross-format comparison, suggesting a top-down modulation of numerical processing. Finally, behavioral results revealed enhanced performance in the mixed-format conditions and a significant correlation between task performance and symbolic mathematical skills. Overall, we provide evidence for distinct mechanisms related to small and large numerosity and differences in numerical encoding based on task demands. (shrink)

The phenomena, molecular path in a liquid or a gas, fluctuating price stoke, fission and fusion, quantum field theory, relativistic wave motion, etc., are modeled through the nonlinear time fractional clannish random Walker’s parabolic equation, nonlinear time fractional SharmaTassoOlver equation, and the nonlinear space-time fractional KleinGordon equation. The fractional derivative is described in the sense of conformable derivative. From there, the G ′ / G, 1 / G -expansion method is found to be ensuing, effective, and (...) capable to provide functional solutions to nonlinear models concerning physical and engineering problems. In this study, an extension of the G ′ / G, 1 / G -expansion method has been introduced. This enhancement establishes broad-ranging and adequate fresh solutions. In addition, some existing solutions attainable in the literature also confirm the validity of the suggested extension. We believe that the extension might be added to the literature as a reliable and efficient technique to examine a wide variety of nonlinear fractional systems with parameters including solitary and periodic wave solutions to nonlinear FDEs. (shrink)

This article deals with optimal control applied to vaccination and treatment strategies for an SIRS epidemic model with logistic growth and delay. The delay is incorporated into the model in order to modeled the latent period or incubation period. The existence for the optimal control pair is also proved. Pontryagin’s maximum principle with delay is used to characterize these optimal controls. The optimality system is derived and then solved numerically using an algorithm based on the (...) forward and backward difference approximation. (shrink)

This paper examines the notion that delay in reaching agreement in bargaining may be caused by learning that is independent of the bargaining procedure. In particular, learning is not due to inference from the observed offers and responses of the opponent, but derives from observation of an exogenous, costly signal – we call this 'investigation'. First we observe that even if learning is costless and perfectly informative, investigation may not occur in equilibrium. Under more general conditions, however, uninformed agents (...) typically have an incentive to try to manipulate their prior beliefs through investigation. The main result is that investigation by an uninformed agent may result in significant delay occurring before agreement is reached. We show that this delay may be sustained in the limit as the length of time period vanishes, and that this result depends crucially on the properties of the information production technology underlying investigation. Also, the delay we observe is shown to be robust to changes in the bargaining procedure. (shrink)

The dynamics behaviors of Kaldor–Kalecki business cycle model with diffusion effect and time delay under the Neumann boundary conditions are investigated. First the conditions of time-independent and time-dependent stability are investigated. Then, we find that the time delay can give rise to the Hopf bifurcation when the time delay passes a critical value. Moreover, the normal form of Hopf bifurcations is obtained by using the center manifold theorem and normal form theory of the partial differential equation, which (...) can determine the bifurcation direction and the stability of the periodic solutions. Finally, numerical results not only validate the obtained theorems, but also show that the diffusion coefficients play a key role in the spatial pattern. With the diffusion coefficients increasing, different patterns appear. (shrink)

The subject of general utterances (al-lafdh al-āmm) being certain or presumptive in their usage as an indication to all their members is controversial amongst the methodists. Ḥanafī methodists suggest that the indication of general utterances to all of their members as certain and unless they are specified with a certain evidence, they can’t be specified with a presumptive evidence. Like the ḥanafī methodists, the ẓāhirī methodists also suggest that the general utterance is certain indicant for all of its members and (...) can be specified only with another evidence in the same rank. The main difference between the two groups focuses on whether al-khabar al-wāhid (single prophetic narration) is a certain or a presumptive evidence in terms of certitude. According to ḥanafīs, al-khabar al-wāhid is a presumptive evidence and unless the general utterances in Qur’ān are specified initially with another certain evidence, they can’t be specified with al-khabar al-wāhid. However, al-khabar al-wāhid is a certain evidence according to ẓāhirīs and it can specify general utterances in Qur’ān. In this study, the comparison of the views of the methodists of two schools regarding the indication of general utterances in Quran and their specification (takhsīs) with al-akhbar al-wāhid is made and their influence on Islamic Law regulations is studied afterwards. In this study, the two sect’s approaches are compared over the provision of reading al-Fatehah during prayer, the number of milk sucking to establish the kinship, the rights of women divorced with bain talaq and the execution of the death penalty in the Harem region.Summary: The purpose of this study is to try to demonstrate that an assertion in the Ph.D. thesis, The History and Doctrine of Ẓāhirī Madhhab, completed by Amr Osman in 2010 is incorrect. It can be summarized that in his study, Amr Osman claims that the affiliation of the schools to ahl-al-hadith and ahl-al-ra’y in conventional classification is wrong. According to him, contrary to what is known, the School of Ẓāhiriyya is closer to School of Ḥanafiyya rather than schools coming out of ahl-al-hadith. In this study, one of the arguments that he relied on to support his claim is studied in order to prove that his claim was inaccurate. Osman claims that ẓāhirīs are closer to ḥanifīs, based on the view that in both schools the general utterances embrace all of their members in their usage and they are a certain indicant to all of their members. At this stage, although the views of both schools are common, the ḥanifīs don’t accept the idea that the general statements of Qur’ān can be established with al-khabar-al-wāhid, those which they acknowledge as presumptive as of certitude. However, according to the ẓāhirīs, the certitude of al-khabar al-wāhid is as precise as the narrated report, so it can specify the general statements of Qur’ān which are in equal power. The related dispute between the schools has been reflected on many Islamic law regulations. Some of them are:1. Ḥanafīs state that the correct Quranic prayer may be performed by reading any or a few verses of the Qur’ān in prayer, which is a practice based on the verse “Read what you can read from the Qur’ān now”. On the other hand, the ẓāhirīs have established the related order based on the report “There is no prayer without reading Umm Al-Quran (Surah al-Fatehah)” and it is obligatory (fardh) to read Surah al-Fatehah in prayers.2. Because that the terms milk-mother and milk sister are in general form in the verse “It is forbidden to you to marry these people...Your milk-mothers who nursed you, your milk-sisters who nursed you” the ḥanafīs clarify that it is sufficient for a child to breastfeed only one time in order to form a milk-kinship. They do not act in accordance with the solitary report (al-khabar-al-wāhids) which indicate that the milk kinship specifying the verse shall only be formed with at least three or five breastfeeding. However, one of the ẓāhirīs, Dāwūd al-Ẓāhirī, has specified the verse with the report indicating that the kinship shall not be formed with less than three breastfeeding by the child, and Ibn Ḥazm has specified it with Salim hadith which indicates that the kinship shall be formed with five breastfeeding.3. According to ḥanafīs, there is an alimony and inhabiting right of the widow woman to be procured by the husband within the period of delay who divorced her either with irreversible divorce (talāq al-bāin) or reversible divorce (talāq al-ric‘ī) according to the generalization of the verse “Give shelter to them (the women you have divorced) in some part of your household within your capacity.” They did not act with the report of Fātima binti Qays, who specified the generalization of the verse. On the other hand, the ẓāhirīs recognize the abovementioned rights only for the women who got divorced with irreversible divorce or the ones who are pregnant, specifying the verse with the report indicating that His Holiness the Prophet does not grant alimony and inhabiting to the woman who was divorced with reversible divorce.4. According to ḥanafīs, the criminal who committed a crime that would require a death penalty and took refuge in the Harem region could not be executed while in Ḥarem, according to the common statement of the verse, “Whoever enters there, will be safe.” Dāwūd al-Ẓāhirī, one of the ẓāhirīs has specified the verse with the report indicating that His Holiness the Prophet has authorized the execution of the sentence to Ibn Khattal in Ḥarem on the day of the conquering of Mecca and he states that the death sentence can be executed wherever the criminal is caught, even if it is inside the Harem. Ibn Ḥazm shares the same view with ḥanafīs regarding the provision of this issue. However, the reason for his opinion stems from the fact that the report about Ibn Khattal was an event specific to that day. As it is seen, even though the ḥanefīs and ẓāhirīs share the same opinion about the general utterances being a certain indicant to all their members, they have disagreements upon the argument about the general utterances of Quran being specified by al-khabar al-wāhid and many Islamic Law regulations have been issued by these schools based on such disagreements. According to us, in the final analysis, Amr Osman’s claim must be met with caution. (shrink)

Infants are sensitive to statistics in spoken language that aid word‐form segmentation and immediate mapping to referents. However, it is not clear whether this sensitivity influences the formation and retention of word‐referent mappings across a delay, two real‐world challenges that learners must overcome. We tested how the timing of referent training, relative to familiarization with transitional probabilities (TPs) in speech, impacts English‐learning 23‐month‐olds’ ability to form and retain word‐referent mappings. In Experiment 1, we tested infants’ ability to retain TP (...) information across a 10‐min delay and use it in the service of word learning. Infants successfully mapped high‐TP but not low‐TP words to referents. In Experiment 2, infants readily mapped the same words even when they were unfamiliar. In Experiment 3, high‐ and low‐TP word‐referent mappings were trained immediately after familiarization, and infants readily remembered these associations 10 min later. In sum, although 23‐month‐old infants do not need strong statistics to map word forms to referents immediately, or to remember those mappings across a delay, infants are nevertheless sensitive to these statistics in the speech stream, and they influence mapping after a delay. These findings suggest that, by 23 months of age, sensitivity to statistics in speech may impact infants’ language development by leading word forms with low coherence to be poorly mapped following even a short period of consolidation. (shrink)

Receiving social support from community and extended family has been typical for mothers with infants in human societies past and present. In non-industrialised contexts, infants of mothers with extended family support often have better health and higher survival through the vulnerable infant period, and hence shared infant care has a clear fitness benefit. However, there is scant evidence that these benefits continue in industrialised contexts. Better infant health and development with allocare support would indicate continued evolutionary selection for allocare. (...) The research reported here used multiple logistic regression analysis to test whether a lack of family and other social support for mothers was associated with an increased risk of developmental delay in 9-month-old infants in the UK Millennium Cohort (analysis sample size, 15,696 infants). Extended family-based childcare during work hours and more maternal time spent with friends were the most influential kin and social support variables: infants of mothers with kin-based childcare versus all other childcare arrangements had a lower risk of developmental delay (OR = 0.61, 95% CIs: 0.46–0.82). Infants of mothers who spent no time with friends when compared with those who saw friends every day had double the odds of delay. Greater paternal involvement in infant care was associated with a lower odds of developmental delay. In conclusion, shared care of infants and social support for mothers may influence fitness-related traits in industrialised societies rather than being factors that influenced selection only in the past and in societies which retain close kin networks and a strong local community focus. (shrink)

Chaos distributes with a covert method to condense the dynamic of complexity and satisfies the security requirements of a cryptographic system. This study gives an ability online/offline ID-based short signature scheme using conformable fractional chaotic maps. Furthermore, we establish its security under IBSS existential unforgeability of identity-based short signature under chosen message attack in the random oracle model. Some of the stimulating preparations of obtainable processes are that they give a multiperiod application of the offline storage, which licenses the (...) agent to recycle the offline pre-registered data in time series, rather than one-period usage in all past IBSS processes. (shrink)

The order of stages in a multistage game is often interpreted by looking at earlier stages as involving more long term decisions. For the purpose of making this interpretation precise, the notion of a delay supergame of a bounded multistage game is introduced. A multistage game is bounded if the length of play has an upper bound. A delay supergame is played over many periods. Decisions on all stages are made simultaneously, but with different delays until they become (...) effective. The earlier the stage the longer the delay. A subgame perfect equilibrium of a bounded multistage game generates a subgame perfect equilibrium in every one of its delay supergames. This is the first main conclusion of the paper. A subgame perfect equilibrium set is a set of subgame perfect equilibria all of which yield the same payoffs, not only in the game as a whole, but also in each of its subgames. The second xmain conclusion concerns multistage games with a unique subgame perfect equilibrium set and their delay supergames which are bounded in the sense that the number of periods is finite. If a bounded multistage game has a unique subgame perfect equilibrium set, then the same is true for every one of its bounded delay supergames. Finally the descriptive relevance of multistage game models and their subgame perfect equilibria is discussed in the light of the results obtained. (shrink)

On the basis of the previous publications, a new fractional-order prey-predator model is set up. Firstly, we discuss the existence, uniqueness, and nonnegativity for the involved fractional-order prey-predator model. Secondly, by analyzing the characteristic equation of the considered fractional-order Lotka–Volterra model and regarding the delay as bifurcation variable, we set up a new sufficient criterion to guarantee the stability behavior and the appearance of Hopf bifurcation for the addressed fractional-order Lotka–Volterra system. Thirdly, we perform the (...) computer simulations with Matlab software to substantiate the rationalisation of the analysis conclusions. The obtained results play an important role in maintaining the balance of population in natural world. (shrink)