The innovation of the deep learning modeling scheme plays an important role in promoting the research of complex problems handled with artificial intelligence in smart cities and the development of the next generation of information technology. With the widespread use of smart interactive devices and systems, the exponential growth of data volume and the complex modeling requirements increase the difficulty of deep learning modeling, and the classical centralized deep learning modeling scheme has encountered bottlenecks in the improvement of model performance (...) and the diversification of smart application scenarios. The parallel processing system in deep learning links the virtual information space with the physical world, although the distributed deep learning research has become a crucial concern with its unique advantages in training efficiency, and improving the availability of trained models and preventing privacy disclosure are still the main challenges faced by related research. To address these above issues in distributed deep learning, this research developed a clonal selective optimization system based on the federated learning framework for the model training process involving large-scale data. This system adopts the heuristic clonal selective strategy in local model optimization and optimizes the effect of federated training. First of all, this process enhances the adaptability and robustness of the federated learning scheme and improves the modeling performance and training efficiency. Furthermore, this research attempts to improve the privacy security defense capability of the federated learning scheme for big data through differential privacy preprocessing. The simulation results show that the proposed clonal selection optimization system based on federated learning has significant optimization ability on model basic performance, stability, and privacy. (shrink)

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)

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.

We all have experiences in which it “seems clear” to us that something is true. This kind of clear experience can play significant roles in determining whether we believe something to be true. But what are the significant roles? So far, the literature has focused on optimal cases where a person's clear experience might provide prima facie justification for their belief. This article will develop the hypothesis that, in less optimal cases, these clear experiences can be epistemically damaging. Specifically, it (...) will argue that, in certain cases, such experiences may causally compel belief even in the face of counterevidence. (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)

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)

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)

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 effectively address ageing and develop adequate eldercare needs, among others, new ethical visions are much needed. One of the ways to formulate sound ethical visions for contemporary issues is to reclaim, reinterpret and revive old moral ideas and ideals rooted in different indigenous cultural traditions. Drawing thought, wisdom and inspirations from classical Confucianism, the article offers a Confucian ethical outlook on healthy ageing and social eldercare. The popular perception of ageing in the West as well as China regards old (...) age as a period of inevitable decline. However, Kong Zi (Confucius) treats human life as an ongoing moral pilgrimage, with old age the summit of the lifelong journey. This Confucian ethical view on ageing as the culmination of a lifelong moral cultivation has various important themes. They include the primary feature of learning in healthy ageing, the essential role of social eldercare embedded in the popular Confucian norm ‘filial piety’ ( xiao), intergenerational flourishing and the necessity to respect the rights and dignity of each old person. Such a Confucian socio-ethical vision can not only help identify contemporary failings in the area of eldercare but also generate novel ideas and frameworks to help China and the world to face population ageing and elderly care in a more positive way. (shrink)

As shocking as He Jiankui's genetic experiment resulting in the world's first gene‐edited babies may have been, a socioethical inquiry into this paradigmatic case of scientific misconduct reveals its deep roots in genetic and scientific nationalism, as manifested in the widely accepted practice of yousheng (superior birth or eugenics) in China and the country's authoritarian pursuit of science superpower status. Along with eugenics, bionationalism has long been an international phenomenon. A global sociobioethics or ethical transculturalism is thus necessary to adequately (...) investigate the macrolevel sociopolitical, historical, and transnational forces, such as bionationalism, that structurally shape bioethical issues and people's responses to them, causing the systematic undermining of essential bioethical norms and the instrumentalization of human life. (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)

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 leader–member relationship has been identified as a key determinant of successful working relationships and business outcomes in China. A high-quality leader–member relationship helps managers and employees to meet the demands they face and gives them the opportunity to develop socially, emotionally and morally. Such relationships form the basis of the overall well-being and success of the organisation. This article contributes to relationally oriented leadership theories and more specifically to the leader–member exchange theory by examining the theory in the context (...) of Western expatriate managers and Chinese employees in China. The first aim of the study is to analyse the similarities and differences between the LMX theory, which owes its origins to Western corporate experience, and the social and moral norms of guanxi, a crucial element in the Chinese value system. Since Westerners and Chinese people can give different interpretations to guanxi, the second aim of the article is to discuss the ethical challenges to the Western manager arising from guanxi. The findings of this study have implications not only for China, but also for other Chinese communities where guanxi is endorsed and practised. (shrink)

The ethical behaviour and social responsibility of private companies, and in particular large corporations, is an important area of enquiry in contemporary social, economic and political thinking. In the past, a company's behaviour would be considered responsible as long as it stayed within the law of the society in which it operated or existed. Although this may be necessary, it is no longer sufficient. In this paper, we examine an energy company's response to an ethical incident in New Zealand which (...) prompted different responses across the country about the role of business in society. Thus, we argue that when a corporation is accused of unethical behaviour, executives of the company are usually compelled to offer responses to defend their actions and corporate image. Further, we use communicative response model, social issue life cycle theory, and organisational learning, to analyse the incident and how the company responded. Using social issues life cycle theory and organisational learning theory, we demonstrate that sustained pressure can potentially trigger a change of strategy that may serve to improve the ethical posture of a corporation and thereby improve the corporate image long term. We conclude that, although corporations may understand the significance of social issues to the performance and success of their business, this same understanding does not always translate into meaningful social action. (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)

Corlett (2019) raises two groups of challenges against the two-factor theory of delusions: One focuses on weighing “the evidence for … the two-factor theory”; the other aims to question “the logic of the two-factor theory” (p. 166). McKay (2019) has robustly defended the two-factor theory against the first group. But the second group, which Corlett believes is in many aspects independent of the first group and Darby (2019, p. 180) takes as “[t]he most important challenge to the two-factor theory raised (...) by Dr. Corlett”, has by large remained. Here I offer my two cents in response to the second group. More specifically, I argue that Corlett’s challenges to the logic of the two-factor theory, concerning modularity, double dissociation and cognitive penetration, seem to be based on some misunderstandings of the two-factor theory. (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)

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 Chinese Communist Party government has been forcefully promoting itsjihua shengyu program, known as the “one-child policy,” for more than three decades. A distinctive authoritarian model of population governance has been developed. A pertinent question to be asked is whether China’s one-child policy and the authoritarian model of population governance have a future. The answer must be no; they do not. Although there are many demographic, economic, and social rationales for terminating the one-child policy, the most fundamental reason for opposing (...) its continuation is drawn from ethics. The key ethical rationale offered for the policy is that it promotes the common social good, not only for China and the Chinese people but for the whole human family. The major irony associated with this apparently convincing justification is that, although designed to improve living standards and help relieve poverty and underdevelopment, the one-child policy and the application of the authoritarian model have instead caused massive suffering to Chinese people, especially women, and made them victims of state violence. A lesson from China—one learned at the cost of individual and social suffering on an enormous scale—is that an essential prerequisite for the pursuit of the common good is the creation of adequate constraints on state power. (shrink)

We give a first-order coding without parameters of a copy of in the computably enumerable weak truth table degrees. As a tool, we develop a theory of parameter definable subsets.

We investigate the upper semilattice Eq* of recursively enumerable equivalence relations modulo finite differences. Several natural subclasses are shown to be first-order definable in Eq*. Building on this we define a copy of the structure of recursively enumerable many-one degrees in Eq*, thereby showing that Th has the same computational complexity as the true first-order arithmetic.

In order to explain delusional beliefs, one must first consider what factors should be included in a theory of delusion. Unlike a one-factor theory, a two-factor theory of delusion argues that not only anomalous experience (the first factor) but also an impairment of the belief-evaluation system (the second factor) is required. Recently, two-factor theorists have adopted various Bayesian approaches in order to give a more accurate description of delusion formation. By reviewing the progression from a one-factor theory to a two-factor (...) theory, I argue that in light of the second factor’s requirements, different proposed impairments can be unified within a consistent belief-evaluation system. Under this interpretation of the second factor, I further argue that the role of a mechanism responsible for detecting bizarreness is wrongly neglected. I conclude that the second factor is a compound system which consists of differing functional parts, one of which functions to detect bizarreness in different stages of delusion; moreover, I hold that the impairment can be one or several of these functional parts. (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)

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

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)

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.

ObjectivesAcupuncture therapy has been used for cognitive impairment-related diseases, however, there are still few studies on the overall trend of acupuncture therapy on cognitive impairment based on bibliometric analysis. The purpose of this study was to explore the research trend of the impact of acupuncture on cognitive impairment in the past 15 years, analyze the research trends and hotspots, and provide new ideas and theoretical basis for future research directions.MethodsFrom the Web of Science Core Collection, the relevant literature on the (...) treatment of cognitive impairment with acupuncture from 2007 to 2022 was retrieved. Then, based on the CiteSpace and VOSviewer software of the Java platform, the cooperation between countries and institutions in this field, the co-citation of journals and documents, and the cooperation between authors and authors, etc. were analyzed. In addition, the co-occurrence and burst analysis of keywords are also carried out, and a visual knowledge map is drawn.ResultsAs of August 08, 2022, a total of 394 records related to the treatment of cognitive impairment with acupuncture were identified. The analysis results show: The number and rate of annual publications have steadily increased, with some fluctuations from year to year. The countries that contribute the most to this field are China and the USA. Among them, Beijing University of Chinese Medicine and Capital Medical University are tied for first place in terms of the number of published papers. Tao Jing is the most prolific author and the number one cited author.ConclusionsThe number of publications on acupuncture for cognitive impairment is expected to increase rapidly in future research, suggesting a bright future for the field. Future research hotspots will focus on pain, injury, protocol, diagnosis, guidelines, etc. It is also necessary to strengthen cross-regional and cross-country cooperation among various academic groups. (shrink)

Educational transitions play a pivotal role in shaping educational careers, and ultimately social inequality. Whereas parental socioeconomic status (SES) and cognitive ability have long been identified as key determinants of successful educational transitions, much less is known about the role of socio-emotional skills. To address this gap, the present study investigated whether Big Five personality traits predict success in the transition from secondary school to vocational education and training (VET) above and beyond SES, cognitive ability, and other covariates. Using data (...) from Starting Cohort 4 of the German National Educational Panel Study (NEPS; N = 4,137), we defined seven indicators of successful transition: obtaining a VET position, number of acceptances for VET positions, starting a VET position, (the absence of) dropout intentions and actual dropout, final VET grade, and satisfaction with VET. The results revealed that some Big Five traits were incrementally associated with several indicators of transition success. Conscientiousness emerged as the single most relevant trait, predicting all the transition success indicators but one (dropout intentions). The other Big Five traits had much weaker and less consistent links with transition success. Extraversion predicted the final VET grade and obtaining a VET position; Agreeableness was linked to a higher risk of dropout. Openness and Emotional Stability had no incremental effects on transition success. There was also some evidence for both compensatory and synergistic interactive effects, with Openness moderating mainly the effects of parental SES (on dropout intentions, actual dropout, and number of acceptances), and Agreeableness moderating the effects of cognitive ability (on obtaining a VET position, number of acceptances, and satisfaction with VET). Although individual effect sizes were small, the Big Five’s joint contribution to transition success was non-negligible, and often larger than that of sociodemographic characteristics and cognitive ability. Our results suggest a hitherto underappreciated contribution of personality to successful transitions to VET. (shrink)

Music expertise is known to be beneficial for cognitive function and development. In this study, we conducted 1-year music training for school children in China. The children were assigned to music or second-language after-class training groups. A passive control group was included. We aimed to investigate whether music training could facilitate working memory development compared to second-language training and no training. Before and after the training, auditory WM was measured via a digit span task, together with the vocabulary and block (...) tests of the Wechsler Intelligence Scale for Child IV. The results of the DS task revealed superior development in the music group compared to the other groups. However, further analysis of DS forward and backward tasks indicated that the performance of the three training/non-training groups only differed significantly in DS backward scores, but not in the DS forward scores. We conclude that music training may benefit the central executive system of WM, as reflected by the DS backward task. (shrink)

It is time for a new paper about open questions in the currently very active area of randomness and computability. Ambos-Spies and Kučera presented such a paper in 1999 [1]. All the question in it have been solved, except for one: is KL-randomness different from Martin-Löf randomness? This question is discussed in Section 6.Not all the questions are necessarily hard—some simply have not been tried seriously. When we think a question is a major one, and therefore likely to be hard, (...) we indicate this by the symbol ▶, the criterion being that it is of considerable interest and has been tried by a number of researchers. Some questions are close contenders here; these are marked by ▷. With few exceptions, the questions are precise. They mostly have a yes/no answer. However, there are often more general questions of an intuitive or even philosophical nature behind. We give an outline, indicating the more general questions.All sets will be sets of natural numbers, unless otherwise stated. These sets are identified with infinite strings over {0, 1}. Other terms used in the literature are sequence and real. (shrink)

How does it come about that a person akratically believes that P, while at the same time believing that the available evidence speaks against that P? Among the current accounts, Scanlon offers an intuitive suggestion that one’s seeming experience that P may play an important role in the aetiology of their akratic belief that P. However, it turns out to be quite challenging to articulate what the role of seeming experience is. This paper will offer a novel development of Scanlon’s (...) intuitive suggestion, with a focus on clear-eyed epistemic akrasia. I will argue that the primary role of seeming experience is unlikely to act as the subject’s reason or to provide the subject with prima facie justification; instead, based on the recent work in dogmatism and Cartesian clarity, I will propose a causal account, according to which, when it seems clear to the subject that P, the seeming experience may exert a brute causal force to persistently compel the subject to believe that P. This causal account also has the advantage of helping some existing accounts to explain clear-eyed epistemic akrasia. (shrink)

The coronavirus disease 2019 pandemic has been regarded as a public health emergency that caused a considerable degree of public panic during its early stage. Some irrational behaviors were also triggered as a result of such panic. Although there has been plenty of news coverage on public panic due to the outbreak, research on this phenomenon has been limited. Since panic is the main psychological reaction in the early stage of the pandemic, which largely determines the level of psychological adaptation, (...) time of psychological recovery, and the incidence of PTSD, there exists a demand to conduct investigation on it. From a public governance perspective, the government’s assessment of public panic may affect the efficiency and effectiveness of pandemic prevention and control. Therefore, it is of obvious practical significance to investigate public panic during the COVID-19 pandemic and analyze its influential factors. The self-compiled COVID-19 Social Mentality Questionnaire was used to collect data from a total of 16,616 participants online, and 13,511 valid responses were received. The results from the chi-square test showed that there were differences in gender, educational level, age, pandemic-related knowledge, self-efficacy, risk level, and objective social support. Furthermore, multiple linear regression analysis results showed that self-efficacy, gender, educational level, age, risk level, pandemic-related knowledge, and objective social support were significant predictors of public panic. Among the research variables, self-efficacy, gender, educational level, and age were negative predictors of panic while risk level, pandemic-related knowledge, and objective social support were positive predictors of panic. (shrink)

We investigate the strength of a randomness notion ${\cal R}$ as a set-existence principle in second-order arithmetic: for each Z there is an X that is ${\cal R}$-random relative to Z. We show that the equivalence between 2-randomness and being infinitely often C-incompressible is provable in $RC{A_0}$. We verify that $RC{A_0}$ proves the basic implications among randomness notions: 2-random $\Rightarrow$ weakly 2-random $\Rightarrow$ Martin-Löf random $\Rightarrow$ computably random $\Rightarrow$ Schnorr random. Also, over $RC{A_0}$ the existence of computable randoms is equivalent (...) to the existence of Schnorr randoms. We show that the existence of balanced randoms is equivalent to the existence of Martin-Löf randoms, and we describe a sense in which this result is nearly optimal. (shrink)