The principle of differential marginality (Casajus in Theory and Decis 71(2):163-–174) for cooperative games is a very appealing property that requires equal productivity differentials to translate into equal payoff differentials. In this paper we apply this property to axiomatic characterizations of values. We show that differential marginality implies additivity and symmetry under certain conditions. Based on this result, we propose new characterizations of the equal division and the equal surplus division values. Finally, we characterize two classes of convex combinations of (...) values, i.e., α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document}-egalitarian Shapley values and α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document}-equal surplus division values, by employing differential marginality and establishing the uniqueness of these values on inessential games. (shrink)

Recognising that offers of payment to research participants can serve various purposes—reimbursement, compensation and incentive—helps uncover differences between participants, which can justify differential payment of participants within the same study. Participants with different study-related expenses will need different amounts of reimbursement to be restored to their preparticipation financial baseline. Differential compensation can be acceptable when some research participants commit more time or assume greater burdens than others, or if inter-site differences affect the value of compensation. Finally, it may be permissible (...) to offer differential incentive payments if necessary to advance the goals of a study. We encourage investigators and Institutional Review Boards to think about whether to offer payment, in what amounts and for what purpose, and also to consider whether differential payment can help promote the scientific and ethical goals of clinical research. (shrink)

One shortcoming of the chain rule is that it does not iterate: it gives the derivative of f(g(x)), but not (directly) the second or higher-order derivatives. We present iterated differentials and a version of the multivariable chain rule which iterates to any desired level of derivative. We first present this material informally, and later discuss how to make it rigorous (a discussion which touches on formal foundations of calculus). We also suggest a finite calculus chain rule (contrary to Graham, Knuth (...) and Patashnik's claim that "there's no corresponding chain rule of finite calculus"). (shrink)

ABSTRACTEmotion differentiation, the ability to describe and label our own emotions in a differentiated and specific manner, has been repeatedly associated with well-being. However, it is unclear exactly what type of differentiation is most strongly related to well-being: the ability to make fine-grained distinctions between emotions that are relatively closely related, the ability to make larger distinctions between very distinct emotions, or the combination of both. To determine which type of differentiation is most predictive of well-being, we (...) performed a comprehensive meta-analysis across six datasets. We examined the correlations between these three types of differentiation and several indicators of well-being. Results showed that individuals differentiated most between very distinct emotions and least between more related emotions, and that an index computed across emotions from both the same and di... (shrink)

In this study, we analyse the notion of “differential heterogenesis” proposed by Deleuze and Guattari on a morphogenetic perspective. We propose a mathematical framework to envisage the emergence of singular forms from the assemblages of heterogeneous operators. In opposition to the kind of differential calculus that is usually adopted in mathematical-physical modelling, which tends to assume a homogeneous differential equation applied to an entire homogeneous region, heterogenesis allows differential constraints of qualitatively different kinds in different points of space and time. (...) These constraints can then change in time, opening the possibility for new kinds of differential dynamics and the emergence of distinct entities and forms. Formally, we show that operators with different phase spaces can be assembled on the basis of a result of Rothschild & Stein (1976. Hypoelliptic differential operators and nilpotent groups. Acta Mathematica 137. 247–320). Furthermore, operators with different dynamics can be assembled by means of a partition of the unit.After stating the concept of differential heterogenesis in terms of contemporary mathematics, we show that this construction sheds light on the constitution of the semiotic function. In fact, both the Merleau-Pontian and the Deleuzian approaches share a common conceptualisation of the semiotic function and its emergence in terms of amorphodynamics of heterogeneous assemblages with a divergent actualisation. This divergent actualisation allows the co-constitution of various expression and content planes. Finally, we show that the divergent actualisation can be interpreted as the directions of principal eigenvectors of the actualized flow. (shrink)

In this paper I present an interpretation of Deleuze's concept of the virtual. I argue that this concept is best understood in relation to the problematic of individuation or differentiation, which Deleuze inherits from Duns Scotus. After analysing Scotus' critique of Aristotelian or hylomorphic approaches to the problem of individuation, I turn to Deleuze's account of differentiation and his interpretation of the calculus in chapter 4 of Difference and Repetition. The paper seeks thereby to explicate Deleuze's dialectics or (...) theory of Ideas, his approach to the principle of sufficient reason, and the concept of the virtual itself. (shrink)

ABSTRACTEmotion differentiation refers to the precision with which people can identify and distinguish their emotions and has been associated with well-being in adults. This study investigated ED and its relation with emotional well-being in adolescents. We used an experience sampling method with 72 participants to assess adolescents’ positive and negative emotions at different time points over the course of two weekends and a baseline questionnaire to assess emotional well-being. Differentiating negative emotions was related to less negativity intensity and propensity, (...) and to the belief that emotions are malleable. Differentiating positive emotions was not related to any of the assessed well-being variables. Together, these results suggest that a detailed awareness of one’s negative emotional states is an important dimension of well-being, also in adolescence. (shrink)

Conscientious disobedients often face the demand to differentiate themselves from criminals whose law-breaking actions are not undergirded by conscientious convictions. In public and philosophical discourse, conscientious disobedients are often criticised on the basis that their actions render them no different from criminals. I provide a qualified defence of disobedients in this essay. I argue that the differentiation demand can be satisfied even by disobedients who engage in what are typically regarded as radical acts of disobedience. In practical terms, this (...) means that even disobedients who engage in actions such as arson, looting, rioting, vandalism or vigilantism can also successfully differentiate themselves from criminals. (shrink)

Ineffability, the degree to which percepts or concepts resist linguistic coding, is a fairly unexplored nook of cognitive science. Although philosophical preoccupations with qualia or nonconceptual content certainly touch upon the area, there has been little systematic thought and hardly any empirical work in recent years on the subject. We argue that ineffability is an important domain for the cognitive sciences. For examining differential ineffability across the senses may be able to tell us important things about how the mind works, (...) how different modalities talk to one another, and how language does, or does not, interact with other mental faculties. (shrink)

The differentiation of trait anxiety and depression in nonclinical and clinical populations is addressed. Following the tripartite model, it is assumed that anxiety and depression share a large portion of negative affectivity, but differ with respect to bodily hyperarousal and anhedonia. In contrast to the tripartite model, NA is subdivided into worry and dysthymia, which leads to a four-variable model of anxiety and depression encompassing emotionality, worry, dysthymia, and anhedonia. Item-level confirmatory factor analyses and latent class cluster analysis based (...) on a large nation-wide representative German sample substantiate the construct validity of the model. Further evidence concerning convergent and discriminant validity with respect to related constructs is obtained in two smaller nonclinical and clinical samples. Factors influencing the association between components of anxiety and depression are discussed. (shrink)

One way in which the practice of inclusion can be actualised in classrooms is through the use of consistent, appropriate differentiated instruction. What remains elusive, however, is insight into what teachers in different contexts think and believe about differentiation, how consistently they differentiate instruction and what challenges they experience in doing so. In the study reported on here high school classrooms in a private and a government school in Lesotho were compared in order to determine teachers’ thoughts and beliefs (...) about differentiation, the frequency of differentiated instruction, and the challenges faced by teachers who implement this inclusive practice. Sampled teachers offered their views on what they understood differentiated instruction to be, the frequency of differentiated instruction, and identified challenges via an administered questionnaire. Data analysis was based on frequency counts and bar charts for comparative purposes. Findings indicate that private school teachers have a higher frequency of differentiated teaching practice, with time constraints indicated as the main challenge. Government school teachers had a lower frequency of differentiation, and identified a lack of resources, and the learner-teacher ratio as challenges, among others. In the study we highlighted the critical role that private schools can play in the national call for the implementation of inclusive teaching in Lesotho, in terms of active collaboration with surrounding government schools. Private schools, with their resources and access to professional development opportunities, can become catalysts in the implementation of inclusive teaching practices. (shrink)

Two prominent relational egalitarians, Elizabeth Anderson and Niko Kolodny, object to giving people in a democratic community differential voting weights on the grounds that doing so would lead to unequal relations between them. Their claim is that deviating from a “one-person, one-vote” scheme is incompatible with realizing relational egalitarian justice. In this article, I argue that they are wrong. I do so by showing that people can relate as moral, epistemic, social, and empirical equals in a scheme with differential voting (...) weights. I end the article by showing that from the perspective of relational egalitarianism, it is sometimes true that differential voting weights are more just than equal voting weights. (shrink)

In this musing we consider how social distancing, the primary public health measure introduced to mitigate the spread of the COVID-19 virus, is creating social encounters characterized by a self-and-other-consciousness and an atmosphere of suspicion, leading to what we call “alienated embodied communication.” Whilst interaction rituals dominated by avoidance, fear and distrust are novel for many individuals who occupy positions of social privilege, Black and ethnic minority writers have demonstrated that the alienated bodily communication of COVID-19 social distancing is “nothing (...) new” for people who routinely experience marginalization as a result of racism. Our aim in this musing, then, is to reflect on how on-going experiences of stigma, shame, and marginalization can shape how social distancing is registered on an embodied and existential level, and therefore how social distancing may differentially impact individuals with lived experiences of racism. (shrink)

Recognizing that offers of payment to research participants can serve various purposes—reimbursement, compensation, and incentive—helps uncover differences between participants that can justify differential payment of participants within the same study. Participants with different study-related expenses will need different amounts of reimbursement to be restored to their pre-participation financial baseline. Differential compensation can be acceptable when some research participants commit more time or assume greater burdens than others, or if inter-site differences affect the value of compensation. Finally, it may be permissible (...) to offer differential incentive payments if necessary to advance a study’s goals. We encourage investigators and Institutional Review Boards to think not only about whether to offer payment, in what amounts, and for what purpose, but also to consider whether differential payment can help promote the scientific and ethical goals of clinical research. (shrink)

The “DNA is a program” metaphor is still widely used in Molecular Biology and its popularization. There are good historical reasons for the use of such a metaphor or theoretical model. Yet we argue that both the metaphor and the model are essentially inadequate also from the point of view of Physics and Computer Science. Relevant work has already been done, in Biology, criticizing the programming paradigm. We will refer to empirical evidence and theoretical writings in Biology, although our arguments (...) will be mostly based on a comparison with the use of differential methods (in Molecular Biology: a mutation or alike is observed or induced and its phenotypic consequences are observed) as applied in Computer Science and in Physics, where this fundamental tool for empirical investigation originated and acquired a well-justified status. In particular, as we will argue, the programming paradigm is not theoretically sound as a causal(as in Physics) or deductive(as in Programming) framework for relating the genome to the phenotype, in contrast to the physicalist and computational grounds that this paradigm claims to propose. (shrink)

We consider first-order theories of topological fields admitting a model-completion and their expansion to differential fields . We give a criterion under which the expansion still admits a model-completion which we axiomatize. It generalizes previous results due to M. Singer for ordered differential fields and of C. Michaux for valued differential fields. As a corollary, we show a transfer result for the NIP property. We also give a geometrical axiomatization of that model-completion. Then, for certain differential valued fields, we extend (...) the positive answer of Hilbert’s seventeenth problem and we prove an Ax–Kochen–Ershov theorem. Similarly, we consider first-order theories of topological fields admitting a model-companion and their expansion to differential fields, and under a similar criterion as before, we show that the expansion still admits a model-companion. This last result can be compared with those of M. Tressl: on one hand we are only dealing with a single derivation whereas he is dealing with several, on the other hand we are not restricting ourselves to definable expansions of the ring language, taking advantage of our topological context. We apply our results to fields endowed with several valuations. (shrink)

In this paper I argue that ethics and evidence are intricately intertwined within the clinical practice of differential diagnosis. Too often, when a disease is difficult to diagnose, a physician will dismiss it as being “not real” or “all in the patient’s head.” This is both an ethical and an evidential problem. In the paper my aim is two-fold. First, via the examination of two case studies (late-stage Lyme disease and Addison’s disease), I try to elucidate why this kind of (...) dismissal takes place. Then, I propose a potential solution to the problem. I argue that instead of dismissing a patient’s illness as “not real,” physicians ought to exercise a compassionate suspension of judgment when a diagnosis cannot be immediately made. I argue that suspending judgment has methodological, epistemic, and ethical virtues and therefore should always be preferred to patient dismissal in the clinical setting. (shrink)

The University of Tehran English Proficiency Test (UTEPT) is a high-stakes entrance examination taken by more than 10,000 master’s degree holders annually. The examinees’ scores have a significant influence on the final decisions concerning admission to the University of Tehran Ph.D. programs. As a test validation investigation, the present study, which is a bias detection research in nature, utilized multistep logistic regression (LR) procedure to examine the presence of gender differential item functioning (DIF) in the UTEPT with a sample of (...) 6,555 examinees who took the test in November 2006. Specifically, the LR DIF two-degree of freedom Chi-squared test of significance was employed to test the significance of DIF. Following what has been recently suggested in the literature, the test of significance for DIF was accompanied by a measure of magnitude, namely the R-squared effect size for LR DIF, for the interpretation of which the two widely accepted classification schemes were used comparatively. The results reveal that 39 of the 100 items in the test display significant gender differences. However, these group differences are viewed as “negligible” based on both of the schemes. Accordingly, it could be argued that the UTEPT is a gender DIF-free test, though the Reading Comprehension section of the test remains in need of further analysis as it seems that the general trend of DIF indices at the item level may hint at an inclination towards males. (shrink)

Questions about the relation between shame and embarrassment are often posed in discussion of emotion but have rarely been examined at length. In this study I assemble and examine distinctions that have been proposed in the literature with the aim of identifying the criteria that have been used to differentiate shame and embarrassment. Relevant empirical studies are also reviewed. Despite the attention paid to the question of the difference between shame and embarrassment consensus on differentiating criteria has not been reached (...) nor has there been consideration of what kind of question is being posed. Three positions that have been adopted are identified and critically evaluated. (shrink)

If the traditional problem of demandingness is that a theory demands too much of all agents, for example by asking them to maximize utility in every decision, then we should ask whether there is a related problem of “differential demandingness”, when a theory places vastly different demands on different agents. I argue that even according to common-sense morality, the demands faced by particular agents depend on a variety of contingent factors. These include the general circumstances, the compliance of others, the (...) available resources, the agent’s relevant relationships, the agent’s psychological constitution, and the agent’s knowledge. Some agents, for instance, find themselves in a “sacrifice hazard”: a situation where morality calls for a huge unforeseen sacrifice. I argue that if moral demands are differential, it is harder than one might think to assess a theory’s general level of demandingness in the abstract. (shrink)

In this paper I develop a systemic discrimination approach to defining a narrowly construed category of ‘hate speech’, as speech that harms to a sufficient degree to warrant government regulation. This is important due to the lack of definitional clarity, and the extraordinarily wide usage, of the term. This article extends current literature on how hate speech can harm by identifying under what circumstances speakers have the capacity to harm, and under what circumstances targets are vulnerable to harm. It also (...) shows how the capacity to harm can be mobile and involve the construction of new targets. Finally, it bridges the gap between conceptual understandings of hate speech and policy designed to regulate it. (shrink)

In The Face of Emotions, which was Carroll Izard’s first major attempt at elaborating his differential emotions theory, he stated that the book “presents a theoretical framework for the study of emotions and their role in personality and interpersonal processes.” Yet, over the years, his contribution to personality theory has generally been overshadowed by the attention focused on his views on facial expressions and the structure of emotions. This article will begin with a brief overview of the DET perspective on (...) personality development. Then, it will examine how the DET framework can be used to organize recent findings from three lines of research on adult personality. It will conclude with suggestions for future research as well as some personal recollections. (shrink)

The ability to distinguish between subtle differences among emotions of similar valence is labelled emotion differentiation (ED). Previous research has demonstrated that people high in ED are less likely to use disengagement regulation strategies (i.e. avoidance/distraction) during negative affective states.The present eye-tracking study examined associations between ED and visual attention/avoidance of affective stimuli. A total of 160 participants viewed emotional video clips (positive/ negative), which were concurrently presented with a non-affective distractor image. After each video, participants verbally described their (...) experienced emotions with adjectives in an open-response format. Moreover, they completed an ED questionnaire.The computed ED specificity index for the negative videos (the number of specific adjectives divided by all adjectives used) was positively associated with the scores on the ED questionnaire and visual revisits for the negative videos (how many times the participants gazed back and forth between video and distractor). This viewing style might reflect more active exploratory behaviour directed toward acquiring information about the negative stimulus and its context. The ED measures were not associated with the gaze behaviour for positive videos. (shrink)

The derivative is a basic concept of differential calculus. However, if we calculate the derivative as change in distance over change in time, the result at any instant is 0/0, which seems meaningless. Hence, Newton and Leibniz used the limit to determine the derivative. Their method is valid in practice, but it is not easy to intuitively accept. Thus, this article describes the novel method of differential calculus based on the double contradiction, which is easier to accept intuitively. Next, the (...) geometrical meaning of the double contradiction is considered as follows. A tangent at a point on a convex curve is iterated. Then, the slope of the tangent at the point is sandwiched by two kinds of lines. The first kind of line crosses the curve at the original point and a point to the right of it. The second kind of line crosses the curve at the original point and a point to the left of it. Then, the double contradiction can be applied, and the slope of the tangent is determined as a single value. Finally, the meaning of this method for the foundation of mathematics is considered. We reflect on Dehaene’s notion that the foundation of mathematics is based on the intuitions, which evolve independently. Hence, there may be gaps between intuitions. In fact, the Ancient Greeks identified inconsistency between arithmetic and geometry. However, Eudoxus developed the theory of proportion, which is equivalent to the Dedekind Cut. This allows the iteration of an irrational number by rational numbers as precisely as desired. Simultaneously, we can define the irrational number by the double contradiction, although its existence is not guaranteed. Further, an area of a curved figure is iterated and defined by rectilinear figures using the double contradiction. (shrink)

This paper considers two kinds of stochastic reentrant job shop scheduling problems, i.e., the SRJSSP with the maximum tardiness criterion and the SRJSSP with the makespan criterion. Owing to the NP-complete complexity of the considered RJSSPs, an effective differential evolutionary algorithm combined with two uncertainty handling techniques, namely, DEA_UHT, is proposed to address these problems. Firstly, to reasonably control the computation cost, the optimal computing budget allocation technique is applied for allocating limited computation budgets to assure reliable evaluation and identification (...) for excellent solutions or individuals, and the hypothesis test technique is added to execute a statistical comparison to reduce some unnecessary repeated evaluation. Secondly, a reentrant-largest-order-value rule is designed to convert the DEA’s individual to the SRJSSP’s solution. Thirdly, a conventional active decoding scheme for the job shop scheduling problem is extended to decode the solution for obtaining the criterion value. Fourthly, an Insert-based exploitation strategy and an Interchange-based exploration strategy are devised to enhance DEA’s exploitation ability and exploration ability, respectively. Finally, the test results and comparisons manifest the effectiveness and robustness of the proposed DEA_UHT. (shrink)

Graphic pattern (e.g. geometric design) and number-based code (e.g. digital sequencing) can store and transmit complex information more efficiently than referential modes of representation. The analysis of the two genres and their relation to one another has not advanced significantly beyond a general classification based on motion-centred geometries of symmetry. This article examines an intriguing example of patchwork coverlets from the maritime societies of Oceania, where information referencing a complex genealogical system is lodged in geometric designs. By drawing attention to (...) the interplay of graphic pattern and number-based code and its role in the knowledge economies of maritime societies, the article offers new insight into possible ways of designing a digital informational surface that captures the behaviour of an operational system, allowing both for differentiation and integration. (shrink)

Justifications of group-differentiated rights commonly overlook a crucial practical consideration: if rights are to be allocated on the basis of group membership, how should we determine which individuals belong to which group? Assuming that social identities are fixed and transparent runs the risk of creating further injustices, whilst acknowledging that social groups are porous and heterogeneous runs the risk of rendering group-differentiated rights impracticable. In this paper, I develop a schema for determining group membership which avoids both horns of this (...) dilemma. (shrink)

In this paper I develop a systemic discrimination approach to defining a narrowly construed category of ‘hate speech’, as speech that harms to a sufficient degree to warrant government regulation. This is important due to the lack of definitional clarity, and the extraordinarily wide usage, of the term. This article extends current literature on how hate speech can harm by identifying under what circumstances speakers have the capacity to harm, and under what circumstances targets are vulnerable to harm. It also (...) shows how the capacity to harm can be mobile and involve the construction of new targets. Finally, it bridges the gap between conceptual understandings of hate speech and policy designed to regulate it. (shrink)

There is a similarity between the most technical scientific reasoning and the most humanistic literary reasoning. While engineers and historians make use of both metaphors and stories, engineers specialize in metaphors, and historians in stories. Placing metaphor, or pure comparison, at one end of a scale and simply a listing of events, or pure story, at the other, it can be seen that what connects them is a theme. The theme providing the connecting link between poles for both the engineer (...) and the historian is time. Themes in engineering that mention time are those titled differential equations. The differential equation is story-like because it speaks of time and therefore organizes experience in time, at least implicitly. Time- speaking themes shape the raw experience, as a story does when it is more than a mere unthematized chronicle. The chaotic nature of non-linear differential equations parallels the chaotic nature of history in that large results need not have large causes. Narration becomes difficult in chaotic systems because the knowledge of initial conditions is rarely sufficiently detailed to allow for accurate explanation or prediction for either engineers or historians. (shrink)

How does shame differ from guilt? Empirical psychology has recently offered distinct and seemingly incompatible answers to this question. This article brings together four prominent answers into a cohesive whole. These are that (a) shame differs from guilt in being a social emotion; (b) shame, in contrast to guilt, affects the whole self; (c) shame is linked with ideals, whereas guilt concerns prohibitions and (d) shame is oriented towards the self, guilt towards others. After presenting the relevant empirical evidence, we (...) defend specific interpretations of each of these answers and argue that they are related to four different dimensions of the emotions. This not only allows us to overcome the conclusion that the above criteria are either unrelated or conflicting with one another, it also allows us to tell apart what is constitutive from what is typical of them. -/- . (shrink)

Problems of functional style differentiation of modern literary language are considered and analyzed in the article. Taking into account the communicative and pragmatic function, various substyles and sublanguages formed as a result of practical language usage in society are singled out on the example of the scientific style.

It is often argued that human emotions, and the cognitions that accompany them, involve refinements of, and extensions to, more basic functionality shared with other species. Such refinements may rely on common or on distinct processes and representations. Multi-level theories of cognition and affect make distinctions between qualitatively different types of representations often dealing with bodily, affective and cognitive attributes of self-related meanings. This paper will adopt a particular multi-level perspective on mental architecture and show how a mechanism of subsystem (...) differentiation could have allowed an evolutionarily “old” role for emotion in the control of action to have altered into one more closely coupled to meaning systems. We conclude by outlining some illustrative consequences of our analysis that might usefully be addressed in research in comparative psychology, cognitive archaeology, and in laboratory research on memory for emotional material. (shrink)

This unique book provides a self-contained conceptual and technical introduction to the theory of differential sheaves. This serves both the newcomer and the experienced researcher in undertaking a background-independent, natural and relational approach to "physical geometry". In this manner, this book is situated at the crossroads between the foundations of mathematical analysis with a view toward differential geometry and the foundations of theoretical physics with a view toward quantum mechanics and quantum gravity. The unifying thread is provided by the theory (...) of adjoint functors in category theory and the elucidation of the concepts of sheaf theory and homological algebra in relation to the description and analysis of dynamically constituted physical geometric spectrums. (shrink)