We study the Turing degrees which contain a real of effective packing dimension one. Downey and Greenberg showed that a c.e. degree has effective packing dimension one if and only if it is not c.e. traceable. In this paper, we show that this characterization fails in general. We construct a real $A\leq_T\emptyset''$ which is hyperimmune-free and not c.e. traceable such that every real $\alpha\leq_T A$ has effective packing dimension 0. We construct (...) a real $B\leq_T\emptyset'$ which is not c.e. traceable such that every real $\alpha\leq_T B$ has effective packing dimension 0. (shrink)

This paper presents a refinement of a result by Conidis, who proved that there is a real $X$ of effective packing dimension $0\lt \alpha\lt 1$ which cannot compute any real of effective packing dimension $1$. The original construction was carried out below $\emptyset''$, and this paper’s result is an improvement in the effectiveness of the argument, constructing such an $X$ by a limit-computable approximation to get $X\leq_{T}\emptyset'$.

Recently, the Dimension Problem for effective Hausdorff dimension was solved by J. Miller in [14], where the author constructs a Turing degree of non-integral Hausdorff dimension. In this article we settle the Dimension Problem for effective packing dimension by constructing a real of strictly positive effective packing dimension that does not compute a real of effective packing dimension one (on the other hand, it is known via (...) [10, 3, 7] that every real of strictly positive effective Hausdorff dimension computes reals whose effective packing dimensions are arbitrarily close to, but not necessarily equal to, one). (shrink)

Classical fractal dimensions have recently been effectivized by characterizing them in terms of real-valued functions called gales, and imposing computability and complexity constraints on these gales. This paper surveys these developments and their applications in algorithmic information theory and computational complexity theory.

We prove various results connected together by the common thread of computability theory.First, we investigate a new notion of algorithmic dimension, the inescapable dimension, which lies between the effective Hausdorff and packing dimensions. We also study its generalizations, obtaining an embedding of the Turing degrees into notions of dimension.We then investigate a new notion of computability theoretic immunity that arose in the course of the previous study, that of a set of natural numbers with no (...) co-enumerable subsets. We demonstrate how this notion of $\Pi ^0_1$ -immunity is connected to other immunity notions, and construct $\Pi ^0_1$ -immune reals throughout the high/low and Ershov hierarchies. We also study those degrees that cannot compute or cannot co-enumerate a $\Pi ^0_1$ -immune set.Finally, we discuss a recently discovered truth-table reduction for transforming a Kolmogorov–Loveland random input into a Martin-Löf random output by exploiting the fact that at least one half of such a KL-random is itself ML-random. We show that there is no better algorithm relying on this fact, in the sense that there is no positive, linear, or bounded truth-table reduction which does this. We also generalize these results to the problem of outputting randomness from infinitely many inputs, only some of which are random.Abstract prepared by David J. Webb.E-mail: [email protected]: https://arxiv.org/pdf/2209.05659.pdf. (shrink)

This paper continues the study of the metric topology on $2^{\mathbb {N}}$ that was introduced by S. Binns. This topology is induced by a directional metric where the distance from $Y\in2^{\mathbb {N}}$ to $X\in2^{\mathbb {N}}$ is given by \[\limsup_{n}\frac{C(X\upharpoonright n|Y\upharpoonright n)}{n}.\] This definition is closely related to the notions of effective Hausdorff and packing dimensions. Here we establish that this is a path-connected topology on $2^{\mathbb {N}}$ and that under it the functions $X\mapsto\operatorname{dim}_{\mathcal{H}}X$ and $X\mapsto\operatorname{dim}_{p}X$ are continuous. We (...) also investigate the scalar multiplication operation that was introduced by Binns. The multiplication of a real $X\in2^{\mathbb {N}}$ by an element $\alpha\in[0,1]$ represents a dilution of the information in $X$ by a factor of $\alpha$ . Our main result is to show that every regular real is the dilution of a real of Hausdorff dimension 1. That is, that the information in every regular real can be maximally compressed. (shrink)

We examine a definition of the mutual information of two reals proposed by Levin in [5]. The mutual information iswhereK is the prefix-free Kolmogorov complexity. A realAis said to have finite self-information ifI is finite. We give a construction for a perfect Π10class of reals with this property, which settles some open questions posed by Hirschfeldt and Weber. The construction produces a perfect set of reals withK≤+KA+f for any given Δ20fwith a particularly nice approximation and for a specific choice of (...) f it can also be used to produce a perfect Π10set of reals that are low for effective Hausdorff dimension and effective packing dimension. The construction can be further adapted to produce a single perfect set of reals that satisfyK≤+KA+f for allfin a ‘nice’ class of Δ20functions which includes all Δ20orders. (shrink)

We examine the sequences A that are low for dimension, i.e. those for which the effective dimension relative to A is the same as the unrelativized effective dimension. Lowness for dimension is a weakening of lowness for randomness, a central notion in effective randomness. By considering analogues of characterizations of lowness for randomness, we show that lowness for dimension can be characterized in several ways. It is equivalent to lowishness for randomness, namely, (...) that every Martin-Löf random sequence has effective dimension 1 relative to A, and lowishness for K, namely, that the limit of KA/K is 1. We show that there is a perfect [Formula: see text]-class of low for dimension sequences. Since there are only countably many low for random sequences, many more sequences are low for dimension. Finally, we prove that every low for dimension is jump-traceable in order nε, for any ε > 0. (shrink)

The present study extends the meaningful work and ethics literature by comparing three ethics-related antecedents. The second contribution of this paper is that in using a multi-dimensional MFW construct we offer a more fine-tuned understanding of the impact of ethical antecedents on different dimensions of MFW, such as expressing full potential and integrity with self. Using an international data set from 879 employees and structural equation modelling, we confirmed an updated seven-dimension Comprehensive Meaningful Work Scale. The structural model found (...) that fairness, responsible leadership and worthy work are all significant and positively related to the majority of meaningfulness dimensions. However, different antecedents are related to different dimensions of MFW, showing that a complex and multi-level combination of ethics-related practices are required to cultivate MFW. All relationships were in the expected positive direction except responsible leadership, which was negatively related to the MFW dimension of integrity with self. Across the seven dimensions of MFW, only the dimension ‘Service to Others’ was uniformly not predicted by any antecedent. However, all three antecedents significantly related to important dimensions of MFW not usually measured in the ethics literature, such as ‘Unity with Others’ and ‘Expressing Full Potential’. In addition, we conducted dominance analysis to test the relative importance of the three antecedent across the MFW dimensions, and found that worthy work is the most dominant antecedent, although all three antecedents are the most dominant for at least one MFW dimension—further highlighting the importance of exploring MFW as a multi-dimensional construct. We discuss the implications for MFW theory and practice. (shrink)

The present study extends the meaningful work and ethics literature by comparing three ethics-related antecedents. The second contribution of this paper is that in using a multi-dimensional MFW construct we offer a more fine-tuned understanding of the impact of ethical antecedents on different dimensions of MFW, such as expressing full potential and integrity with self. Using an international data set from 879 employees and structural equation modelling, we confirmed an updated seven-dimension Comprehensive Meaningful Work Scale. The structural model found (...) that fairness, responsible leadership and worthy work are all significant and positively related to the majority of meaningfulness dimensions. However, different antecedents are related to different dimensions of MFW, showing that a complex and multi-level combination of ethics-related practices are required to cultivate MFW. All relationships were in the expected positive direction except responsible leadership, which was negatively related to the MFW dimension of integrity with self. Across the seven dimensions of MFW, only the dimension ‘Service to Others’ was uniformly not predicted by any antecedent. However, all three antecedents significantly related to important dimensions of MFW not usually measured in the ethics literature, such as ‘Unity with Others’ and ‘Expressing Full Potential’. In addition, we conducted dominance analysis to test the relative importance of the three antecedent across the MFW dimensions, and found that worthy work is the most dominant antecedent, although all three antecedents are the most dominant for at least one MFW dimension—further highlighting the importance of exploring MFW as a multi-dimensional construct. We discuss the implications for MFW theory and practice. (shrink)

To further develop three-dimensional (3D) applications, it is important to elucidate the negative effects of 3D applications on the human body and mind. Thus, this study investigated differences in the effects of visual fatigue on cognition and brain activity using visual and auditory tasks induced by watching a 1-h movie in two dimensions (2D) and 3D. Eighteen young men participated in this study. Two conditions were randomly performed for each participant on different days, namely, watching the 1-h movie on television (...) in 2D (control condition) and 3D (3D condition). Before and after watching the 1-h movie on television, critical flicker fusion frequency (CFF: an index of visual fatigue), and response accuracy and reaction time for the cognitive tasks were determined. Brain activity during the cognitive tasks was evaluated using a multi-channel near-infrared spectroscopy system. In contrast to the control condition, the decreased CFF, and the lengthened reaction time and the decreased activity around the right primary somatosensory cortex during Go/NoGo blocks in the visual task at post-viewing in the 3D condition were significant, with significant repeated measures correlations among them. Meanwhile, in the auditory task, the changes in cognitive performance and brain activity during the Go/NoGo blocks were not significant in the 3D condition. These results suggest that the failure or delay in the transmission of visual information to the primary somatosensory cortex due to visual fatigue induced by watching a 3D movie reduced the brain activity around the primary somatosensory cortex, resulting in poor cognitive performance for the visual task. This suggests that performing tasks that require visual information, such as running in the dark or driving a car, immediately after using a 3D application, may create unexpected risks in our lives. Thus, the findings of this study will help outlining precautions for the use of 3D applications. (shrink)

This study investigates the Proteus effect from the first-person perspective and during avatar embodiment in actual exercise. In addition to the immediate measurements of the Proteus effect, prolonged effects such as next-day perception and exercise-related outcomes are also explored. We theorized the Proteus effect as altered perceived self-concept and explored the association between virtual reality avatar manipulation and self-concept in the exercise context. While existing studies have mainly investigated the Proteus effect in a non-VR environment or after VR embodiment, we (...) aim to contribute to the literature by addressing this concern to explore how the Proteus effect works in actual VR exercise. Through a 2 × 2 between-subject experiment, the results partially support the Proteus effect. Regarding actual physical activity, embodying an avatar with a six pack during exercise creates fewer body movements. No significant effect was found for perceived exertion. We also explored the role of sex as a potential moderator in the association of the Proteus effect on exercise outcomes. The Proteus effect was supported by immediate and next-day self-efficacy for core-muscle exercise only among female participants. The between-subject design allowed us to probe how avatar manipulation of muscular body shape with a six pack as opposed to normal body shape influences participants’ self-concept and exercise outcomes, as limited VR studies have employed within-subject comparisons. This also contributes to the literature by providing an upward comparison as opposed to the previous downward comparison regarding body fitness. The overall results supported the Proteus effect in the context of core-muscle exercise when comparing normal and ideal body shape avatars. However, the Proteus effect as an altered self-concept and its effects on self-efficacy for exercise were supported among females but not males. Whereas the female participants who embodied avatars with a six pack associated themselves more with the muscular concept than other people, the male participants who embodied avatars with a six pack perceived themselves as more normal than others. Theoretical and practical implications are discussed. (shrink)

As more and more firms operate globally, an understanding of the effects of cultural differences on ethical decision making becomes increasingly important for avoiding potential business pitfalls and for designing effective international marketing management programs. Although several articles have addressed this area in general, differences along specific, cultural dimensions have not been directly examined. Hence, the purpose of this study was to examine differences in ethical decision making within Hofstede's cultural framework. The results confirm the utility of Hofstede's cultural (...) dimensions and place ethical decision making within an overall theoretical framework. Sales agents from a high power distance, uncertainty avoidant, Confucian, collectivist culture (i.e., Taiwan) placed more value on company and fellow employee interests (vis-à-vis self interests) than did managers from a masculine, individualistic culture (i.e., the United States). American and Taiwanese managers did not differ in their deontological norms or on the importance that they placed on customer interests. The theoretical and managerial importance of these findings are also discussed. (shrink)

Employee performance plays a crucial role in the productivity of organizations, especially in the hospitality industry in Malaysia. This work performance is influenced by leadership style, and finding the type of leadership style that is suitable to apply to employees is crucial, especially in the midst of the COVID-19 pandemic. Transformational leadership theory is selected for this study in determining leadership styles. There are four dimensions under transformational leadership theory, namely idealized influence, individualized consideration, inspirational motivation and intellectual stimulation. Data (...) were collected online from 400 employees working in the hospitality industry in Malaysia and analyzed using partial least square structure equation modeling. The findings show that only two dimensions of transformational leadership, namely idealized influence and inspirational motivation, have a significant positive influence on employee performance. Implications in the context of human resource management and recommendations to increase employee performance are also discussed. (shrink)

The classic action-effect (Kahneman & Tversky, 1982a) describes a phenomenon in which people associate stronger emotional regret with negative outcomes when the outcomes are a result of an action c...

The lack of attention to sustainability, as a concept with multiple dimensions, has presented a developmental gap in green marketing literature, sustainability, and marketing literature for decades. Based on the established premise of customer–corporate (C–C) identification, in which consumers respond favorably to companies with corporate social responsibility initiatives that they identify with, we propose that consumers would respond similarly to companies with sustainability initiatives. We postulate that consumers care about protecting and preserving favorable economic environments (an economic dimension of (...) sustainability) as much as they care about natural environments. Thus, we investigate how two sustainability dimensions (i.e., environmental and economic) and price can influence consumer responses. Using an experimental method, we demonstrate that consumers favor sustainability in both dimensions by giving positive evaluations of the company and purchase intent. In addition, consumers respond more negatively to poor company sustainability than to high company sustainability. In comparison, consumers respond more negatively to the company’s poor commitment to caring for the environment than to the company’s poor commitment to economic sustainability. We also find that consumers do not respond favorably to low prices when they have information about the firm’s poor environmental sustainability. Finally, we find support for an interaction effect between consumer support for sustainability and corporate sustainability; that is, consumers evaluate a company more favorably if the company shares the consumers’ social causes. Overall, we conclude, from our empirical study, support for the idea that consumers do respond to multiple dimensions of sustainability. (shrink)

Based upon the quintuple helix model (QHM), this study explores whether the differences in firms' emission reduction effectiveness can be attributed to the five institutional helices related to educational system, economic development, political–legal system, cultural orientation, and the natural capital. Using a set of listed European firms for the 2015–2020 period, we show that firms with better emission reduction effectiveness operate in nations with more public educational expenditure and scientific production, more extensive economic development, and better institutional and governance quality. (...) Moreover, emission reduction strategies are more pronounced in firms located in countries characterized by less masculinity, individualism, power distance, and uncertainty avoidance, and more long-term orientation and indulgence. In addition, we find that companies with better emission reduction effectiveness are found in countries with more natural capital, characterized by a life in harmony with nature and employing the finite resources available in a sustainable and environmentally conscious manner. Moreover, employing a two-stage model to identify the most relevant helix, we find that the political–legal system helix is the most pivotal in promoting firms' commitment to reducing environmental emissions. (shrink)

Given a rich environment, how do we decide on what information to use? A view of a single entity (e.g., a group of birds) affords many distinct interpretations, including their number, average size, and spatial extent. An enduring challenge for cognition, therefore, is to focus resources on the most relevant evidence for any particular decision. In the present study, subjects completed three tasks—number discrimination, surface area discrimination, and convex hull discrimination—with the same stimulus set, where these three features were orthogonalized. (...) Therefore, only the relevant feature provided consistent evidence for decisions in each task. This allowed us to determine how well humans discriminate each feature dimension and what evidence they relied on to do so. We introduce a novel computational approach that fits both feature precision and feature use. We found that the most relevant feature for each decision is extracted and relied on, with minor contributions from competing features. These results suggest that multiple feature dimensions are separately represented for each attended ensemble of many items and that cognition is efficient at selecting the appropriate evidence for a decision. (shrink)

The fourth edition of this bestselling title is designed to help you think critically and thoughtfully about ethical decisions you'll face in practice-in any health care discipline. Utilizing a unique 6-step decision making process designed by the author, this multi-disciplinary text provides an expert framework for making effective choices that lead to a professional and caring response to patients and clients.