In first order logic without equality, but with arbitrary relations and functions the ∃*∀∃* class is the unique maximal solvable prefix class. We show that the satisfiability problem for this class is decidable in deterministic exponential time The result is established by a structural analysis of a particular infinite subset of the Herbrand universe and by a polynomial space bounded alternating procedure.

We consider the relationship between the computational complexity classes NP and EL . Taking into account the inclusion or incomparability of these classes, the existence or nonexistence of immune sets in their differences, and the existence or nonexistence of sparse sets in the differences, there are exactly 24 different cases for their relationship. We show that 16 cases are impossible in the real nonrelativized world as well as in any relativized world. Each of the remaining 8 cases is realizable in (...) appropriate relativized worlds. Further we examine which of the 8 cases is most probably for a random oracle. (shrink)

According to Craig Callender [2022], the ‘received view’ across the social sciences is that, when it comes to time and preference, only exponential time discounting is rational. Callender argues that this view is false, even pernicious. Here I endorse what I take to be Callender’s main argument, but only in so far as the received view is understood in a particular way. I go on to propose a different way of understanding the received view that makes it (...) true. In short: When time discounting is suitably conceived, the exponential form of the discounting function is indeed uniquely rational. (shrink)

In this paper, the stability of switched neural networks with interval parameter uncertainties and time delays is investigated. First, the conditions for the existence and uniqueness of the equilibrium point of the system are discussed. Second, the average dwell time approach and M-matrix property are employed to obtain conditions to ensure the globally exponential stability of the delayed SNNs under constrained switching. Third, by resorting to inequality technique and the idea of vector Lyapunov function, sufficient condition to (...) ensure the robust exponential stability of the delayed SNNs under arbitrary switching is derived. The form of the constructed Lyapunov functions is simple, which has certain commonality in studying delayed SNNs, and the proposed results not only are explicit but also reveal the relationship between the constrained switching and the arbitrary switching of the SNNs. Finally, two numerical examples are presented to illustrate the effectiveness and less conservativeness of the main results compared with the existing literature. (shrink)

We study the deviations from the exponential decay law, both in quantum field theory (QFT) and quantum mechanics (QM), for an unstable particle which can decay in (at least) two decay channels. After a review of general properties of non-exponential decay in QFT and QM, we evaluate in both cases the decay probability that the unstable particle decays in a given channel in the time interval between t and t+dt. An important quantity is the ratio of the (...) probability of decay into the first and the second channel: this ratio is constant in the Breit-Wigner limit (in which the decay law is exponential) and equals the quantity Γ1/Γ2, where Γ1 and Γ2 are the respective tree-level decay widths. However, in the full treatment (both for QFT and QM) it is an oscillating function around the mean value Γ1/Γ2 and the deviations from this mean value can be sizable. Technically, we study the decay properties in QFT in the context of a superrenormalizable Lagrangian with scalar particles and in QM in the context of Lee Hamiltonians, which deliver formally analogous expressions to the QFT case. (shrink)

In this work a double exponential time inseparability result is proven for a finitely axiomatizable first order theory Q₊. The theory, subset of Presburger theory of addition S₊, is the additive fragment of Robinson system Q. We prove that every set that separates Q₊` from the logically false sentences of addition is not recognizable by any Turing machine working in double exponential time. The lower bound is given both in the non-deterministic and in the linear alternating (...) time models. The result implies also that any theory of addition that is consistent with Q₊—in particular any theory contained in S₊—is at least double exponential time difficult. Our inseparability result is an improvement on the known lower bounds for arithmetic theories. Our proof uses a refinement and adaptation of the technique that Fischer and Rabin used to prove the difficulty of S₊. Our version of the technique can be applied to any incomplete finitely axiomatizable system in which all of the necessary properties of addition are provable. (shrink)

This paper deals with the exponential stabilization problem for a class of nonlinear switched systems with mixed delays under asynchronous switching. The switching signal of the switched controller involves delay, which results in the asynchronous switching between the candidate controllers and subsystems. By constructing the parameter-dependent Lyapunov-Krasovskii functional and the average dwell time approach, some sufficient conditions in forms of linear matrix inequalities are presented to ensure the exponential stability of the switched nonlinear system under arbitrary switching (...) signals. In addition, through the special deformation of the matrix and Schur complement, the controllers with asynchronous switching are designed. Finally, a numerical example and a practical example of river pollution control are provided to show the validity and potential of the developed results. (shrink)

This paper investigates the exponential synchronization of complex dynamical networks based on the sampled-data control method. The sampled-data control means that the control input remains unchanged for a long time after each sampling, which can reduce the sampling number. By using the stability theory of the dynamical systems, this paper provides a novel sampling controller and estimates the bound of the sampling interval. Finally, a numerical example is given to demonstrate the effectiveness of the proposed design technique.

In this paper, dynamic behavior analysis has been discussed for a class of switched complex-valued neural networks with interval parameter uncertainties and impulse disturbance. Sufficient conditions for guaranteeing the existence, uniqueness, and global robust exponential stability of the equilibrium point have been obtained by using the homomorphism mapping theorem, the scalar Lyapunov function method, the average dwell time method, and M-matrix theory. Since there is no result concerning the stability problem of switched neural networks defined in complex number (...) domain, the stability results we describe in this paper generalize the existing ones. The effectiveness of the proposed results is illustrated by a numerical example. (shrink)

In the framework of the rigged Hilbert space, unstable quantum systems associated with first-order poles of the analytically continued S-matrix can be described by Gamow vectors which are generalized vectors with exponential decay and a Breit-Wigner energy distribution. This mathematical formalism can be generalized to quasistationary systems associated with higher-order poles of the S-matrix, which leads to a set of Gamow vectors of higher order with a non-exponential time evolution. One can define a state operator from the (...) set of higher-order Gamow vectors which obeys the exponential decay law. We shall discuss to what extent the requirement of an exponential time evolution determines the form of the state operator for a quasistationary microphysical system associated with a higher-order pole of the S-matrix. (shrink)

How should one discount utility across time? The conventional wisdom in social science is that one should use an exponential discount function. Such a function is a representation of the axioms that provide a well-defined utility function plus a condition known as stationarity. Yet stationarity doesnt really have much intuitive normative pull on its own. Here I try to cast it in a normative glow by deriving stationarity from two explicitly normative premises, both suggested by the philosophical thesis (...) of temporal neutralism. Putting the argument in this form helps us better understand exponential discounting and challenges to it. (shrink)

I find much to like in Craig Callender's [2022] arguments for the rational permissibility of non-exponential time discounting when these arguments are viewed in a conditional form: viz., if one thinks that time discounting is rationally permissible, as the social scientist does, then one should think that non-exponential time discounting is too. However, time neutralists believe that time discounting is rationally impermissible, and thus they take zero time discounting to be the normative (...) standard. The time neutralist rejects time discounting because they think it is rationally impermissible to prefer to live a worse life in expectation because of arbitrariness. Callender’s attack on the time-neutralist position is the following: the time-neutralist’s non-arbitrariness intuition assumes the existence of nonexistent ‘pure’ time preferences. In response, I aim to clarify the time-neutralist position and show that the non-arbitrariness argument does not rely on the existence of pure time preferences. Instead, the debate between time neutralism and permissivism about time discounting boils down to a methodological question: can we ever criticize the content of preferences? If so, we should embrace time neutralism. (shrink)

Working in the weakening of constructive Zermelo-Fraenkel set theory in which the subset collection scheme is omitted, we show that the binary refinement principle implies all the instances of the exponentiation axiom in which the basis is a discrete set. In particular binary refinement implies that the class of detachable subsets of a set form a set. Binary refinement was originally extracted from the fullness axiom, an equivalent of subset collection, as a principle that was sufficient to prove that the (...) Dedekind reals form a set. Here we show that the Cauchy reals also form a set. More generally, binary refinement ensures that one remains in the realm of sets when one starts from discrete sets and one applies the operations of exponentiation and binary product a finite number of times. (shrink)

This paper is about time preferences, the phenomenon that the very same things are usually considered the less valuable the farther in the future they are obtained. The utilities of those things are discounted at a certain rate. The paper presents a novel normative argument for exponential discount rates, whatever their empirical adequacy. It proposes to take indexical utility seriously, i.e. utilities referring to indexical propositions (that speak of ‘I’, ‘now’, etc.) as opposed to non-indexical propositions. Economic focus (...) is only on the latter, while the former are neglected. The potential ignorance of when is now generates a difference between indexical and non-indexical utility that can be exploited for a novel argument in favour of exponential discount rates. (shrink)

The exponential Papapetrou metric induced by scalar field conforms to observational data not worse than the vacuum Schwarzschild solution. Here, we analyze the origin of this metric as a peculiar space-time within a wide class of scalar and antiscalar solutions of the Einstein equations parameterized by scalar charge. Generalizing the three families of static solutions obtained by Fisher, Janis et al. :878. https://doi.org/10.1103/PhysRevLett.20.878, 1968), and Xanthopoulos and Zannias :2564, 1989), we prove that all three reduce to the same (...) exponential metric provided that scalar charge is equal to central mass, thereby suggesting the universal character of such background scalar field. (shrink)

This paper deals with stochastically globally exponential stability for stochastic impulsive differential systems with discrete delays and infinite distributed delays. By using vector Lyapunov function and average dwell-time condition, we investigate the unstable impulsive dynamics and stable impulsive dynamics of the suggested system, and some novel stability criteria are obtained for SIDSs with DDs and IDDs. Moreover, our results allow the discrete delay term to be coupled with the nondelay term, and the infinite distributed delay term to be (...) coupled with the nondelay term. Finally, two examples are given to verify the effectiveness of our theories. (shrink)

Four decades have passed since the EU and China established diplomatic relations in 1975, and now became mutually indispensable economic partners, presenting both an opportunity and challenge. During that time, after the first market reforms were introduced in 1978, China has transitioned from a predominantly agricultural to industrial and service-oriented economy. On 11 December 2001, China also became the 143rd member of the WTO. The aim of this research is to quantitatively compare the US, EU and Chinese GDP from (...) 1995 to 2014, the US and Chinese outward FDI from 1995 to 2013, and the EU 28 Total Imports from and Exports to the US and China between 2002 to 2014, and analyse the impact of the exponentially rising Chinese investments in the European Union (EU). We have found that while the US economy experienced a regression in general, and exhibited outward FDI exponential decrease in particular, the Chinese outward FDI sustained an exponential growth. Our analysis has shown that the now weakened US dollar and diminished US economic and industrial power, along with the US designed and archaic post World War II European institutions, vitiated by the recent US Economic Recession, which has swept along the EU and all other US dependent foreign economies globally, are and will continue to experience the primary impact of the exponentially rising economic investment of China in the EU. Furthermore, we have found that the Chinese economic growth has been affecting both the EU identity and policies. Yet, its full effect is waiting to be realized. The Chinese investment in the EU is estimated to peak during the next decade, when China will become by far the foremost economic partner of the EU. This crossroad may be reached as soon as in few years’ time and contribute towards the EU – Asian regional stabilization. In the changing context of the Sino – EU - US relations, due to the exponentially growing economic prosperity and rising global influence of China, the EU international institutions and socio-political structures will re-emerge with the once forgotten access to the 21st Century Silk Road Economic Belt, “The Silk Road II”, between China and the EU in the foreseeable future. (shrink)

Extreme events, which are usually characterized by generalized extreme value models, can exhibit long-term memory, whose impact needs to be quantified. It was known that extreme recurrence intervals can better characterize the significant influence of long-term memory than using the GEV model. Our statistical analyses based on time series datasets following the Lévy stable distribution confirm that the stretched exponential distribution can describe a wide spectrum of memory behavior transition from exponentially distributed intervals to power-law distributed ones, extending (...) the previous evaluation of the stretched exponential function using Gaussian/exponential distributed random data. Further deviation and discussion of a historical paradox are also provided, based on the theoretical analysis of the Bayesian law and the stretched exponential distribution. (shrink)

Education is increasingly vocational and structured to serve the ongoing exponential increase in economic growth. Climate change is an outcome of these same economic values and praxes. Attempts to shift these values and our approach to technology are continually absorbed and overcome by the pressing motif of economic growth. In this article, Ruth Irwin uses Martin Heidegger's concept of the technological enframing of modernity to view economic growth. John Maynard Keynes's notion of economic growth has impacted the pace of (...) consumerism that now permeates every aspect of knowing about the world we live in. Irwin asks us to think through technological enframing anew by looking to an early mechanical Greek artifact, the Antikythera mechanism, which depicts a cyclical notion of time used by ancient cultures to define the rhythm of economic productivity. The earth-centric cosmos embodied by this mechanism helped the Mesopotamian economy stay within the parameters of the local ecology and demonstrates that cyclical economic growth may enable a civilization to maintain a steady state over time and survive for millennia. An earth-centric cosmology creates a different set of values, one that emphasizes the need to regulate the pace of consumerism rather than allowing it free rein “as by an Invisible Hand.” The role of education in this exploration is twofold: first, it is a pivotal site for cultural exploration and transformation; and second, the expectations of the state strictly limit the forms education can take, so that as long as promoting economic growth defines state expectations, education will remain subservient to these values. If we aim to overcome climate change, Irwin concludes, we need to transform the expectations for education from society as well as from teachers. (shrink)

Considering the three intrinsic components of streamflow time series, the overall performance of the streamflow modeling tool is associated with the correct estimation of these components. In this study, a new hybrid method based on the wavelet transform as a multiresolution forecasting tool and exponential smoothing method, with two presented scenarios, was introduced. To this end, the performance of the proposed method was investigated versus four conventional methods of the autoregressive integrated moving average, ES ad-hoc, artificial neural network, (...) and wavelet-ANN for daily and monthly streamflow modeling of West Nishnabotna and Trinity River watersheds with different hydro-geomorphological conditions. In the presented WES technique, firstly, WT is employed for decomposing the observed signal to one approximation and more diverse components of subseries. Then, for the first scenario, only two subseries are introduced to the model as input parameters; however, for the second scenario, decomposed subseries are separately used as the inputs of ES models. The obtained results indicated that combining WT with the ES method and ANN led to more accurate modeling. The proposed methodology that used all decomposed subseries separately improved the efficiency of models up to 30% and 10% for the daily dataset and up to 88% and 57% for the monthly dataset, respectively, for the West Nishnabotna and Trinity Rivers. (shrink)

The central problem considered in this paper is whether a given recursive structure is recursively isomorphic to a polynomial-time structure. Positive results are obtained for all relational structures, for all Boolean algebras and for the natural numbers with addition, multiplication and the unary function 2x. Counterexamples are constructed for recursive structures with one unary function and for Abelian groups and also for relational structures when the universe of the structure is fixed. Results are also given which distinguish primitive recursive (...) structures, exponential-time structures and structures with honest witnesses. (shrink)

A world product time series covering two million years is well fit by either a sum of four exponentials, or a constant elasticity of substitution (CES) combination of three exponential growth modes: “hunting,” “farming,” and “industry.” The CES parameters suggest that farming substituted for hunting, while industry complemented farming, making the industrial revolution a smoother transition. Each mode grew world product by a factor of a few hundred, and grew a hundred times faster than its predecessor. This weakly (...) suggests that within the next century a new mode might appear with a doubling time measured in days, not years. (shrink)

Time discounting is the phenomenon that a desired result in the future is perceived as less valuable than the same result now. Economic theories can take this psychological fact into account in several ways. In the economic literature the most widely used type of additive time discounting is exponential discounting. In exponential discounting, the fall of valuation depends by a constant factor on the length of the delay period. It is well known, however, that exponential (...) time discounting often does not describe well how people actually behave. Most people are averse to short delays in gratification now, while their future selves may not mind a bit of extra waiting. This behaviour can be described well by non-exponential discounting functions such as hyperbolic discounting. In hyperbolic discounting, valuations fall rapidly for small delay periods, but the fall gets slower for longer delay periods. Hyperbolic discounting captures phenomena such as procrastination, addiction and in general inconsistency over time. This chapter investigates whether forms of non-exponential discounting, in particular close to the so called Quasi-Hyperbolic model, could also be characterized in terms of dynamically consistent choices when individuals discount the welfare of future selves as well as their payoffs. (shrink)

What if gravity satisfied the Klein-Gordon equation? Both particle physics from the 1920s-30s and the 1890s Neumann-Seeliger modification of Newtonian gravity with exponential decay suggest considering a "graviton mass term" for gravity, which is _algebraic_ in the potential. Unlike Nordström's "massless" theory, massive scalar gravity is strictly special relativistic in the sense of being invariant under the Poincaré group but not the 15-parameter Bateman-Cunningham conformal group. It therefore exhibits the whole of Minkowski space-time structure, albeit only indirectly concerning (...) volumes. Massive scalar gravity is plausible in terms of relativistic field theory, while violating most interesting versions of Einstein's principles of general covariance, general relativity, equivalence, and Mach. Geometry is a poor guide to understanding massive scalar gravity: matter sees a conformally flat metric due to universal coupling, but gravity also sees the rest of the flat metric in the mass term. What is the 'true' geometry, one might wonder, in line with Poincaré's modal conventionality argument? Infinitely many theories exhibit this bimetric 'geometry,' all with the total stress-energy's trace as source; thus geometry does not explain the field equations. The irrelevance of the Ehlers-Pirani-Schild construction to a critique of conventionalism becomes evident when multi-geometry theories are contemplated. Much as Seeliger envisaged, the smooth massless limit indicates underdetermination of theories by data between massless and massive scalar gravities---indeed an unconceived alternative. At least one version easily could have been developed before General Relativity; it then would have motivated thinking of Einstein's equations along the lines of Einstein's newly re-appreciated "physical strategy" and particle physics and would have suggested a rivalry from massive spin 2 variants of General Relativity. The Putnam-Grünbaum debate on conventionality is revisited with an emphasis on the broad modal scope of conventionalist views. Massive scalar gravity thus contributes to a historically plausible rational reconstruction of much of 20th-21st century space-time philosophy in the light of particle physics. An appendix reconsiders the Malament-Weatherall-Manchak conformal restriction of conventionality and constructs the 'universal force' influencing the causal structure. Subsequent works will discuss how massive gravity could have provided a template for a more Kant-friendly space-time theory that would have blocked Moritz Schlick's supposed refutation of synthetic _a priori_ knowledge, and how Einstein's false analogy between the Neumann-Seeliger-Einstein modification of Newtonian gravity and the cosmological constant \Lambda generated lasting confusion that obscured massive gravity as a conceptual possibility. (shrink)

Weak measurements offer new insights into the behavior of quantum systems. Combined with post-selection, quantum mechanics predicts a range of new experimentally testable phenomena. In this paper I consider weak measurements performed on time-dependent pre- and post-selected ensembles, with emphasis on the decay of excited states. The results show that the standard exponential decay law is a limiting case of a more general law that depends on both the time of post-selection and the choice of final state. (...) The generalized law is illustrated for two interesting choices of post-selection. (shrink)

Craig Callender attempts to overturn conventional wisdom within decision theory by contending that rational intertemporal choices need not always conform to an exponential discounting function. He argues that there are cases in which hyperbolic discounting is the height of rationality. This paper does not seek to undermine Callender’s conclusions, but instead raises two interrelated theoretical concerns with his way securing them. The first concern is with his dismissal of influential dual-system explanations of rationality. It is argued that Callender’s criticisms (...) of said explanations fail to assess them at anything like their full weight. It is then suggested that dual-systems approaches in cognitive science do have substantial theoretical problems, but that Callender fails to identify them. The second concern builds on the first and suggests that Callender’s arguments against consensus normative standards might motivate a more dramatically reimagined notion of rationality than the one he seems to embrace. (shrink)

Under the presupposition that human time perception is distorted in intertemporal choice, this study constructs a time scale in the framework of axiomatic measurement. First, the conditions (homogeneity of degree one or two) to identify the form of a time scale are proposed so that one can determine whether the hyperbolic or exponential is a more suitable function for modeling people’s discounting. Homogeneity of degree one implies that subjective time delay is measured by a power (...) scale and its discount function becomes a power-exponential type, whereas homogeneity of degree two implies that subjective time delay is measured by a log scale and its discount function becomes a hyperbolic type. Second, a method is shown for constructing a model that can reflect subadditive and superadditive discounting. A non-commutative and non-associative concatenation operation is provided to generate a time string consisting of subdivided durations that incorporates the effect of repeated delay with a subdivided duration. The discounting model is yielded by substituting these strings in an exponential model equipped with a generalized time scale, and the determination of subadditivity or superadditivity depends on whether the discount function value of a product by the non-commutative and non-associative operation is, respectively, smaller or greater than that of a product by an operation of the usual extensive structure. (shrink)

We consider the time delay of massive, non-relativistic, one-dimensional particles due to a tunneling potential. In this setting the well-known Hartman effect asserts that often the sub-ensemble of particles going through the tunnel seems to cross the tunnel region instantaneously. An obstacle to the utilization of this effect for getting faster signals is the exponential damping by the tunnel, so there seems to be a trade-off between speedup and intensity. In this paper we prove that this trade-off is (...) never in favor of faster signals: the probability for a signal to reach its destination before some deadline is always reduced by the tunnel, for arbitrary incoming states, arbitrary positive and compactly supported tunnel potentials, and arbitrary detectors. More specifically, we show this for several different ways to define “the same incoming state” and “the same detector” when comparing the settings with and without tunnel potential. The arrival time measurements are expressed in the time-covariant approach, but we also allow the detection to be a localization measurement at a later time. (shrink)

Modelling of contagious disease usually employs compartmental SEIR-like models where the waiting times in respective compartments are exponentially distributed. In this paper, we are interested in investigating how the distributions of sojourn times in infective compartments affect the dynamics and persistence of the contagious bovine pleuropneumonia, a chronic respiratory disease of cattle. Two kinds of extreme distributions of the sojourn times are considered: a Dirac delta-function and truncated Gaussian function leading to a model with (non-constant) delay and the classical (...) class='Hi'>exponential distribution that stands for a model without delay. Expressions of the basic reproductive numbers are derived and dynamical behaviours are discussed for the three models. It is found that the spreading of disease exhibits wave-like oscillations for the time-delay dynamics. In contrast, the disease appears to last longer when the spreading is described by the classical dynamics without delay. Subsequently, the time-delay dynamics turns out to be more appropriate for the description of an experimental epidemic of CBPP. (shrink)

To express fine-grained resource-sensitive reasoning, a temporal soft linear logic (TSLL) is introduced as an extension of both Girard's (propositional classical) linear logic (CLL) and Lafont's (propositional classical) soft linear logic (SLL). It is known that the linear exponential operator in CLL can express a specific infinitely reusable resource, i.e. it is reusable not only for any number, but also many times. In contrast, the soft exponential operator in SLL, which is a weak version of the linear (...) class='Hi'>exponential operator, can express a specific usable resource, i.e. it is usable in any number, but only once (i.e. it is consumed after use). In TSLL, the resource operators (i.e. linear and soft exponentials) and some temporal operators are combined based on the interpretation that “time” is regarded as a “resource”. The completeness theorem (with respect to phase semantics) for TSLL and the cut-elimination and decidability theorems for some subsystems of TSLL are proved as the main results of this paper. A decidable subsystem, called a bounded soft linear logic (BSLL), which has a restricted soft exponential operator, can represent a specific finitely usable resource. (shrink)

Accurate prediction of battery quality using early-cycle data is critical for battery, especially lithium battery in microgrid networks. To effectively predict the lifetime of lithium-ion batteries, a time series classification method is proposed that classifies batteries into high-lifetime and low-lifetime groups using features extracted from early-cycle charge-discharge data. The proposed method is based on a smooth localized complex exponential model that can extract battery features from time-frequency maps and self-adaptively select the time-frequency resolution to maximize the (...) discrepancy of data from the two groups. A smooth localized complex exponential periodogram is then calculated to obtain the time-frequency decomposition of the whole time series data for further classification. The experimental results show that, by using battery features extracted from the first 128 charge-discharge processes, the proposed method can accurately classify batteries into high-lifetime and low-lifetime groups, with classification accuracy and specificity as high as 95.12% and 92.5%, respectively. (shrink)

Freight transportation plays a critical role in improving company performance in the modern manufacturing industry. To reduce costs, companies must take advantage of the use of large vehicles. It caused fewer deliveries, but inventory costs and degradation quality are high. One of the joint economic lot size problems in supply chain is Integrated Single-Vendor Single-Buyer Inventory Problem. This study developed the I-SVSB-IP model that considers raw materials’ exponential quality degradation and transportation costs. The objective function of this research was (...) to maximize the Joint Total Profit. Three decision variables used were inventory cycle time, raw material ordering frequency, and frequency of delivery of finished products to buyers. This study proposed a sophisticated Chimp Optimization Algorithm procedure to solve the I-SVSB-IP problem. A case study on the food industry in Indonesia was presented to optimize the I-SVSB-IP. The results showed that the ChOA procedure had produced an optimal solution compared to the state-of-the-art algorithm. This study also demonstrated a sensitivity analysis of decision and transportation variables to cost, revenue, and JTP. The results show that increasing transport frequency of ordering raw materials and finished products to buyers enhances the total cost and reduces joint total profit. In addition, increasing the rate of quality degradation of raw materials reduces JTP. (shrink)

We propose a new integrative framework of external time monitoring in prospective memory (PM) tasks and its relation with performance. Starting from existing empirical regularities and our theoretical analysis, the framework predicts that external monitoring in PM tasks comprises a first stage of loose monitoring to keep track of the passage of time, and a subsequent stage of finer-grained monitoring, based on interval reduction, to meet the PM deadline. Following our framework, we predicted and observed in three different (...) datasets (N = 375): (1) a marked increase in external monitoring frequency in the final part of the period of the PM task, well captured by a proportional rate exponential growth function; (2) a positive association between individual compliance with this monitoring pattern and PM performance; (3) a positive relation between monitoring frequency in the time window immediately preceding the PM deadline and PM performance at the individual level; and (4) good individual compliance with an interval reduction pattern in external monitoring, especially in the time window closer to the PM deadline. These results support the proposed integrative framework, which has the potential to foster future research on external monitoring in PM and in other fields of cognitive science. (shrink)

In 1984, Danecki proved that satisfiability in IPDL, i.e., Propositional Dynamic Logic (PDL) extended with an intersection operator on programs, is decidable in deterministic double exponential time. Since then, the exact complexity of IPDL has remained an open problem: the best known lower bound was the ExpTime one stemming from plain PDL until, in 2004, the first author established ExpSpace-hardness. In this paper, we finally close the gap and prove that IPDL is hard for 2-ExpTime, thus 2-ExpTime-complete. We (...) then sharpen our lower bound, showing that it even applies to IPDL without the test operator interpreted on tree structures. (shrink)

Irregularity may occur on the earth’s surface in the form of mountains due to the imperfection of the earth’s crust. To explore the influence of horizontally polarized shear waves on mountains, we considered the fluid-saturated porous medium over an orthotropic semi-infinite medium with rigid and soft mountain surfaces for wave propagation. The mountain surface is defined mathematically as a periodic function of the time domain. The physical interpretation of materials’ structure has been explained in rectangular Cartesian coordinate system originated (...) at the contact interface of layer and half-space. The displacement of the mountains has been derived by solving energy equations analytically. The influence of rigid and soft mountain surfaces on the phase velocity of shear waves has been demonstrated graphically. (shrink)

Reinforcement schemes are a class of non-Markovian stochastic processes. Their non-Markovian nature allows them to model some kind of memory of the past. One subclass of such models are those in which the past is exponentially discounted or forgotten. Often, models in this subclass have the property of becoming trapped with probability 1 in some degenerate state. While previous work has concentrated on such limit results, we concentrate here on a contrary effect, namely that the time to become trapped (...) may increase exponentially in 1/x as the discount rate, 1− x, approaches 1. As a result, the time to become trapped may easily exceed the lifetime of the simulation or of the physical data being modeled. In such a case, the quasi-stationary behavior is more germane. We apply our results to a model of social network formation based on ternary (three-person) interactions with uniform positive reinforcement. (shrink)

In this paper, a discrete-time dynamic duopoly model, with nonlinear demand and cost functions, is established. The properties of existence and local stability of equilibrium points have been verified and analyzed. The stability conditions are also given with the help of the Jury criterion. With changing of the values of parameters, the system shows some new and interesting phenomena in terms to stability and multistability, such as V-shaped stable structures and different shape basins of attraction of coexisting attractors. The (...) eye-shaped structures appear where the period-doubling and period-halving bifurcations occur. Finally, by utilizing critical curves, the changes in the topological structure of basin of attraction and the reason of “holes” formation are analyzed. As a result, the generation of global bifurcation, such as contact bifurcation or final bifurcation, is usually accompanied by the contact of critical curves and boundary. (shrink)

In the last few decades, great progress has been made in both genetic and genomic research. The development of the Human Genome Project has increased our knowledge of the genetic basis of diseases and has given a tremendous momentum to the development of new technologies that make widespread genetic testing possible and has increased the availability of previously inaccessible genetic information. Two examples of this exponential evolution are the increasing implementation of next-generation sequencing technologies in the clinical context and (...) the expanding commercial offer of genetic tests directly-to-consumers.Firstly, the rapid development of next generation sequencing technologies has substantially reduced both the cost and the time required to sequence an entire human genome. These technologies are increasingly being used in the clinical setting with the goal of diagnosing conditions of presumed genetic origin that cannot be explained by targeted sequencing approaches. (shrink)

This paper investigates two assumptions of the exponential discounted utility theory (EDU) to which Callender draws our attention: namely that we can cleanly distinguish pure from impure temporal preferences, and that past discounting can be ignored. Drawing on recent empirical work in this area, we argue that in so far as one might have thought that past-directed preferences are more pure than future ones, then there is evidence that people’s pure preferences (in so far as we can make sense (...) of that notion) show more interpersonal variation than has previously been thought. (shrink)

The intuition guiding the de…nition of computation has shifted over time, a process that is re‡ected in the changing formulations of the Church-Turing thesis. The theory of computation began with logic and gradually moved to the capacity of …nite automata. Consequently, modern computer models rely on general physical principles, with quantum computers representing the extreme case. The paper discusses this development, and the challenges to the Church-Turing thesis in its physical form, in particular, Kieu’s quantum computer and relativistic hyper-computation. (...) Finally, the robustness of the boundary between polynomial and exponential time complexity is considered in connection with quantum computers and quantum information theory. (shrink)

Each phenomenon contains variable components, which are conservative. Because of their conservation, they accumulate. Present phenomena contain constituents of phenomena, belonging to the past which form the present and the future, and their dependence on time is an exponential one - S = Sₒe^t-tᵖ. We assume that before and after tₒ = t-tᵖ = 0 the change pertains to phenomena of one type. The dependency is for each defined phenomenon of one and the same type. The concrete aspect (...) of the change S will depend on the type of the phenomenon. We show in our study how in some cosmological phenomena, the exponential dependence on time is present. The processes of radioactive disintegration of atomic nuclei, are also phenomena of this type. We present the real phenomena as a sum of exponents. Each phenomenon originates, develops and is destroyed. In reality most phenomena are formed as a composition of exponential dependencies of the change. (shrink)

Each phenomenon contains variable components, which are conservative. Because of their conservation, they accumulate. Present phenomena contain constituents of phenomena, belonging to the past which form the present and the future, and their dependence on time is an exponential one - S = Sₒe^t-tᵖ. We assume that before and after tₒ = t-tᵖ = 0 the change pertains to phenomena of one type. The dependency is for each defined phenomenon of one and the same type. The concrete aspect (...) of the change S will depend on the type of the phenomenon. We show in our study how in some cosmological phenomena, the exponential dependence on time is present. The processes of radioactive disintegration of atomic nuclei, are also phenomena of this type. We present the real phenomena as a sum of exponents. Each phenomenon originates, develops and is destroyed. In reality most phenomena are formed as a composition of exponential dependencies of the change. (shrink)

When attempting to predict future events, people commonly rely on historical data. One psychological characteristic of judgmental forecasting of time series, established by research, is that when people make forecasts from series, they tend to underestimate future values for upward trends and overestimate them for downward ones, so-called trend-damping. Events in a time series can be experienced sequentially, or they can also be retrospectively viewed simultaneously, not experienced individually in real time. In one experiment, we studied the (...) influence of presentation mode on two sorts of judgment: predictions of the next event and estimation of the average value of all the events in the presented series. Participants' responses in dynamic mode were anchored on more recent events than in static mode for all types of judgment but with different consequences; hence, dynamic presentation improved prediction accuracy, but not estimation. These results are not anticipated by existing theoretical accounts; we develop and present an agent-based model—the adaptive anchoring model —to account for the difference between processing sequences of dynamically and statically presented stimuli. ADAM captures how variation in presentation mode produces variation in responses in both forecasting and judgment tasks. ADAM's model predictions for the forecasting and judgment tasks fit better with the response data than a linear-regression time series model. Moreover, ADAM outperformed autoregressive-integrated-moving-average and exponential-smoothing models, while neither of these models accounts for people's responses on the average estimation task. (shrink)