In the realistic world, various individuals have distinct personalities, preferences, and attitudes toward new information and behavior acceptance, called population heterogeneity. It is seldom taken into account and theoretically analyzed in information propagation on a weighted network. Therefore, we divide individuals into fashionable and conservative individuals according to their passion degree and willingness for novel behaviors acceptance. Then, we build two behavior adoption threshold models corresponding to fashionable and conservative individuals on the weighted network to explore the effect of population (...) heterogeneity on information propagation. Next, a partition theory based on edge weight and population heterogeneity is proposed to qualitatively analyze the information propagation mechanism. The theoretical analyses and simulation results show that fashionable individuals promote information propagation and behavior adoption. More importantly, the crossover phenomena of phase transition appear. When the fraction of fashionable individuals is relatively large, the increasing pattern of the final adoption size shows a second-order continuous phase transition. In comparison, the increasing pattern alters to first-order discontinuous phase transition with the decrease of the fraction of fashionable individuals. Moreover, reducing weight distribution heterogeneity promotes information propagation and slightly accelerates the change of the phase transition pattern from the first-order discontinuous to the second-order continuous. Besides, increasing the degree distribution heterogeneity accelerates the change of the phase transition pattern. Finally, our theoretical analyses coincide well with the simulation results. (shrink)

In this paper, we study the structural optimization of community governance in smart cities and optimize the structure based on the game analysis of dynamic planning evolution. Theoretically, the connotation and extension of the concept of “self-organization” are cleared, and the environment and conditions of community self-organization formation, the formation process of community self-organization, and the types of community self-organization are discussed. The so-called “self-organization” is a process of spontaneously moving from disorder to order, and the environment and conditions of (...) community self-organization are mainly the openness, nonequilibrium state, and nonlinearity of the system. The key parameters of the contract with the change of the values of each factor make up for the inability to collect data for the empirical study in this paper; then, it presents four linear stages along with the cause such as self-creation, self-expansion, self-maintenance, and self-degeneration, respectively. The types of community self-organization mainly include community self-organization with random aggregation, socialized community self-organization, and stable community self-organization with autonomy orientation. By systematically sorting out the relationship between community self-organization and government, while confirming the positive significance of community self-organization to community cultural governance, various complex conflicts and game relationships will deeply affect the actual effectiveness of cultural governance and provide useful knowledge reference for future community cultural governance. (shrink)

The current study investigated the relationship between peer relationships and cooperative tendencies in college students, and explored the mediating role of interpersonal trust and the moderating role of social value orientation in that relationship. A questionnaire was distributed to 406 college students, and the results showed that: peer relationships significantly positively predicted cooperative tendencies; interpersonal trust partially mediated the relationship between peer relationships and cooperative tendencies; and social value orientation moderated the relationship between peer relationships and cooperative tendencies. In particular, (...) prosocial college students were more susceptible to peer relationships than pro-self college students. The findings of the current study indicated that college students with good peer relationships and prosocial value orientation are more likely to show the willingness to cooperate. (shrink)

Covering the basics as well as recent research results, this book provides a very readable introduction to the exciting interface of computability and ...

Military metaphors are pervasive in biomedicine, including HIV research. Rooted in the mind set that regards pathogens as enemies to be defeated, terms such as “shock and kill” have become widely accepted idioms within HIV cure research. Such language and symbolism must be critically examined as they may be especially problematic when used to express scientific ideas within emerging health-related fields. In this article, philosophical analysis and an interdisciplinary literature review utilizing key texts from sociology, anthropology, history, and Chinese and (...) African studies were conducted to investigate the current proliferation of military metaphors. We found the use of these metaphors to be ironic, unfortunate, and unnecessary. To overcome military metaphors we propose to give them less aggressive meanings, and/or replace them with more peaceful metaphors. Building on previous authors' work, we argue for the increased use of “journey” metaphors as meaningful, cross-culturally app... (shrink)

Two ways of describing a group are considered. 1. A group is finite-automaton presentable if its elements can be represented by strings over a finite alphabet, in such a way that the set of representing strings and the group operation can be recognized by finite automata. 2. An infinite f.g. group is quasi-finitely axiomatizable if there is a description consisting of a single first-order sentence, together with the information that the group is finitely generated. In the first part of the (...) paper we survey examples of FA-presentable groups, but also discuss theorems restricting this class. In the second part, we give examples of quasi-finitely axiomatizable groups, consider the algebraic content of the notion, and compare it to the notion of a group which is a prime model. We also show that if a structure is bi-interpretable in parameters with the ring of integers, then it is prime and quasi-finitely axiomatizable. (shrink)

This study focuses on the effects of socially responsible human resource management practices on female employees’ turnover intentions and the moderating effect of supervisor gender on this relationship. With a sample of 212 female employees from eight different industries in Finland, the results indicate that SR-HRM practices promoting equal career opportunities and work–family integration play a significant role in reducing women's turnover intentions. The study adds to the academic discourse of corporate social responsibility by highlighting the impact of the organizational-level (...) HRM determinants on the individual-level outcome. In addition, supervisor gender makes a difference in the studied relationship: female supervisors have a stronger and more significant impact on the relationship than male supervisors. Our findings suggest that organizational measures which support work–family integration should be taken seriously to decrease female employees’ turnover intentions. Male supervisors could adopt some gender-incongruent leadership behaviors, such as individualized emotional concern and caring when dealing with female employees. In the future, other gender combinations in the supervisor–employee relationship would merit research. (shrink)

§1. Introduction. Natural sets that can be enumerated by a computable function always seem to be either actually computable or of the same complexity as the Halting Problem, the complete r.e. set K. The obvious question, first posed in Post [1944] and since then called Post's Problem is then just whether there are r.e. sets which are neither computable nor complete, i.e., neither recursive nor of the same Turing degree as K?Let be the r.e. degrees, i.e., the r.e. sets modulo (...) the equivalence relation of equicomputable with the partial order induced by Turing computability. This structure is a partial order with least element 0, the degree of the computable sets, and greatest element 1 or 0′, the degree of K. Post's problem then asks if there are any other elements of.The solution of Post's problem by Friedberg [1957] and Muchnik [1956] was followed by various algebraic or order theoretic results that were interpreted as saying that the structure was in some way well behaved:Theorem 1.1. Every countable partial ordering or even uppersemilattice can be embedded into.Theorem 1.2. For every nonrecursive r.e. degreeathere are r.e. degreesb, c < asuch thatb ∨ c = a.Theorem 1.3. For every pair of nonrecursive r.e. degreesa < bthere is an r.e. degreecsuch thata < c < b. (shrink)

We describe a strongly minimal theory S in an effective language such that, in the chain of countable models of S, only the second model has a computable presentation. Thus there is a spectrum of an -categorical theory which is neither upward nor downward closed. We also give an upper bound on the complexity of spectra.

To monopolize the scientific data gained by Japanese physicians and researchers from vivisections and other barbarous experiments performed on living humans in biological warfare programs such as Unit 731, immediately after the war the United States government secretly granted those involved immunity from war crimes prosecution, withdrew vital information from the International Military Tribunal for the Far East, and publicly denounced otherwise irrefutable evidence from other sources such as the Russian Khabarovsk trial. Acting in “the national interest” and for the (...) security of the US, authorities in the US tramped justice and morality, and engaged in what the English common law tradition clearly defines as “complicity after the fact.” To repair this historical injustice, the US government should issue an official apology and offer appropriate compensation for having covered up Japanese medical war crimes for six decades. To help prevent similar acts of aiding principal offender in the future, international declarations or codes of human rights and medical ethics should include a clause banning any kind of complicity in any unethical medicine—whether before or after the fact—by any state or group for whatever reasons. (shrink)

The biinterpretability conjecture for the r.e. degrees asks whether, for each sufficiently large k, the [Formula: see text] relations on the r.e. degrees are uniformly definable from parameters. We solve a weaker version: for each k ≥ 7, the [Formula: see text] relations bounded from below by a nonzero degree are uniformly definable. As applications, we show that Low 1 is parameter definable, and we provide methods that lead to a new example of a ∅-definable ideal. Moreover, we prove that (...) automorphisms restricted to intervals [d, 1], d ≠ 0, are [Formula: see text]. We also show that, for each c ≠ 0, can be interpreted in [0, c] without parameters. (shrink)

Trust is indispensable not only for interpersonal relationships and social life, but for good quality healthcare. As manifested in the increasing violence and tension in patient-physician relationships, China has been experiencing a widespread and profound crisis of patient–physician trust. And globally, the crisis of trust is an issue that every society, either developing or developed, has to face in one way or another. Yet, in spite of some pioneering works, the subject of patient-physician trust and mistrust – a crucial matter (...) in healthcare especially because there are numerous ethical implications – has largely been marginalized in bioethics as a global discourse. Drawing lessons as well as inspirations from China, this paper demonstrates the necessity of a trust-oriented bioethics and presents some key theoretical, methodological and philosophical elements of such a bioethics. A trust-oriented bioethics moves beyond the current dominant bioethical paradigms through putting the subject of trust and mistrust in the central agenda of the field, learning from the social sciences, and reviving indigenous moral resources. In order for global bioethics to claim its relevance to the things that truly matter in social life and healthcare, trust should be as vital as such central norms like autonomy and justice and can serve as a potent theoretical framework. (shrink)

Bike sharing, as an innovative travel mode featured by mobile internet and sharing, offers a new transport mode for short trips and has a huge positive impact on urban transportation and environmental protection. However, bike-sharing operators face some operational challenges, especially in sustainable development and profitability. Studies show that the customers’ willingness to pay is a key factor affecting bike-sharing companies’ operating conditions. Based on the theories of perceived value, this study conducts an empirical analysis of factors that affect bike-sharing (...) users’ willingness to pay for bike-sharing through measurement scales, user surveys, and structural equation models. We designed a five-point Likert-type scale containing 11 latent variables affecting willingness to pay and a total of 34 measurement items. We investigate bike-sharing users in China’s first and second-tier cities, with a total of 502 participants. The results show that perceived value, payment awareness, trust, and environmental awareness constitute key factors that directly affect bike-sharing users’ willingness to pay. And perceived usefulness, perceived ease-of-use, perceived cost, and perceived risk indirectly affect bike-sharing users’ willingness to pay. However, we found no significant effects of perceived entertainment on perceived value or word of mouth on willingness to pay. Our results are expected to provide theoretical and practical implications for bike-sharing programs. (shrink)

The interplay between computability and randomness has been an active area of research in recent years, reflected by ample funding in the USA, numerous workshops, and publications on the subject. The complexity and the randomness aspect of a set of natural numbers are closely related. Traditionally, computability theory is concerned with the complexity aspect. However, computability theoretic tools can also be used to introduce mathematical counterparts for the intuitive notion of randomness of a set. Recent research shows that, conversely, concepts (...) and methods originating from randomness enrich computability theory.The book covers topics such as lowness and highness properties, Kolmogorov complexity, betting strategies and higher computability. Both the basics and recent research results are desribed, providing a very readable introduction to the exciting interface of computability and randomness for graduates and researchers in computability theory, theoretical computer science, and measure theory. (shrink)

Drawing from a wide range of primary historical and sociological sources, this book presents medical ethics in China from a Chinese-Western comparative perspective, and in doing so it provides a fascinating exploration of cultural differences and commonalities exhibited by China and the West in medicine and medical ethics. The book focuses on a number of key issues in medical ethics including: attitudes towards foetuses; disclosure of information by medical professionals; informed consent; professional medical ethics; and human rights. This careful examination (...) not only provides insights into Chinese viewpoints, but also sheds light on the appropriate methods for comparative culture and ethical research. Through its analysis, Jing-Bao Nie seeks to put forward a theory of "transcultural bioethics", an ethical paradigm which upholds the primacy of morality whilst resisting cultural stereotypes, and appreciating the internal plurality, richness, dynamism and openness of medical ethics in any culture. Medical Ethics in China will be of particular interest to students and academics in the fields of Medical Law, Bioethics and Medical Ethics as well as Chinese/Asian Studies and Comparative (Chinese-Western) Cultural Studies. (shrink)

Contemporary bioethical issues are inherently cross-cultural and global in their scope. This is not surprising, as bioethical matters touch everyone in one way or another. Moral quandaries in health-care, life sciences, and biotechnology do not respect natural and human boundaries, the boundaries between and within nation-states, ethnicities, cultures, communities, and social groups. In addition, the simultaneously large-scale and intimate interactions between and within different cultures and civilizations and the rapid pace at which they change are phenomena that distinguish our times (...) from previous eras. Bioethics—as a particular domain of public discourse and an academic discipline—has thus been rapidly... (shrink)

To investigate the phenomenon of patient–physician mistrust in China, a qualitative study involving 107 physicians, nurses and health officials in Guangdong Province, southern China, was conducted through semi-structured interviews and focus groups. In this paper we report the key findings of the empirical study and argue for the essential role of medical professionalism in rebuilding patient-physician trust. Health professionals are trapped in a vicious circle of mistrust. Mistrust leads to increased levels of fear and self-protection by doctors which exacerbate difficulties (...) in communication; in turn, this increases physician workloads, adding to a strong sense of injustice and victimization. These factors produce poorer healthcare outcomes and increasingly discontented and angry patients, escalate conflicts and disputes, and result in negative media coverage, all these ultimately contributing to even greater levels of mistrust. The vicious circle indicates not only the crisis of patient-physician relationship but the crisis of medicine as a profession and institution. Underlying the circle is the inherent conflict of interest in the healthcare system by which health professionals and hospitals have become profit-driven. This institutional conflict of interest seriously compromises the fundamental principle of medical professionalism—the primacy of patient welfare—as well as the traditional Chinese ideal of “medicine as the art of humanity”. Patient trust can be restored through rectifying this institutional conflict of interest and promoting medical professionalism via a series of recommended practical measures. (shrink)

: Since the late 1970s, American appraisals of Chinese medical ethics and Chinese responses to American bioethics range from frank criticism to warm appreciation, from refutation to acceptance. Yet in the United States as well as in China, American bioethics and Chinese medical ethics have been seen, respectively, as individualistic and communitarian. In this widely-accepted general comparison, the great variation in the two medical moralities, especially the diversity of Chinese experiences, has been unfortunately minimized, if not totally ignored. Neither American (...) bioethics nor Chinese medical ethics is a field with only one dominant way of thinking. Medical moralities in America and China--traditional and modern--have always been plural and diverse. For example, American and Chinese cultures and medical moralities both exhibit individualistic and communitarian traditions. For this reason, bioethics in general and cross-cultural bioethics in particular must be fundamentally interpretive. Interpretive cross-cultural bioethics appreciates the plurality of medical morality within any culture. It can serve as a vital means of social and cultural criticism through engaged interpretations. (shrink)

There exists a serious shortage of organs for transplantation in China, more so than in most Western countries. Confucianism has been commonly used as the cultural and ethical reason to explain the reluctance of Chinese and other East-Asian people to donate organs for medical purposes. It is asserted that the Confucian emphasis on xiao (filial piety) requires individuals to ensure body intactness at death. However, based on the original texts of classical Confucianism and other primary materials, we refute this popular (...) view. We base our position on the related Confucian norms of filial piety and ren (humaneness, humanity or benevolence), the tension between differentiated love and universal love, and belief in the goodness of human nature. In light of this, we argue that the Confucian ethical outlook actually calls for organ donation at an individual level, and supports an opt-out (presumed consent) system at the level of social policy. Furthermore, because the popular view is based on a number of dominant but misleading modes of thinking about cultural differences, our revisionist account of Confucian moral duties regarding organ donation has implications for developing a more adequate transcultural and global bioethics. These will be discussed and expanded upon. (shrink)

How many factors, i.e. departures from normality, are necessary to explain a delusion? Maher’s classic one-factor theory argues that the only factor is the patient’s anomalous experience, and a delusion arises as a normal explanation of this experience. The more recent two-factor theory, on the other hand, contends that a second factor is also needed, with reasoning abnormality being a potential candidate, and a delusion arises as an abnormal explanation of the anomalous experience. In the past few years, although there (...) has been an increasing number of scholars offering a variety of arguments in defence of Maher’s one-factor theory, these arguments have not been adequately addressed by two-factor theorists. This paper aims to address this gap by critically examining the arguments on three crucial issues: the intelligibility of delusions, the dissociation between anomalous experiences and delusions, and the empirical evidence of a second factor. I will argue that the Maherian notion of anomalous experience is not sufficient for explaining delusions and the two-factor theory is on the right track in its search for the missing factor in the aetiology of delusions. (shrink)

According to a bodily view of pain, pains are objects which are located in body parts. This bodily view is supported by the locative locutions for pain in English, such as that “I have a pain in my back.” Recently, Liu and Klein (Analysis, 80(2), 262–272, 2020) carry out a cross-linguistic analysis, and they claim that (1) Mandarin has no locative locutions for pain and (2) the absence of locative locutions for pain puts the bodily view at risk. This paper (...) rejects both claims. Regarding the philosophical claim, I argue that a language without locative locutions for pain only poses a limited challenge to the bodily view. Regarding the empirical claim, I identify the possible factors which might have misled Liu and Klein about the locative locutions for pain in Mandarin, and argue that Mandarin has a wide range of locative locutions for pain by conducting a corpus analysis. I conclude that compared to English, Mandarin lends no less, if not more, support to the bodily view of pain. (shrink)

The Jordan decomposition theorem states that every function $f \colon \, [0,1] \to \mathbb {R}$ of bounded variation can be written as the difference of two non-decreasing functions. Combining this fact with a result of Lebesgue, every function of bounded variation is differentiable almost everywhere in the sense of Lebesgue measure. We analyze the strength of these theorems in the setting of reverse mathematics. Over $\mathsf {RCA}_{0}$, a stronger version of Jordan’s result where all functions are continuous is equivalent to (...) $\mathsf {ACA}_0$, while the version stated is equivalent to ${\textsf {WKL}}_{0}$. The result that every function on $[0,1]$ of bounded variation is almost everywhere differentiable is equivalent to ${\textsf {WWKL}}_{0}$. To state this equivalence in a meaningful way, we develop a theory of Martin–Löf randomness over $\mathsf {RCA}_0$. (shrink)

Two theories on the origins of COVID-19 have been widely circulating in China and the West respectively, one blaming the United States and the other a highest-level biocontainment laboratory in Wuhan, the initial epicentre of the pandemic. Both theories make claims of biological warfare attempts. According to the available scientific evidence, these claims are groundless. However, like the episodes of biological warfare during the mid-twentieth century, the spread of these present-day conspiracy theories reflects a series of longstanding and damaging trends (...) in the international scene which include deep mistrust, animosities, the power of ideologies such as nationalism, and the sacrifice of truth in propaganda campaigns. Also, the threats associated with biological warfare, bioterrorism, and the accidental leakage of deadly viruses from labs are real and growing. Thus, developing a better global governance of biosafety and biosecurity than exists at present is an urgent imperative for the international community in the broader context of a looming Cold War II. For such a governance, an ethical framework is proposed based upon the triple ethical values of transparency, trust, and the common good of humanity. (shrink)

We show that the elementary theory of the recursively enumerable tt-degrees has the same computational complexity as true first-order arithmetic. As auxiliary results, we prove theorems about exact pairs and initial segments in the tt-degrees.

We use Demuth randomness to study strong lowness properties of computably enumerable sets, and sometimes of Δ20 sets. A set A⊆N is called a base for Demuth randomness if some set Y Turing above A is Demuth random relative to A. We show that there is an incomputable, computably enumerable base for Demuth randomness, and that each base for Demuth randomness is strongly jump-traceable. We obtain new proofs that each computably enumerable set below all superlow Martin-Löf random sets is strongly (...) jump traceable, using Demuth tests. The sets Turing below each ω2-computably approximable Martin-Löf random set form a proper subclass of the bases for Demuth randomness, and hence of the strongly jump traceable sets. The c.e. sets Turing below each ω2-computably approximable Martin-Löf random set satisfy a new, very strong combinatorial lowness property called ω-traceability. (shrink)

We give new examples of FA presentable torsion-free abelian groups. Namely, for every n2, we construct a rank n indecomposable torsion-free abelian group which has an FA presentation. We also construct an FA presentation of the group in which every nontrivial cyclic subgroup is not FA recognizable.

BackgroundMedical professionalism has been developing in the Peoples’ Republic of China as one way to better address perennial and new challenges in healthcare in an ever-changing society. Among many recent developments in this area is promotion by the national Chinese Medical Doctor Association of the principles and values contained in the international document, “Medical Professionalism in the New Millennium: A Physician Charter.”ObjectiveTo discover Chinese physicians’ attitudes toward and understanding of medical professionalism.MethodologyThe authors distributed a self-reporting questionnaire that included 34 statements (...) and four case scenarios concerning the general principles of medical professionalism: the primacy of patients’ welfare, respect for patients’ autonomy, promotion of social justice, and professional self-regulation. The questionnaire included controversial issues such as the role of the family in decision making and reporting medical errors. A total of 2,966 practicing physicians, randomly selected from the Chinese Medical Association database, were surveyed, and 1,198 valid questionnaires were returned. Our sample covered 23 provinces and 51 cities throughout the Peoples’ Republic of China.ResultsMore than 80 percent of the physicians who responded agreed that the physician-patient relationship should be a relationship of trust founded on professional altruism, and that informed consent is necessary. More than 95 percent agreed that physicians should promote professional self-regulation as well as social justice. More than half agreed with the principle of the primacy of patients’ welfare (62.8 percent), and that physicians have a responsibility to report medical errors and incompetent colleagues (51.0 percent). In certain cases, a great majority of Chinese physicians favored familism and paternalism.LimitationsThe study does not include data on how Chinese physicians practice medical professionalism, or the perspectives of physicians working in smaller cities and in rural areas.ConclusionsBased on responses to the survey, Chinese physicians strongly support the majority of the fundamental principles and responsibilities of medical professionalism, including dedication, altruism, social justice, self-regulation, and informed consent. However, their support for the primacy of patients’ welfare as a general principle, and the physician’s responsibility to report medical errors and incompetent colleagues, is relatively low. To help advance medical professionalism in the People’s Republic of China, professional development programs and medical ethics education should not only emphasize the general principles involved, but also formulate guidelines on how these principles can be carried out in practice. (shrink)

Aiming at the problem of radar target recognition of High-Resolution Range Profile under low signal-to-noise ratio conditions, a recognition method based on the Constrained Naive Least-Squares Generative Adversarial Network, Short-time Fourier Transform, and Convolutional Neural Network is proposed. Combining the Least-Squares Generative Adversarial Network with the Wasserstein Generative Adversarial Network with Gradient Penalty, the CN-LSGAN is presented and applied to the HRRP denoise. The frequency domain and phase features of HRRP are gained by STFT in order to facilitate feature learning (...) and also match the input data format of the CNN. These experimental results show that the CN-LSGAN has better data augmentation performance and can effectively avoid the model collapse compared to the generative adversarial network and LSGAN. Also, the method has better recognition performance than the one-dimensional CNN method and the Long Short-Term Memory network method. (shrink)

A global socio‐bioethics is called upon to address the ethical challenges arising from the revolutionary gene editing technologies such as CRISPR‐Cas9, which offers the capability to rewrite the human genome. The ethical inquiry Françoise Baylis has undertaken in the book Altered Inheritance: CRISPR and the Ethics of Human Genome Editing (Harvard University Press, 2019) operates at individual, societal and global levels. Baylis has not only presented insights on how to practice “slow science” and achieve broad societal consensus through empowering the (...) public, but she also shown what a global socio‐bioethics approach can offer for the further development of bioethics. (shrink)

v. [1]. Ru -- v. [2]. Shi -- v. [3]. Dao.

We prove that each Σ 0 2 set which is hypersimple relative to $\emptyset$ ' is noncuppable in the structure of the Σ 0 2 enumeration degrees. This gives a connection between properties of Σ 0 2 sets under inclusion and and the Σ 0 2 enumeration degrees. We also prove that some low non-computably enumerable enumeration degree contains no set which is simple relative to $\emptyset$ '.

This paper studies how the concept WATER is metonymically and metaphorically extended to six super-domains: NATURE, LIFE SUSTAINER, MOVEMENT, POWER, PURITY, and WOMAN. We demonstrate that these six target domains are related to each other in intricate ways and within each are a number of sub-domains. This complicated semantic network of WATER is formed via speakers’ embodied experience with their physical as well as cultural environment. We believe that our detailed discussion of the WATER network will contribute to the current (...) research on the relationship between metaphor and metonymy. (shrink)

Since the early 1970s, despite popular opposition, to control the rapid growth of population the Chinese government has been carrying out the strictest and most comprehensive family planning policy in the world. In addition to contraceptive methods and sterilization, artificial abortionhas been used as an important measure of birth control under the policy. Many women have been required, persuaded, and even forced by the authorities to abort fetuses no matter how much they want to give birth.

Let S∞ denote the topological group of permutations of the natural numbers. A closed subgroup G of S∞ is called oligomorphic if for each n, its natural action on n-tuples of natural numbers has onl...