We investigate how weak square principles are denied by Chang’s Conjecture and its generalizations. Among other things we prove that Chang’s Conjecture does not imply the failure of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square_{\omega_1, 2}}$$\end{document}, i.e. Chang’s Conjecture is consistent with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square_{\omega_1, 2}}$$\end{document}.

L S Penrose’s Limit Theorem – which is implicit in Penrose [7, p. 72] and for which he gave no rigorous proof – says that, in simple weighted voting games, if the number of voters increases indefinitely and the relative quota is pegged, then – under certain conditions – the ratio between the voting powers of any two voters converges to the ratio between their weights. Lindner and Machover [4] prove some special cases of Penrose’s Limit Theorem. They give a (...) simple counter-example showing that the theorem does not hold in general even under the conditions assumed by Penrose; but they conjecture, in effect, that under rather general conditions it holds ‘almost always’ – that is with probability 1 – for large classes of weighted voting games, for various values of the quota, and with respect to several measures of voting power. We use simulation to test this conjecture. It is corroborated with respect to the Penrose–Banzhaf index for a quota of 50% but not for other values; with respect to the Shapley–Shubik index the conjecture is corroborated for all values of the quota. (shrink)

In the last decade, the Poincaré conjecture has probably been the most famous statement among all the contributions of Poincaré to the mathematics community. There have been many papers and books that describe various attempts and the final works of Perelman leading to a positive solution to the conjecture, but the evolution of Poincaré’s works leading to this conjecture has not been carefully discussed or described, and some other historical aspects about it have not been addressed either. (...) For example, one question is how it fits into the overall work of Poincaré in topology, and what are some other related questions that he had raised. Since Poincaré did not state the Poincaré conjecture as a conjecture but rather raised it as a question, one natural question is why he did this. In order to address these issues, in this paper, we examine Poincaré’s works in topology in the framework of classifying manifolds through numerical and algebraic invariants. Consequently, we also provide a full history of the formulation of the Poincaré conjecture which is richer than what is usually described and accepted and hence gain a better understanding of overall works of Poincaré in topology. In addition, this analysis clarifies a puzzling question on the relation between Poincaré’s stated motivations for topology and the Poincaré conjecture. (shrink)

Answering a question of Sakai :29–45, 2013), we show that the existence of an \-Erdős cardinal suffices to obtain the consistency of Chang’s Conjecture with \. By a result of Donder, volume 872 of lecture notes in mathematics. Springer, Berlin, pp 55–97, 1981) this is best possible. We also give an answer to another question of Sakai relating to the incompatibility of \ and \ \twoheadrightarrow \) for uncountable \.

Answering a question of Sakai :29–45, 2013), we show that the existence of an ω1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega _1$$\end{document}-Erdős cardinal suffices to obtain the consistency of Chang’s Conjecture with □ω1,2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\square _{\omega _1, 2}$$\end{document}. By a result of Donder, volume 872 of lecture notes in mathematics. Springer, Berlin, pp 55–97, 1981) this is best possible. We also give an answer to another question of Sakai (...) relating to the incompatibility of □λ,2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\square _{\lambda, 2}$$\end{document} and ↠\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \twoheadrightarrow $$\end{document} for uncountable κ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa $$\end{document}. (shrink)

We introduce a natural principleStrong Chang Reflectionstrengthening the classical Chang Conjectures. This principle is between a huge and a two huge cardinal in consistency strength. In this note we prove that it implies the existence of an inner model with a huge cardinal. The technique we explore for building inner models with huge cardinals adapts to show thatdecisiveideals imply the existence of inner models with supercompact cardinals. Proofs for all of these claims can be found in [10].1,2.

We determine the consistency strength of the negation of the transversal hypothesis. We also study other variants of Chang's conjecture.

We prove that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${(\omega_3, \omega_2) \twoheadrightarrow (\omega_2, \omega_1)}$$\end{document} implies there is an inner model with a weak repeat measure.

Context: Philosophy of science is the branch of philosophy that deals with methods, foundations, and implications of science. It is a theory of how to create scientific knowledge. Presently, there is widespread agreement on how to do science, namely conjectures, ideally in the form of a mathematical model, and refutations, testing the model using empirical evidence. Problem: Many social scientists are using a conception of science created for the physical sciences. Expanding philosophy of science so that it more successfully encompasses (...) social systems would create new avenues of inquiry. Two dimensions could be added to philosophy of science: the amount of attention paid to the observer and the amount of impact of a theory on the system described. Method: My approach is to illuminate underlying assumptions. I claim that there are at least three epistemologies and that they can be combined to form a more robust conception of knowledge and of how to do research. There are at least four models and four basic elements being used by scientists. Results: The article identifies the logical propositions underlying second-order science. It suggests strategies for developing second-order science. And it describes several methods that can be used to practice second-order science, including how past theories have not only described but also changed the phenomenon being studied. Implications: The task for members of the scientific community, particularly social scientists, is to practice second-order science and to develop further its theories and methods. A practical implication is to accept methods for acting as well as theories as a contribution to science, since methods explicitly define the role of an observer/ participant. Constructivist content: The paper is an extension of the work of Heinz von Foerster and other second-order cyberneticians. (shrink)

A belief in a firm correspondence between objects, ideas, and their representation in language pervaded the works of Anne Robert Jacques Turgot

(1727–1781) in 1750. This conviction is particularly manifest in Turgot’s sharp critique of Berkeley’s philosophical system and his remarks on Maupertuis’s reconstruction of the origin of language. During the 1750s Turgot’s epistemological views underwent a change, apparent in two of his contributions to the Encyclopédie: the entries Existence and Étymologie (1756). These articles included a reassessment of Berkeleyan immaterialism, facing (...) an ultimate crisis of definition and representation. A similar development may be traced in contemporary works by Condillac and Diderot. Turgot’s Encyclopédie entries also envisaged a new science, an archeology of the human mind aided by the examination of linguistic development and change. This entailed the scientific verification of conjectures in any historical account of ideas, turning etymological

and psychological inquiries into what Turgot termed ‘experimental metaphysics’. (shrink)

Revolutionary developments in economics are rare. The conservative bias of the field and its enshrined knowledge make it difficult to introduce new ideas not in line with received theory. Happiness research, however, has the potential to change economics substantially in the future. Its findings, which are gradually being taken into account in standard economics, can be considered revolutionary in three respects: the measurement of experienced utility using psychologists' tools for measuring subjective well-being; new insights into how human beings value goods (...) and services and social conditions that include consideration of such non-material values as autonomy and social relations; and policy consequences of these new insights that suggest different ways for government to affect individual well-being. In Happiness, emphasizing empirical evidence rather than theoretical conjectures, Bruno Frey substantiates these three revolutionary claims for happiness research. After tracing the major developments of happiness research in economics and demonstrating that we have gained important new insights into how income, unemployment, inflation, and income demonstration affect well-being, Frey examines such wide-ranging topics as democracy and federalism, self-employment and volunteer work, marriage, terrorism, and watching television from the new perspective of happiness research. Turning to policy implications, Frey describes how government can provide the conditions for people to achieve well-being, arguing that a crucial role is played by adequate political institutions and decentralized decision making. Happiness demonstrates the achievements of the economic happiness revolution and points the way to future research.Bruno S. Frey is Professor of Economics at the University of Zurich, Visiting Professor at the Swiss Federal Institute of Technology, and Research Director of CREMA. He is co-editor of Economics and Psychology: A Promising New Cross-Disciplinary Field. (shrink)

Revolutionary developments in economics are rare. The conservative bias of the field and its enshrined knowledge make it difficult to introduce new ideas not in line with received theory. Happiness research, however, has the potential to change economics substantially in the future. Its findings, which are gradually being taken into account in standard economics, can be considered revolutionary in three respects: the measurement of experienced utility using psychologists' tools for measuring subjective well-being; new insights into how human beings value goods (...) and services and social conditions that include consideration of such non-material values as autonomy and social relations; and policy consequences of these new insights that suggest different ways for government to affect individual well-being. In Happiness, emphasizing empirical evidence rather than theoretical conjectures, Bruno Frey substantiates these three revolutionary claims for happiness research. After tracing the major developments of happiness research in economics and demonstrating that we have gained important new insights into how income, unemployment, inflation, and income demonstration affect well-being, Frey examines such wide-ranging topics as democracy and federalism, self-employment and volunteer work, marriage, terrorism, and watching television from the new perspective of happiness research. Turning to policy implications, Frey describes how government can provide the conditions for people to achieve well-being, arguing that a crucial role is played by adequate political institutions and decentralized decision making. Happiness demonstrates the achievements of the economic happiness revolution and points the way to future research.Bruno S. Frey is Professor of Economics at the University of Zurich, Visiting Professor at the Swiss Federal Institute of Technology, and Research Director of CREMA. He is co-editor of Economics and Psychology: A Promising New Cross-Disciplinary Field. (shrink)

Housman reads assueta euolitans; the former word is a conjecture of his own, the latter a conjecture of Ellis, which I think he would have ignored if the relevant fascicle of the Thesaurus had been available to show that euolitare occurs once in Columella and then not before the sixth century. If assueto is sound, mundi must be changed to mundo or to another noun. Bentley read mundo, and this may well be the right solution: the eagle carries (...) thunderbolts to the sky, “cui scilicet per diuturnas operas assueuerat”. Shackleton Bailey emends to nisu. If emendation were required, I suggest that motu would be palaeographically more satisfactory; the assumed process of corruption is well illustrated by 3.82, motu GL: modum M: mundo LV. (shrink)

Todorčević showed that Rado's Conjecture implies CC*, a strengthening of Chang's Conjecture. We generalize this by showing that also CC**, a global version of CC*, follows from RC. As a corollary we obtain that RC implies Semistationary Reflection and, i.e. the statement that all forcings that preserve the stationarity of subsets of ω1 are semiproper.

We introduce a natural generalization of Borel's Conjecture. For each infinite cardinal number $\kappa$, let ${\sf BC}_{\kappa}$ denote this generalization. Then ${\sf BC}_{\aleph_0}$ is equivalent to the classical Borel conjecture. Assuming the classical Borel conjecture, $\neg{\sf BC}_{\aleph_1}$ is equivalent to the existence of a Kurepa tree of height $\aleph_1$. Using the connection of ${\sf BC}_{\kappa}$ with a generalization of Kurepa's Hypothesis, we obtain the following consistency results: 1. If it is consistent that there is a 1-inaccessible cardinal (...) then it is consistent that ${\sf BC}_{\aleph_1}$.2. If it is consistent that ${\sf BC}_{\aleph_1}$, then it is consistent that there is an inaccessible cardinal.3. If it is consistent that there is a 1-inaccessible cardinal with $\omega$ inaccessible cardinals above it, then $\neg{\sf BC}_{\aleph_{\omega}} + (\forall n < \omega){\sf BC}_{\aleph_n}$ is consistent.4. If it is consistent that there is a 2-huge cardinal, then it is consistent that ${\sf BC}_{\aleph_{\omega}}$.5. If it is consistent that there is a 3-huge cardinal, then it is consistent that ${\sf BC}_{\kappa}$ for a proper class of cardinals $\kappa$ of countable cofinality. (shrink)

We show that both Rado's Conjecture and strong Chang's Conjecture imply that there are no special ℵ2-Aronszajn trees if the Continuum Hypothesis fails. We give similar result for trees of higher heights and we also investigate the influence of Rado's Conjecture on square sequences.

We show that both Rado's Conjecture and strong Chang's Conjecture imply that there are no special ℵ2-Aronszajn trees if the Continuum Hypothesis fails. We give similar result for trees of higher heights and we also investigate the influence of Rado's Conjecture on square sequences.

Magnetoencephalography is increasingly used for presurgical planning in people with medically refractory focal epilepsy. Localization of interictal epileptiform activity, a surrogate for the seizure onset zone whose removal may prevent seizures, is challenging and depends on the use of multiple complementary techniques. Accurate and reliable localization of epileptiform activity from spontaneous MEG data has been an elusive goal. One approach toward this goal is to use a novel Bayesian inference algorithm—the Champagne algorithm with noise learning—which has shown tremendous success in (...) source reconstruction, especially for focal brain sources. In this study, we localized sources of manually identified MEG spikes using the Champagne algorithm in a cohort of 16 patients with medically refractory epilepsy collected in two consecutive series. To evaluate the reliability of this approach, we compared the performance to equivalent current dipole modeling, a conventional source localization technique that is commonly used in clinical practice. Results suggest that Champagne may be a robust, automated, alternative to manual parametric dipole fitting methods for localization of interictal MEG spikes, in addition to its previously described clinical and research applications. (shrink)

Includes translations of the important manuscripts in silk found at the famous Mawangdui Tomb in 1973.

Theories of language production have long been expressed as connectionist models. We outline the issues and challenges that must be addressed by connectionist models of lexical access and grammatical encoding, and review three recent models. The models illustrate the value of an interactive activation approach to lexical access in production, the need for sequential output in both phonological and grammatical encoding, and the potential for accounting for structural effects on errors and structural priming from learning.

Is flexibility or formality more useful for organizations that are pursuing improved performance? Organizational structure scholars offer opposing answers to this question, and empirical results have been mixed. Our study contributes to this research by describing a mediational model that links organizational flexibility to performance via opportunity exploitation. Specifically, we argue that flexible firms are able to exploit a greater number of opportunities, which, in turn, can improve performance. We also argue that the indirect effect of flexibility on performance via (...) opportunity exploitation is stronger when top executives display higher affective commitment for their firms, meaning that they have a positive emotional attachment to their firms. Top executives with higher affective commitment can mitigate the downsides experienced by the staff of flexible firms, such as uncertainty and negative affect, which improves the outcomes of flexibility. Drawing on a sample of 211 firms and their founders, we find support for our hypotheses. (shrink)

ObjectivePeer victimization is a substantial early life stressor linked to psychiatric symptoms and poor academic performance. However, the sex-specific cognitive or behavioral outcomes of bullying have not been well-described in preadolescent children.MethodsUsing the baseline dataset of the Adolescent Brain Cognitive Development Study 2.0.1 data repository, we evaluated associations between parent-reported bullying victimization, suicidality, and non-suicidal self-injury, as well as internalizing and externalizing behavioral problems, cognition, and academic performance.ResultsOf the 11,015 9-10-year-old children included in the analyses, 15.3% experienced bullying victimization, as (...) reported by the primary caregiver. Of these, boys were more likely to be bullied than girls. Children who were bullied were more likely to display NSSI or passive suicidality and active suicidality. Bullied children also had lower cognitive scores, greater behavioral problems, and poorer grades. Across all participants, boys had poorer grades and greater behavioral problems than girls; however, bullied boys had greater behavioral problems than girls in several areas. Compared to their non-bullied peers, bullied children with greater non-suicidal self-injury or suicidality also had greater behavioral problems and poorer grades.ConclusionThese findings highlight the sex-specific effects of bullying, and the negative associations of bullying victimization with cognitive performance, behavioral problems, and academic performance. Future longitudinal studies will identify the natural history and neural correlates of these deficits during adolescence. (shrink)

Racially disparate policing, prosecution, and punishment harm individuals, families, and communities. These practices must be understood within the context of the development of the criminal legal system as a means of racialized social control. This context permits a critical examination of the way criminalization has been and is still deployed to subject poor and racialized communities to systemic injustices. This commentary frames a call for interventions to integrate a health justice approach to ensure that they advance racial and health equity (...) to promote the well-being of individuals, families, and communities. (shrink)