In the present paper some tools are given to state the exact number of roots for some simple classes of exponential terms . The result were obtained by generalizing Sturm's technique for real closed fields. Moreover for arbitrary non-zero terms t certain estimations concerning the location of roots of t are given. MSC: 03C65, 03C60, 12L12.

Assuming “Schanuel's Condition” for a certain class of exponential fields, Sturm's technique for polynomials in real closed fields can be extended to more complicated exponential terms in the corresponding exponential field. Hence for this class of terms the exact number of zeros can be calculated. These results give deeper insights into the model theory of exponential fields. MSC: 03C65, 03C60, 12L12.

In this paper we prove, modulo Schanuel's Conjecture, that there are algorithms which decide if two exponential polynomials in π are equal in ℝ and if two exponential polynomials in π and i coincide in ℂ.

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)

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)

V i 2 ⊢A iff for some term t :S i 2 ⊢ “2 i exists→ A”, a bounded first-order formula, i ≥1. V i 2 is not Π b 1 -conservative over S i 2 . Any model of V 2 not satisfying Exp satisfies the collection scheme BΣ 0 1 . V 1 3 is not Π b 1 -conservative over S 2.

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)

We characterize the sets of all Π2 and all equation image theorems of IΠ−1 in terms of restricted exponentiation, and use these characterizations to prove that both sets are not deductively equivalent. We also discuss how these results generalize to n > 0. As an application, we prove that a conservation theorem of Beklemishev stating that IΠ−n + 1 is conservative over IΣ−n with respect to equation image sentences cannot be extended to Πn + 2 sentences. © 2011 WILEY-VCH (...) Verlag GmbH & Co. KGaA, Weinheim. (shrink)

The sunspot data seems to indicate that the Sun is likely to enter Maunder Minimum, then it will mean that low Sun activity may cause low temperature in Earth. If this happens then it will cause a phenomenon which is called by some climatology experts as “The Little Ice Age” for the next 20-30 years, starting from the next few years. Therefore, the Earth climate in the coming years tend to be cooler than before. This phenomenon then causes us to (...) ask: what can we do as human being in Earth to postpone or avoid the worsening situation in terms of Earth cooling temperature in the coming years? We think this is a more pressing problem for the real and present danger that we are facing in the Earth. What we are suggesting in this paper is that perhaps it is possible to model Sun-Earth interaction in terms of Shannon entropy. Since Shannon entropy can be expressed as bits of information, then it would mean that perhaps we can do something with Earth temperature by controlling the amount of information transfer and storage in the Earth. This proposal is somewhat in resemblance with message of a 2012 movie “A Thousand words” where we shall strive to love our neighbours and nature, instead of being absorbed in a culture of less-meaningful fast-talk (starred by Eddie Murphy). (shrink)

We develop a combinatorial model to study the evolution of graphs underlying proofs during the process of cut elimination. Proofs are two-dimensional objects and differences in the behavior of their cut elimination can often be accounted for by differences in their two-dimensional structure. Our purpose is to determine geometrical conditions on the graphs of proofs to explain the expansion of the size of proofs after cut elimination. We will be concerned with exponential expansion and we give upper and lower (...) bounds which depend on the geometry of the graphs. The lower bound is computed passing through the notion of universal covering for directed graphs. In this paper we present ground material for the study of cut elimination and structure of proofs in purely combinatorial terms. We develop a theory of duplication for directed graphs and derive results on graphs of proofs as corollaries. (shrink)

Given an ordered fieldK, we compute the natural valuation and skeleton of the ordered multiplicative group (K >0, ·, 1, <) in terms of those of the ordered additive group (K,+,0,<). We use this computation to provide necessary and sufficient conditions on the value groupv(K) and residue field $\bar K$ , for theL ∞ε-equivalence of the above mentioned groups. We then apply the results to exponential fields, and describev(K) in that case. Finally, ifK is countable or a power (...) series field, we derive necessary and sufficient conditions onv(K) and $\bar K$ forK to be exponential. In the countable case, we get a structure theorem forv(K). (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)

Using coding devices based on a theorem due to Zsigmondy, Birkhoff and Vandiver, we first define in terms of successor S and coprimeness predicate $\perp$ a full arithmetic over the set of powers of some fixed prime, then we define in the same terms a restriction of the exponentiation. Hence we prove the main result insuring that all arithmetical relations and functions over prime powers and their opposite are $\{S, \perp\}$ -definable over Z. Applications to definability over Z (...) and N are stated as corollaries of the main theorem. (shrink)

This contribution is aimed at some provocation by questioning the basic assumptions of current development discourse. It asks for conceptual clarification and differentiation on the meaning of various process terms. It needs to be recognised that the word development remains a metaphor than can indeed be extended but can also become over-extended and ossified. The concept of development is then contrasted with the process of maturation. It is argued that the concept of maturation is, better able to indicate the (...) final goal of the process than most other process terms, recognises inherent limitations and follows natural cycles better than exponential growth, sustained development or endless progress. (shrink)

In terms of medical science and legal responsibility, the sleep disorder category of parasomnias, chiefly REM sleep behavior disorder and somnambulism, pose an enigmatic dilemma. During an episode of parasomnia, individuals are neither awake nor aware, but their actions appear conscious. As these actions move beyond the innocuous, such as eating and blurting out embarrassing information, and enter the realm of rape and homicide, their degree of importance and relevance increases exponentially. Parasomnias that result in illegal activity, particularly violence, (...) are puzzling phenomena for medicine and the law. Via a review of the pertinent medical literature, a general overview of the current scientific knowledge of parasomnias will be provided. Though this knowledge is far from complete, it can provide some neurobiological information about the nature of parasomnia, including conclusions about a sleepwalker’s level of intention as well as factors that predispose one to such episodes. Although a parasomniac’s complete lack of consciousness warrants acquittal from criminal liability, it does not exclude responsibility for subjecting oneself to exacerbating factors that result in these violent parasomnias. Individuals should be held accountable if they could be expected to control these factors. In addition, they should undergo appropriate treatment and management in order to prevent future parasomnia behaviors. Establishing a legal defense for parasomnia will prove difficult due to the strong potential for malingering, so specific criteria will be outlined in order to distinguish between true and fraudulent claims of crimes committed during parasomniac states. (shrink)

We give an exponential lower bound on number of proof-lines in the proof system K of modal logic, i.e., we give an example of K-tautologies ψ₁, ψ₂,... s.t. every K-proof of ψi must have a number of proof-lines exponential in terms of the size of ψi. The result extends, for the same sequence of K-tautologies, to the systems K4, Gödel—Löb's logic, S and S4. We also determine some speed-up relations between different systems of modal logic on formulas (...) of modal-depth one. (shrink)

There has been an exponential rise in use of the term vulnerability across a number of political and policy arenas, including child protection, sexual offences, poverty, development, care for the elderly, patient autonomy, globalisation, war, public health and ecology. Yet despite its increasing deployment, the exact meaning and parameters of this concept remain somewhat elusive. In this article, we explore the interaction of two very different strategies—one in which vulnerability is relied upon by those seeking improved social justice as (...) a mechanism by which to identify, problematise and compel state responses to a universal condition of precarious dependency, and the other in which it is used as a category of neo-liberal governance which legitimates state encroachment whilst constructing ‘vulnerable’ individuals as ‘risk-managers’ who must behave ‘responsibly’ in the face of disadvantage. We suggest that the co-existence of these divergent approaches highlights the fluidity and malleability of the concept of vulnerability. Using sex work as a specific case study, we explore the ways in which vulnerability bears multiple meanings, and has been used in recent times in the furtherance of moralistic and regressive agendas, which collude with, rather than challenge, state power. Without seeking to reject the label or normative import of vulnerability, we call, therefore, for a more circumspect approach to its usage, and a more critical evaluation of recent claims which hail it as a mechanism, preferable to the conventional use of equality paradigms, by which to secure progressive feminist outcomes. (shrink)

“Hardwired” is a term commonly used to describe the properties of certain behaviors or brain regions. As its usage has increased exponentially in the past 50 years, both in popular media and the scholarly literature, the concept appears to have gained a cloak of respectability in scientific discourse. However, its specific meaning is difficult to pinpoint. In this paper, I examine how “hardwired” has been used in the psychological and neuroscientific literature. The analysis reveals two major themes: one centers on (...) certain purported characteristics of behaviors or brain regions, such as fixedness; the other places these and other characteristics within an evolutionary framework. Overall, the analysis reveals a degree of overlap between “hardwiring” and the folk biology concept of innateness. Various complications arise from such overlap, casting doubts on the usefulness and legitimacy of “hardwired” in scientific discourse. (shrink)

We give an exponential lower bound on the number of proof-lines in intuitionistic propositional logic, IL, axiomatised in the usual Frege-style fashion; i.e., we give an example of IL-tautologies A1,A2,… s.t. every IL-proof of Ai must have a number of proof-lines exponential in terms of the size of Ai. We show that the results do not apply to the system of classical logic and we obtain an exponential speed-up between classical and intuitionistic logic.

This paper is concerned with implicit computational complexity of the exptime computable functions. Modifying the lexicographic path order, we introduce a path order EPO. It is shown that a termination proof for a term rewriting system via EPO implies an exponential bound on the lengths of derivations. The path order EPO is designed so that every exptime function is representable as a term rewrite system compatible with EPO (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim).

In the last two decades, interest in narrative conceptions of identity has grown exponentially, though there is little agreement about what a "life-narrative" might be. In connecting Kierkegaard with virtue ethics, several scholars have recently argued that narrative models of selves and MacIntyre's concept of the unity of a life help make sense of Kierkegaard's existential stages and, in particular, explain the transition from "aesthetic" to "ethical" modes of life. But others have recently raised difficult questions both for these readings (...) of Kierkegaard and for narrative accounts of identity that draw on the work of MacIntyre in general. While some of these objections concern a strong kind of unity or "wholeheartedness" among an agent's long-term goals or cares, the fundamental objection raised by critics is that personal identity cannot _be_ a narrative, since stories are artifacts made by persons. In this book, Davenport defends the narrative approach to practical identity and autonomy in general, and to Kierkegaard's stages in particular. (shrink)

This paper proposes communities of practice (CoP) as a process to build moral resilience in healthcare settings. We introduce the starting point of moral distress that arises from ethical challenges when actions of the healthcare professional are constrained. We examine how situations such as the current COVID-19 pandemic can exponentially increase moral distress in healthcare professionals. Then, we explore how moral resilience can help cope with moral distress. We propose the term collective moral resilience to capture the shared capacity arising (...) from mutual engagement and dialogue in group settings, towards responding to individual moral distress and towards building an ethical practice environment. Finally, we look at CoPs in healthcare and explore how these group experiences can be used to build collective moral resilience. (shrink)

We prove almost sure exponential stability for the disease-free equilibrium of a stochastic differential equations model of an SIR epidemic with vaccination. The model allows for vertical transmission. The stochastic perturbation is associated with the force of infection and is such that the total population size remains constant in time. We prove almost sure positivity of solutions. The main result concerns especially the smaller values of the diffusion parameter, and describes the stability in terms of an analogue $$\mathcal{R}_\sigma$$ (...) of the basic reproduction number $$\mathcal{R}_0$$ of the underlying deterministic model, with $$\mathcal{R}_\sigma \le \mathcal{R}_0$$. We prove that the disease-free equilibrium is almost sure exponentially stable if $$\mathcal{R}_\sigma <1$$. (shrink)

With unbridled exponential economic growth, earth systems and social systems are headed for catastrophic meltdown. Meanwhile, much of humanity is highly dependent on current institutions. Second-order cybernetics can help society come to grips with the enormous demand of adapting existing institutions for a regenerative economy. While the current trajectory of increasing consumption and rapid ecological decay will lead to collapse, the progress achieved by civilization can be vindicated by large-scale investment in regenerating natural capital assets, developing open-source technologies for (...) the public good, and rebuilding local agricultural economies dedicated to health and well-being. It is recommended that regenerative practices are supported by academic institutions centered on place-based service-learning. A regenerative economy, in contrast to a growth economy, is part of the pursuit of the long-term establishment of a steady-state economy. This vision does not limit the possibility that humanity will make outstanding technological progress, explore space or merge with artificial intelligence – but argues that appreciating the nature’s technology provided to humanity through eons evolution, and avoiding short-term self-destruction should be priorities. (shrink)

Luxury consumption has grown exponentially across the globe. This growth was fuelled more by the emerging non-Western countries such as India. Consumers in this country are more tech savvy and are a new set of individuals who are totally different from the old, conventional consumers of the Western countries. These new individuals consume luxury to develop their digital self. Unfortunately, this area is not researched in the literature. This article fills this lacuna in extant literature. To address this issue, we (...) comprehensively reviewed the current research from the area of luxury consumption, digital usage, digital self and subsequently developed a conceptual framework. This framework has three stages: individual that has interpersonal, power, symbolic and emotional needs; social dimension that is formulated and develops from the reference groups. Further, individuals develop the ‘we approach’ along with social groups. This approach is associated with strong ties, fortified nods, positive interactions and exclusivity. These elements lead to the development of digital self that provides happiness and pleasure to the individuals in terms of luxury consumption. (shrink)

The capacity to collect and analyse data is growing exponentially. Referred to as ‘Big Data’, this scientific, social and technological trend has helped create destabilising amounts of information, which can challenge accepted social and ethical norms. Big Data remains a fuzzy idea, emerging across social, scientific, and business contexts sometimes seemingly related only by the gigantic size of the datasets being considered. As is often the case with the cutting edge of scientific and technological progress, understanding of the ethical implications (...) of Big Data lags behind. In order to bridge such a gap, this article systematically and comprehensively analyses academic literature concerning the ethical implications of Big Data, providing a watershed for future ethical investigations and regulations. Particular attention is paid to biomedical Big Data due to the inherent sensitivity of medical information. By means of a meta-analysis of the literature, a thematic narrative is provided to guide ethicists, data scientists, regulators and other stakeholders through what is already known or hypothesised about the ethical risks of this emerging and innovative phenomenon. Five key areas of concern are identified: informed consent, privacy, ownership, epistemology and objectivity, and ‘Big Data Divides’ created between those who have or lack the necessary resources to analyse increasingly large datasets. Critical gaps in the treatment of these themes are identified with suggestions for future research. Six additional areas of concern are then suggested which, although related have not yet attracted extensive debate in the existing literature. It is argued that they will require much closer scrutiny in the immediate future: the dangers of ignoring group-level ethical harms; the importance of epistemology in assessing the ethics of Big Data; the changing nature of fiduciary relationships that become increasingly data saturated; the need to distinguish between ‘academic’ and ‘commercial’ Big Data practices in terms of potential harm to data subjects; future problems with ownership of intellectual property generated from analysis of aggregated datasets; and the difficulty of providing meaningful access rights to individual data subjects that lack necessary resources. Considered together, these eleven themes provide a thorough critical framework to guide ethical assessment and governance of emerging Big Data practices. (shrink)

Firms strive hard to achieve a high degree of efficiency on the production frontier, and it is where they compete to excel with their competitors. It is observed from previous studies that standardizing some policies and developing strategies could bring efficiency in production of manufacturing firms. New approaches to the measurement of productive efficiencies are being developed, and analysis of the subject is growing exponentially, since firms are now more concerned about the productivity frontier, besides others. This paper analyzes the (...) necessary factors that contribute to the productive efficiency of an organization. A simple model of production function is constructed to understand its essence and thus contributes to the development of a new ratio that defines productive efficiency in terms of maximization of the efficiency factor that is a common issue in industrial and manufacturing organizations. (shrink)

Bioethics has now become a burgeoning interdisciplinary field of scholarly investigation which has in the past decades migrated from bedside consultations to public policy debates and wider cultural and social consultations that privilege all discourse about everyday life issues. It has made exponential progress in addressing moral issues in science, technology and medicine in the world. In spite of this progress, core bioethics issues, approaches and values are still exclusively Western dominated and largely foreign to most African societies. Although (...) medical ethics has existed since the time of Hippocrates, in Africa, there is a noted sluggish growth and low prestige of ethics education as bioethics is not taught in most higher educational systems of learning, low understanding of its processes as researchers manifest a general lack of appreciation for bioethics and general ignorance characterize those involved in research about ethical practices. This is unfortunate, considering that various research that aim at finding solutions to the multiple problems affecting African societies and the need to address and assess these problems in ethical terms are of crucial importance to Africans. In this work, I argue that Africa lacks human, institutional, infrastructural capacities and a real African authenticity in bioethics. Additionally, African views on bioethics are neither sufficiently developed nor heard. Africans need to confront these current challenges of bioethics to their lives and communities and to develop African conceptions to incorporate African specificities and approaches. (shrink)

The nature of quantum computation is discussed. It is argued that, in terms of the amount of information manipulated in a given time, quantum and classical computation are equally efficient. Quantum superposition does not permit quantum computers to ''perform many computations simultaneously'' except in a highly qualified and to some extent misleading sense. Quantum computation is therefore not well described by interpretations of quantum mechanics which invoke the concept of vast numbers of parallel universes. Rather, entanglement makes available types (...) of computation processes which, while not exponentially larger than classical ones, are unavailable to classical systems. The essence of quantum computation is that it uses entanglement to generate and manipulate a physical representation of the correlations between logical entities, without the need to completely represent the logical entities themselves. (shrink)

The United States’ ambitious Precision Medicine Initiative proposes to accelerate exponentially the adoption of precision medicine, an approach to health care that tailors disease diagnosis, treatment, and prevention to individual variability in genes, environment, and lifestyle. It aims to achieve this by creating a cohort of volunteers for precision medicine research, accelerating biomedical research innovation, and adopting policies geared toward patients’ empowerment. As strategies to implement the PMI are formulated, critical consideration of the initiative's ethical and sociopolitical dimensions is needed. (...) Drawing on scholarship of nationalism and democracy, we discuss the PMI's construction of what we term “genomic citizenship”; the possible normative obligations arising therefrom; and the ethical, legal, and social challenges that will ensue. Although the PMI is a work in progress, discussion of the existing and emerging issues can facilitate the development of policies, structures, and procedures that can maximize the initiative's ability to produce equitable and socially sensitive outcomes. Our analysis can also be applied to other population-based, precision medicine research programs. (shrink)

The volume of clinical research is increasing exponentially—far beyond our ability to process and absorb the results. Given this situation, it may be beneficial to consider reducing the flow at its source. In what follows, I will motivate and critically evaluate the following proposal: researchers should conduct fewer clinical trials. More specifically, I c onsider whether researchers should be permitted to conduct only clinical research of very high quality and, in turn, whether research ethics committees should prohibit all other, lower-quality (...) research, even when it might appear to meet some minimal ethical standard. Following a close analysis of the social-value requirement of ethical clinical research, I argue that this proposal is defensible. The problem identified in this paper has two parts, quantity and quality, and some clarification is needed about the latter because “quality” is a highly contested term in the medical literature. When some scholars advocate for high-quality trials, they mean large-scale, simple, explanatory randomized controlled trials. Others, including myself, have defended a different characterization of high-quality research that tends more toward pragmatic trial design and the use of methods other than RCTs. Pragmatic trials aim to provide evidence that directly supports clinical decision-making in “usual” care settings. Unlike explanatory trials, which aim to abstract away from particular settings and patients, in the hopes of creating ideal conditions for the success of an intervention, pragmatic trials deliberately pursue knowledge of high applicability, through the use of representative subjects, clinically important questions, flexible treatment protocols, patient-oriented outcome measures, and so on. I see applicability as a marker of high-quality research. The context in which research is meant to be applied should be the context in which new interventions are evaluated. (shrink)

The concept of “representation” is used broadly and uncontroversially throughout neuroscience, in contrast to its highly controversial status within the philosophy of mind and cognitive science. In this paper I first discuss the way that the term is used within neuroscience, in particular describing the strategies by which representations are characterized empirically. I then relate the concept of representation within neuroscience to one that has developed within the field of machine learning. I argue that the recent success of artificial neural (...) networks on certain tasks such as visual object recognition reflects the degree to which those systems exhibit inherent inductive biases that reflect the structure of the physical world. I further argue that any system that is going to behave intelligently in the world must contain representations that reflect the structure of the world; otherwise, the system must perform unconstrained function approximation which is destined to fail due to the curse of dimensionality, in which the number of possible states of the world grows exponentially with the number of dimensions in the space of possible inputs. An analysis of these concepts in light of philosophical debates regarding the ontological status of representations suggests that the representations identified within both biological and artificial neural networks qualify as legitimate representations in the philosophical sense. (shrink)