We study model theory of actions of finite groups on substructures of a stable structure. We give an abstract description of existentially closed actions as above in terms of invariants and PAC structures. We show that if the corresponding PAC property is first order, then the theory of such actions has a model companion. Then, we analyze some particular theories of interest (mostly various theories of fields of positive characteristic) and show that in all the cases considered the PAC (...) property is first order. (shrink)

We generalize a well-known theorem binding the elementary equivalence relation on the level of PAC fields and the isomorphism type of their absolute Galois groups. Our results concern two cases: saturated PAC structures and nonsaturated PAC structures.

We achieve several results. First, we develop a variant of the theory of absolute Galois groups in the context of many sorted structures. Second, we provide a method for coding absolute Galois groups of structures, so they can be interpreted in some monster model with an additional predicate. Third, we prove the “Weak Independence Theorem” for pseudo-algebraically closed (PAC) substructures of an ambient structure with no finite cover property (nfcp) and the property [Formula: see text]. Fourth, we describe Kim-dividing (...) in these PAC substructures and show several results related to the SOPnhierarchy. Fifth, we characterize the algebraic closure in PAC structures. (shrink)

We introduce and study the notions of a PAC-substructure of a stable structure, and a bounded substructure of an arbitrary substructure, generalizing [10]. We give precise definitions and equivalences, saying what it means for properties such as PAC to be first order, study some examples (such as differentially closed fields) in detail, relate the material to generic automorphisms, and generalize a "descent theorem" for pseudo-algebraically closed fields to the stable context. We also point out that the elementary invariants of (...) pseudo-algebraically closed fields from [6] are also valid for pseudo-differentially closed fields. (shrink)

We study structures equipped with generic predicates and/or automorphisms, and show that in many cases we obtain simple theories. We also show that a bounded PAC field is simple. 1998 Published by Elsevier Science B.V. All rights reserved.

Bounded PAC substructures of models of stable theory T are generalizations of bounded PAC fields and bounded PAC beautiful pairs generalize Poizat's beautiful pairs. Both notions were introduced in the authors Ph.D. thesis. In this paper, we prove that under the assumption that the PAC property is first order for T, the theory of any bounded PAC structure is simple. Moreover, if the PAC property is first order for T and T does not have the finite cover property, then (...) the theory of any bounded PAC beautiful pair is simple. We, also, give a characterization of dividing in both cases. (shrink)

Contemporary architecture is increasingly grounded in science and mathematics. Architectural discourse has shifted radically from the sometimes disorienting Derridean deconstruction, to engaging scientific terms such as fractals, chaos, complexity, nonlinearity, and evolving systems. That's where the architectural action is -- at least for cutting-edge architects and thinkers -- and every practicing architect and student needs to become conversant with these terms and know what they mean. Unfortunately, the vast majority of architecture faculty are unprepared to explain them to students, not (...) having had a scientific education themselves. Here is an architecture book by an architect/scientist, just in time to help architects in the new millennium. Alexander discusses many of the scientific terms arising in cutting-edge architecture, and explains them to those who don't have scientific training or advanced mathematical knowledge. We find discussions of the evolution of forms; the importance of process in design; iteration; genetic algorithms; sequences of transformations; different levels of scale (i.e. fractals); etc. They are explained here by an architect who is also a scientist, because he wants to change the way architects think and build. Alexander is not merely popularizing other scientists' results and making them accessible to architects: he is in fact presenting new and original scientific work that ties many of these concepts together in a way that will be useful to architects. (shrink)

The article presents proofs of the context freeness of a family of typelogical grammars, namely all grammars that are based on a uni- ormultimodal logic of pure residuation, possibly enriched with thestructural rules of Permutation and Expansion for binary modes.

Identifying biomarkers of developing mental disorder is crucial to improving early identification and treatment—a key strategy for reducing the burden of mental disorders. Cross-frequency coupling between two different frequencies of neural oscillations is one such promising measure, believed to reflect synchronization between local and global networks in the brain. Specifically, in adults phase–amplitude coupling (PAC) has been shown to be involved in a range of cognitive processes, including working and long-term memory, attention, language, and fluid intelligence. Evidence suggests that increased (...) PAC mediates both temporary and lasting improvements in working memory elicited by transcranial direct-current stimulation and reductions in depressive symptoms after transcranial magnetic stimulation. Moreover, research has shown that abnormal patterns of PAC are associated with depression and schizophrenia in adults. PAC is believed to be closely related to cortico-cortico white matter (WM) microstructure, which is well established in the literature as a structural mechanism underlying mental health. Some cognitive findings have been replicated in adolescents and abnormal patterns of PAC have also been linked to ADHD in young people. However, currently most research has focused on cross-sectional adult samples. Whereas initial hypotheses suggested that PAC was a state-based measure due to an early focus on cognitive, task-based research, current evidence suggests that PAC has both state-based and stable components. Future longitudinal research focusing on PAC throughout adolescent development could further our understanding of the relationship between mental health and cognition and facilitate the development of new methods for the identification and treatment of youth mental health. (shrink)

Some opponents of abortion claim that fetuses are persons from the moment of conception. Following Berg (2017), let us call these individuals “Personhood-At-Conception” (or PAC), opponents of abortion. Berg argues that if fetuses are persons from the moment of conception, then miscarriage kills far more people than abortion. As such, PAC opponents of abortion face the following dilemma: They must “immediately” and “substantially” shift their attention, resources, etc., toward preventing miscarriage or they must admit that they do not actually believe (...) that fetuses are persons from the moment of conception (or, at least, they must recognize that they are not acting in ways that are consistent with this belief). In this essay, I show that Berg’s argument fails at each step. Specifically, after outlining her argument (in section 1), I consider the central claim of Berg’s style of argument: That “miscarriage…is much deadlier than abortion.” In section 2, I argue that this claim is false (when taken literally) and misleading otherwise. In section 3, I show that Berg’s style of argument is identical in structure to a criticism that is sometimes levied against the recent “Black Lives Matter” movement. In the latter context, the argument has been vehemently rejected. I argue that Berg’s style of argument should be rejected for the same reasons. Finally, in section 4, I show that Berg’s suggestion that opponents of abortion should divert “substantial” amounts of money and attention to miscarriage prevention faces two problems. First, these claims are made without any evidence regarding the actual priorities and spending habits of PAC opponents of abortion. If we are told “not enough is being done,” one wonders: What is being done and how much counts as “enough”? Berg gives no answer to either question. Second, even if it is true that opponents of abortion do not pay substantial attention to miscarriage prevention, Berg fails to notice that this may be for good reason. I conclude that PAC opponents of abortion do not face the dilemma that Berg presents. (shrink)

We present a quantum model for the motion of N point particles, implying nonlocal (i.e., superluminal) influences of external fields on the trajectories, that is nonetheless fully relativistic. In contrast to other models that have been proposed, this one involves no additional space-time structure as would be provided by a (possibly dynamical) foliation of space-time. This is achieved through the interplay of opposite microcausal and macrocausal (i.e., thermodynamic) arrows of time. PACS numbers 03.65.Ud; 03.65.Ta; 03.30.+p..

This thesis is concerned with the expansions of algebraic structures and their fit in Shelah’s classification landscape.The first part deals with the expansion of a theory by a random predicate for a substructure model of a reduct of the theory. Let T be a theory in a language $\mathcal {L}$. Let $T_0$ be a reduct of T. Let $\mathcal {L}_S = \mathcal {L}\cup \{S\}$, for S a new unary predicate symbol, and $T_S$ be the $\mathcal {L}_S$ -theory that axiomatises the (...) following structures: $$ consist of a model $\mathscr {M}$ of T and S is a predicate for a model $\mathscr {M}_0$ of $T_0$ which is a substructure of $\mathscr {M}$. We present a setting for the existence of a model-companion $TS$ of $T_S$. As a consequence, we obtain the existence of the model-companion of the following theories, for $p>0$ a prime number: • $\mathrm {ACF}_p$, $\mathrm {SCF}_{e,p}$, $\mathrm {Psf}_p$, $\mathrm {ACFA}_p$, $\mathrm {ACVF}_{p,p}$ in appropriate languages expanded by arbitrarily many predicates for additive subgroups;• $\mathrm {ACF}_p$, $\mathrm {ACF}_0$ in the language of rings expanded by a single predicate for a multiplicative subgroup;• $\mathrm {PAC}_p$ -fields, in an appropriate language expanded by arbitrarily many predicates for additive subgroups.From an independence relation in T, we define independence relations in $TS$ and identify which properties of are transferred to those new independence relations in $TS$, and under which conditions. This allows us to exhibit hypotheses under which the expansion from T to $TS$ preserves $\mathrm {NSOP}_{1}$, simplicity, or stability. In particular, under some technical hypothesis on T, we may draw the following picture : Configuration $T_0\subseteq T$ Generic expansion $TS$ $T_0 = T$ Preserves stability $T_0\subseteq T$ Preserves $\mathrm {NSOP}_{1}$ $T_0 = \emptyset $ Preserves simplicityIn particular, this construction produces new examples of $\mathrm {NSOP}_{1}$ not simple theories, and we study in depth a particular example: the expansion of an algebraically closed field of positive characteristic by a generic additive subgroup. We give a full description of imaginaries, forking, and Kim-forking in this example.The second part studies expansions of the group of integers by p-adic valuations. We prove quantifier elimination in a natural language and compute the dp-rank of these expansions: it equals the number of independent p-adic valuations considered. Thus, the expansion of the integers by one p-adic valuation is a new dp-minimal expansion of the group of integers. Finally, we prove that the latter expansion does not admit intermediate structures: any definable set in the expansion is either definable in the group structure or is able to “reconstruct” the valuation using only the group operation.prepared by Christian d’Elbée.E-mail: [email protected]: https://choum.net/~chris/page_perso. (shrink)

The gap between the decision to engage in physical activity and subsequent behavioral enactment is considerable for many. Action control theories focus on this discordance in an attempt to improve the translation of intention into behavior. The purpose of this mini-review was to overview one of these approaches, the multi-process action control framework, which has evolved from a collection of previous works. The main concepts and operational structure of M-PAC was overviewed followed by applications of the framework in physical (...) activity, and concluded with unanswered questions, limitations, and possibilities for future research. In M-PAC, it is suggested that three layered processes build upon each other from the formation of an intention to a sustained profile of physical activity action control. Intention-behavior discordance is because of strategic challenges in goal pursuit and automatic tendencies. Regulatory processes are employed to hold the relationship between reflective processes and behavior concordant by countering these strategic challenges and automatic tendencies until the development of reflexive processes begin to co-determine action control. Results from 29 observational and preliminary experimental studies generally support the proposed M-PAC framework. Future research is needed to explore the temporal dynamic between reflexive and regulatory constructs, and implement M-PAC interventions in different forms, and at different levels of scale. (shrink)

About 25 years ago, it came to light that a single combinatorial property determines both an important dividing line in model theory and machine learning. The following years saw a fruitful exchange of ideas between PAC-learning and the model theory of NIP structures. In this article, we point out a new and similar connection between model theory and machine learning, this time developing a correspondence between stability and learnability in various settings of online learning. In particular, this gives many new (...) examples of mathematically interesting classes which are learnable in the online setting. (shrink)

This article addresses the question which structures occur as fixed structures of stable structures with a generic automorphism. In particular we give a Galois theoretic characterization. Furthermore, we prove that any pseudofinite field is the fixed field of some model ofACFA, any one-free pseudo-differentially closed field of characteristic zero is the fixed field of some model ofDCFA, and that any one-free PAC field of finite degree of imperfection is the fixed field of some model ofSCFA.

Business scholars pay increasing attention to the expanded influence of stakeholders on firm strategies, legitimacy, and competitiveness. At the same time, analysts have noted that the transformed regulatory and legislative environments of recent decades have encouraged firms to become much more politically active. Surprisingly, relatively little research has tied together these two trends. The present study integrates perspectives on stakeholder management with research on corporate political activity to develop an understanding of the structural sources of stakeholder mobilization in professional grassroots (...) lobbying campaigns. This study employs a unique, original data source to consider how the adoption of grassroots lobbying by a firm relates to its industry, degree of inside lobbying, partisan PAC contributions, and more. This research shows that corporate grassroots lobbying is shaped most significantly by a firm’s degree of inside lobbying, as highly active firms take a diversified strategy for gaining influence. Firms in industries with a heavy public presence as well as those concerned with taxation, government appropriations, and economic development also adopt these strategies readily. PAC contributions to Republican, but not Democratic, candidates also heighten firms’ propensity to lobby the public. (shrink)

Peace and conflict studies education has grown significantly in the last 30 years, mainly in Higher Education. This article critically analyzes the ways in which this field might be subject to poststructural critique, and posits Bourdieusian second-order reflexivity as a means of responding to these critiques. We propose here that theory-building within PACS education is often limited by the dominance of Galtung and Freire, and that, while the foundational ideas of positive and negative peace, structural and cultural violence, conscientization, reflexivity (...) and critical pedagogy are still relevant today, they nevertheless need to be combined in new ways with each other, and with Bourdieu’s notions of habitus and field, to adequately respond to poststructural critique. Thus, we call here for greater field-based reflexivity in twenty-first century PACS. (shrink)

Publication date: 22 December 2020 Source: International Letters of Social and Humanistic Sciences Vol. 89 Author: Oleg Tarnopolsky, Marina Kabanova The article analyzes using Content and Language Integrated Learning for teaching one of the optional humanities disciplines to Ukrainian university students of different majors. The discipline discussed in the article as an example of using CLIL methodology is “The Fundamentals of Psychology and Pedagogy” and it is in the list of optional humanities subjects for the first-year students of Alfred Nobel (...) University in Dnipro, Ukraine. However, unlike the other optional humanities disciplines, the methodology underlying this course is based on teaching the subject in English, instead of Ukrainian, following the CLIL approach widely used in the European education but still little known in Ukraine. The purpose of the paper is to expose and analyze the original methodology developed that conditioned the specific structure of the relevant course, and the specific learning activities used in it. The essence of the developed CLIL theory-based methodology and its practical application are manifested through learning activities that include students’ mini-lectures/workshop-type presentations, brainstorming, case-studies, discussions, and a learning project with its results summarized in students’ essays, abstracts, and summaries written in English. The students collect the information required for completing their tasks not only from the teacher’s lectures and the recommended literature but also by way of doing extensive Internet-search on psychological and pedagogical sites in English. All this makes CLIL in the case under discussion experiential-interactive, blended, autonomous, and cooperative. As the result, students mostly self-construct their knowledge of the discipline by way of using the target language as the tool for such self-construction. This makes the elaborated course a clear-cut case of constructivism in CLIL pedagogy. Subject Classification Numbers: PACS 01.40.-d. (shrink)

The COVID-19 pandemic has negatively impacted the psychosocial functioning of children and families. It is important to consider adversity in relation to processes of positive adaptation. To date, there are no empirically validated multi-item scales measuring COVID-related positive adaptation within families. The aim of the current study was to develop and validate a new measure: the Family Positive Adaptation during COVID-19 Scale. The sample included 372 female and 158 male caregivers of children ages 5–18 years old from the United Kingdom, (...) the United States, Canada, and Australia, who completed measures in May 2020. Participants responded to a 14-item survey indexing a range of perceived coping and adaptation behaviors at the beginning of the pandemic. An exploratory factor analysis yielded an optimal one-factor solution comprised of seven items related to family cohesion, flexibility, routines, and meaning-making. Multigroup confirmatory factor analysis demonstrated measurement invariance across female and male caregivers, demonstrating that the factor structure, loadings, and thresholds did not vary by caregiver sex. There was evidence for concurrent validity with significant bivariate correlations between the Family PACS scores and measures of caregiver positive coping, parenting practices, couple satisfaction, and family functioning, but not negatively-valenced constructs. Findings inform our conceptualization of how families have adapted to adverse pandemic-related conditions. Further, we provide preliminary support for the Family PACS as a practical tool for evaluating positive family adaptation during this global crisis, with implications for future widespread crises. (shrink)

The essays that follow grew out of a workshop held at the Center for Buddhist Studies, University of California, Berkeley, in March 2018, on the topic of conceptuality and non-conceptuality in Buddhist philosophy. Discussions at the workshop focused specifically on the tenability of the claim made by the two Buddhist epistemologists Dignāga and Dharmakīrti that perceptual cognitions are non-conceptual and yet also contribute to the contents of conceptual thought. The four contributions collected here present just a few of the resulting (...) reflections.This essay explores the Dharmakīrtian1 notion of a "concept" in the specific context of a "pseudo-perception", that is, cognitive events that... (shrink)

The Probably Approximately Correct (PAC) learning is a machine learning model introduced by Leslie Valiant in 1984. The PACi reducibility refers to the PAC reducibility independent of size and computation time. This reducibility in PAC learning resembles the reducibility in Turing computability. The ordering of concept classes under PAC reducibility is nonlinear, even when restricted to particular concrete examples.Due to the resemblance to Turing Reducibility, we suspected that there could be incomparable PACi and PAC degrees for the PACi and PAC (...) reducibilities as in Turing incomparable degrees. In 1957 Friedberg and in 1956 Muchnik independently solved the Post problem by constructing computably enumerable sets A and B of incomparable degrees using the priority construction method. We adapt this idea to PACi and PAC reducibilities and construct two effective concept classes C and D such that C is not reducible to D and vice versa. When considering PAC reducibility it was necessary to work on the size of an effective concept class, thus we use Kolmogorov complexity to obtain the size. The non-learnability of concept classes in the PAC learning model is explained by the existence of PAC incomparable degrees.Analogous to the Turing jump, we give a jump operation on effective concept classes for the zero jump. To define the zero jump operator for PACi degrees the join of all the effective concept classes is constructed and proved that it is a greatest element. There are many properties proven for existing degrees. Thus we can explore proving those properties to PACi and PAC degrees. But if we prove an embedding from those degrees to PACi and PAC degrees then those properties will be true for PACi and PAC degrees without explicitly proving them.Abstract prepared by Dodamgodage Gihnee M. Senadheera and taken directly from the thesisE-mail: [email protected]: https://www.proquest.com/docview/2717762461/abstract/ACD19F29A8774AF6PQ/1?accountid=13864. (shrink)

We compute that the index set of PAC-learnable concept classes is m-complete Σ30\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Sigma^{0}_{3}}$$\end{document} within the set of indices for all concept classes of a reasonable form. All concept classes considered are computable enumerations of computable Π10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Pi^{0}_{1}}$$\end{document} classes, in a sense made precise here. This family of concept classes is sufficient to cover all standard examples, and also has the property that PAC learnability (...) is equivalent to finite VC dimension. (shrink)

Computer scientists have provided a distinct justification of Occam’s Razor. Using the probably approximately correct framework, they provide a theorem that they claim demonstrates that we should favor simpler hypotheses. The argument relies on a philosophical interpretation of the theorem. I argue that the standard interpretation of the result in the literature is misguided and that a better reading does not, in fact, support Occam’s Razor at all. To this end, I state and prove a very similar theorem that, if (...) interpreted the same way, would justify the contradictory Anti-Occam’s Razor—the principle that we should favor more complex hypotheses. (shrink)

At the time of his death in May 1961, Maurice Merleau-Ponty held the chair of Philosophy at the College de France. Together with Jean-Paul Sartre and Simone de Beauvoir, he was cofounder of the successful and influential review Les Temps Modernes. However, after Merleau-Ponty's two studies of Marxist theory and practice (Humanisme et Terreur and Les Aventures de la Dialectique), he alienated both orthodox Marxists and "mandarins of the left" such as Sartre and de Beauvoir. Perhaps his most lasting contribution (...) to the interpretation of human existence was his formulation of a positive philosophical approach to psychology the foundations of which were clearly outlined in The Structure of Behavior and later more fully developed in Phenomenology of Perception. (shrink)

Whether or not quantum physics can account for molecular structure is a matter of considerable controversy. Three of the problems raised in this regard are the problems of molecular structure. We argue that these problems are just special cases of the measurement problem of quantum mechanics: insofar as the measurement problem is solved, the problems of molecular structure are resolved as well. In addition, we explore one consequence of our argument: that claims about the reduction or emergence (...) of molecular structure cannot be settled independently of the choice of a particular resolution to the measurement problem. Specifically, we consider how three standard putative solutions to the measurement problem inform our under- standing of a molecule in isolation, as well as of chemistry’s relation to quantum physics. (shrink)

The central problem of social theory is 'structure and agency'. How do the objective features of society influence human agents? Determinism is not the answer, nor is conditioning as currently conceptualised. It accentuates the way structure and culture shape the social context in which individuals operate, but it neglects our personal capacity to define what we care about most and to establish a modus vivendi expressive of our concerns. Through inner dialogue, 'the internal conversation', individuals reflect upon their (...) social situation in the light of current concerns and projects. On the basis of a series of unique, in-depth interviews, Archer identifies three distinctive forms of internal conversation. These govern agents' responses to social conditioning, their individual patterns of social mobility and whether or not they contribute to social stability or change. Thus the internal conversation is seen as being the missing link between society and the individual, structure and agency. (shrink)

What is structural rationality? Specifically, what is the distinctive feature of structural requirements of rationality? Some philosophers have argued, roughly, that the distinctive feature of structural requirements is coherence. But what does coherence mean, exactly? Or, at least, what do structuralists about rationality have in mind when they claim that structural rationality is coherence? This issue matters for making progress in various active debates concerning rationality. In this paper, I analyze three strategies for figuring out what coherence means in the (...) debates on structural rationality. I argue that these strategies face problems. (shrink)

The epistemic probability of A given B is the degree to which B evidentially supports A, or makes A plausible. This paper is a first step in answering the question of what determines the values of epistemic probabilities. I break this question into two parts: the structural question and the substantive question. Just as an object’s weight is determined by its mass and gravitational acceleration, some probabilities are determined by other, more basic ones. The structural question asks what probabilities are (...) not determined in this way—these are the basic probabilities which determine values for all other probabilities. The substantive question asks how the values of these basic probabilities are determined. I defend an answer to the structural question on which basic probabilities are the probabilities of atomic propositions conditional on potential direct explanations. I defend this against the view, implicit in orthodox mathematical treatments of probability, that basic probabilities are the unconditional probabilities of complete worlds. I then apply my answer to the structural question to clear up common confusions in expositions of Bayesianism and shed light on the “problem of the priors.”. (shrink)

Why do speakers of all languages use different grammatical structures under different communicative circumstances to express the same idea? In this comprehensive study, Professor Lambrecht explores the relationship between the structure of sentences and the linguistic and extra-linguistic contexts in which they are used. His analysis is based on the observation that the structure of a sentence reflects a speaker's assumptions about the hearer's state of knowledge and consciousness at the time of the utterance. This relationship between speaker (...) assumptions and formal sentence structure is governed by rules and conventions of grammar, in a component called 'information structure'. Four independent but interrelated categories are analysed: presupposition and assertion, identifiability and activation, topic, and focus. (shrink)