Say that α is an n-strongly c. e. real if α is a sum of n many strongly c. e. reals, and that α is regular if α is n-strongly c. e. for some n. Let Sn be the set of all n-strongly c. e. reals, Reg be the set of regular reals and CE be the set of c. e. reals. Then we have: S1 ⊂ S2 ⊂ · · · ⊂ Sn ⊂ (...) · · · ⊂ ⊂ Reg ⊂ CE. This gives a hierarchy of the c. e. reals. We also study the regularity of the d. c. e. reals. (shrink)

This thesis is divided into three parts, the first and second ones focused on combinatorics and classification problems on discrete and geometrical objects in the context of descriptive set theory, and the third one on generalized descriptive set theory at singular cardinals of countable cofinality.Descriptive Set Theory (briefly: DST) is the study of definable subsets of Polish spaces, i.e., separable completely metrizable spaces. One of the major branches of DST is Borel reducibility, successfully used in the last 30 years to (...) solve and compare many classification problems. One of our goals is the classification of knots, very familiar and tangible objects in everyday life, which also play an important role in modern mathematics. The study of knots and their properties is known as knot theory. Our plan is to gain insight into knots using discrete objects, such as linear and circular orders. This approach was already exploited in [6]. The first part of this work is therefore devoted to countable linear orders and the study of the quasi-order of convex embeddability and its induced equivalence relation. We obtain both combinatorial and descriptive set-theoretic results. We also expand our research to the case of circular orders.Another objective of this first part is to extend the notion of convex embeddability on countable linear orders. We provide a family of quasi-orders of which embeddability is a particular case as well. We study these quasi-orders from a combinatorial point of view and analyse their complexity with respect to Borel reducibility. Furthermore, we extend the analysis of these quasi-orders to the set of uncountable linear orders.The second part of the project deals with classification problems on knots and $3$ -manifolds. The goal here is to apply the results obtained in the first part to the study of proper arcs and knots, establishing lower bounds for the complexity of some natural relations between these geometrical objects. We also obtain some combinatorial results which are particularly interesting when we restrict to the set of wild proper arcs and wild knots, classes which haven’t received much attention so far. These parts are included in the two preprints [4, 5] in collaboration with my supervisor Alberto Marcone, Luca Motto Ros (University of Torino), and Vadim Weinstein (University of Oulu).The second part of this work also includes the classification of non-compact $3$ -manifolds up to homeomorphism (the case of compact $3$ -manifolds has already been solved: indeed, there are only countably many $3$ -manifolds up to homeomorphism; see [7]), and that of Cantor sets of $\mathbb {R}^3$ up to conjugation (answering to Question 5.5 of [3]). Here we resort to algebraic tools. Stone duality gives a neat way to go back-and-forth between totally disconnected Polish spaces and countable Boolean algebras (see [1]). The main ingredient is the Stone space of all ultrafilters on a Boolean algebra. In this work we introduce a weaker concept which we call “blurry filter”. Using blurry filters instead of ultrafilters enables one to extend the class of spaces under consideration beyond totally disconnected. As an application of this method, we show that both homeomorphism on non-compact $3$ -manifolds and conjugation of Cantor sets in $\mathbb {R}^3$ are completely classifiable by countable structures. These results are part of an upcoming paper in collaboration with Vadim Weinstein.The last part of this thesis concerns the natural generalization of descriptive set theory that occurs when countable is replaced by uncountable, called Generalized Descriptive Set Theory (briefly: GDST). In particular, we focus on the case of GDST for a singular cardinal $\kappa $ of countable cofinality. The goal here is to study the generalizations of the Perfect Set Property and the Baire Property to subsets of spaces of higher cardinalities, like the power set $\mathcal {P}(\kappa )$. We consider the question under which large cardinal hypotheses classes of definable subsets of these spaces possess such regularity properties, focusing on rank-into-rank axioms, like I2, and classes of sets definable by $\Sigma _1$ -formulas with parameters from various collections of sets. The obtained results are included in [2], a joint work with my co-supervisor Vincenzo Dimonte and Philipp Lücke (University of Hamburg).Abstract prepared by Martina IannellaE-mail: [email protected]: https://air.uniud.it/handle/11390/1262824. (shrink)

We present a model where ω1 is inaccessible by reals, Silver measurability holds for all sets but Miller and Lebesgue measurability fail for some sets. This contributes to a line of research started by Shelah in the 1980s and more recently continued by Schrittesser and Friedman, regarding the separation of different notions of regularity properties of the real line.

We study regularity properties related to Cohen, random, Laver, Miller and Sacks forcing, for sets of real numbers on the Δ31\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{\Delta}^1_3}$$\end{document} level of the projective hieararchy. For Δ21\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{\Delta}^1_2}$$\end{document} and Σ21\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{\Sigma}^1_2}$$\end{document} sets, the relationships between these properties follows the pattern of the well-known Cichoń diagram for cardinal characteristics of the continuum. It is known that (...) assuming suitable large cardinals, the same relationships lift to higher projective levels, but the questions become more challenging without such assumptions. Consequently, all our results are proved on the basis of ZFC alone or ZFC with an inaccessible cardinal. We also prove partial results concerning Σ31\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{\Sigma}^1_3}$$\end{document} and Δ41\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{\Delta}^1_4}$$\end{document} sets. (shrink)

Emotional regularity is the degree to which a person maintains and returns to a set of emotional states over time. The present investigation examined associations between emotional regularity and extant emotion measures as well as psychologically relevant dimensions of personality, health, and real-world occupational outcomes. Participants included 598 U.S. adults who provided daily experience sampling reports on their emotional states for approximately two months. Results suggest that emotional regularity was related to, but distinct from, well-established measures of emotion including emotional (...) intensity, variability, covariation, inertia, granularity, and emodiversity. Furthermore, emotional regularity significantly predicted measures of personality, psychological health, and occupational outcomes even when accounting for extant emotion measures and sociodemographic covariates. Finally, it explained modest (7.5%) improvement (in terms of cross-validated RSq.) over baseline models containing emotional intensity, variability, and sociodemographic covariates. These findings suggest that emotional regularity may provide an important indicator of healthy emotional functioning and may be a promising area for further scientific discovery. (shrink)

It has recently been argued that Harvey Brown and Oliver Pooley’s ‘dynamical approach’ to special relativity should be understood as what might be called an ontologically and ideologically relationalist approach to Minkowski geometry, according to which Minkowski geometrical structure supervenes upon the symmetries of the best-systems dynamical laws for a material world with primitive topological or differentiable structure. Fleshing out the details of some such primitive structure, and a conception of laws according to which Minkowski geometry could so supervene, has (...) been referred to by some as the ‘constructivist project’. Here, it is explained that Nick Huggett’s work on ‘regularity relationalism’ provides a framework for such an approach, and a relativistic version of Huggett’s regularity relationalism is outlined for that purpose. Finally, by way of examples, it is shown that this approach fails in the simplest cases. Still, reasons are given for which this should not necessarily discourage an advocate of this interpretation of the dynamical approach. _1_ Introduction to the Dynamical Approach _2_ Huggett’s Regularity Relationalism _3_ The Dynamical Approach as a Form of Regularity Relationalism _4_ A Simple Way to Set the Stage _5_ A First Attempt _5.1_ Complex-valued planewave solutions _5.2_ Real-valued planewave solutions _6_ More General Solutions _7_ Summary and Reflections. (shrink)

Many philosophers have become worried about the use of standard real numbers for the probability function that represents an agent's credences. They point out that real numbers can't capture the distinction between certain extremely unlikely events and genuinely impossible ones—they are both represented by credence 0, which violates a principle known as “regularity.” Following Skyrms 1980 and Lewis 1980, they recommend that we should instead use a much richer set of numbers, called the “hyperreals.” This essay argues that this popular (...) view is the result of two mistakes. The first mistake, which this essay calls the “numerical fallacy,” is to assume that a distinction that isn't represented by different numbers isn't represented at all in a mathematical representation. In this case, the essay claims that although the real numbers do not make all relevant distinctions, the full mathematical structure of a probability function does. The second mistake is that the hyperreals make too many distinctions. They have a much more complex structure than credences in ordinary propositions can have, so they make distinctions that don't exist among credences. While they might be useful for generating certain mathematical models, they will not appear in a faithful mathematical representation of credences of ordinary propositions. (shrink)

ABSTRACT It has recently been argued that Harvey Brown and Oliver Pooley’s ‘dynamical approach’ to special relativity should be understood as what might be called an ontologically and ideologically relationalist approach to Minkowski geometry, according to which Minkowski geometrical structure supervenes upon the symmetries of the best-systems dynamical laws for a material world with primitive topological or differentiable structure. Fleshing out the details of some such primitive structure, and a conception of laws according to which Minkowski geometry could so supervene, (...) has been referred to by some as the ‘constructivist project’. Here, it is explained that Nick Huggett’s work on ‘regularity relationalism’ provides a framework for such an approach, and a relativistic version of Huggett’s regularity relationalism is outlined for that purpose. Finally, by way of examples, it is shown that this approach fails in the simplest cases. Still, reasons are given for which this should not necessarily discourage an advocate of this interpretation of the dynamical approach. 1 Introduction to the Dynamical Approach 2 Huggett’s Regularity Relationalism 3 The Dynamical Approach as a Form of Regularity Relationalism 4 A Simple Way to Set the Stage 5 A First Attempt 5.1 Complex-valued planewave solutions 5.2 Real-valued planewave solutions 6 More General Solutions 7 Summary and Reflections. (shrink)

It is proved that the following conditions are equivalent: (a) there exists a complete, atomless, σ-centered Boolean algebra, which does not contain any regular, atomless, countable subalgebra, (b) there exists a nowhere dense ultrafilter on ω. Therefore, the existence of such algebras is undecidable in ZFC. In "forcing language" condition (a) says that there exists a non-trivial σ-centered forcing not adding Cohen reals.

For the computability of subsets of real numbers, several reasonable notions have been suggested in the literature. We compare these notions in a systematic way by relating them to pairs of ‘basic’ ones. They turn out to coincide for full-dimensional convex sets; but on the more general class of regular sets, they reveal rather interesting ‘weaker/stronger’ relations. This is in contrast to single real numbers and vectors where all ‘reasonable’ notions coincide.

In this article, we first question the cogency of the strict delimitation of the object of study of economics in real business cycle theory and investigate its methodological and ontological consequences in the light of Roy Bhaskar's transcendental realism. We discuss the limits of real business cycle theory for detecting regularities, as well as the possibility of refuting conjectures. Finally, we show that our conclusions can be generalized to economic theories relying on the notion of general equilibrium.

We consider semi‐algebraic sets and properties of these sets that are expressible by sentences in first‐order logic over the reals. We are interested in first‐order properties that are invariant under topological transformations of the ambient space. Two semi‐algebraic sets are called topologically elementarily equivalent if they cannot be distinguished by such topological first‐order sentences. So far, only semi‐algebraic sets in one and two‐dimensional space have been considered in this context. Our contribution is a natural characterisation of topological elementary equivalence (...) of regular closed semi‐algebraic sets in three‐dimensional space, extending a known characterisation for the two‐dimensional case. Our characterisation is based on the local topological behaviour of semi‐algebraic sets and the key observation that topologically elementarily equivalent sets can be transformed into each other by means of geometric transformations, each of them mapping a set to a first‐order indistinguishable one. (shrink)

This paper examines the problem of natural kinds, a key problem within feminist theory, and argues for a non-instrumental realist account of group identity. I suggest that a reconstructed theory of essence helps to make sense of group membership because it combines a conventional account of groups with a realist commitment to there being something responsible for the appearance of regularities in the world. The claim that natural kind membership is a matter of similarity relationships manages to avoid metaphysical, universal (...) property-based essentialism and, at the same time, points to interested generative mechanisms underlying the appearance of the regularities that make sense of kind membership. Finally, I suggest that the concepts 'real essence' and 'internal constitution' offer a new way to conceive 'sex' and 'gender', and that Adorno's notion of non-identity is a way to think group membership non-instrumentally. (shrink)

In an era characterized by fast technological progress that introduces new unpredictable scenarios every day, working in the law field may appear very difficult, if not supported by the right tools. In this respect, some systems based on Artificial Intelligence methods have been proposed in the literature, to support several tasks in the legal sector. Following this line of research, in this paper we propose a novel method, called PRILJ, that identifies paragraph regularities in legal case judgments, to support legal (...) experts during the redaction of legal documents. Methodologically, PRILJ adopts a two-step approach that first groups documents into clusters, according to their semantic content, and then identifies regularities in the paragraphs for each cluster. Embedding-based methods are adopted to properly represent documents and paragraphs into a semantic numerical feature space, and an Approximated Nearest Neighbor Search method is adopted to efficiently retrieve the most similar paragraphs with respect to the paragraphs of a document under preparation. Our extensive experimental evaluation, performed on a real-world dataset provided by EUR-Lex, proves the effectiveness and the efficiency of the proposed method. In particular, its ability of modeling different topics of legal documents, as well as of capturing the semantics of the textual content, appear very beneficial for the considered task, and make PRILJ very robust to the possible presence of noise in the data. (shrink)

We show under that every set of reals is I‐regular for any σ‐ideal I on the Baire space such that is proper. This answers the question of Khomskii [7, Question 2.6.5]. We also show that the same conclusion holds under if we additionally assume that the set of Borel codes for I‐positive sets is. If we do not assume, the notion of properness becomes obscure as pointed out by Asperó and Karagila [1]. Using the notion of strong properness (...) similar to the one introduced by Bagaria and Bosch [2], we show under without using that every set of reals is I‐regular for any σ‐ideal I on the Baire space such that is strongly proper assuming every set of reals is ∞‐Borel and there is no ω1‐sequence of distinct reals. In particular, the same conclusion holds in a Solovay model. (shrink)

Twitter is a virtual social network where people share their posts and opinions about the current situation, such as the coronavirus pandemic. It is considered the most significant streaming data source for machine learning research in terms of analysis, prediction, knowledge extraction, and opinions. Sentiment analysis is a text analysis method that has gained further significance due to social networks’ emergence. Therefore, this paper introduces a real-time system for sentiment prediction on Twitter streaming data for tweets about the coronavirus pandemic. (...) The proposed system aims to find the optimal machine learning model that obtains the best performance for coronavirus sentiment analysis prediction and then uses it in real-time. The proposed system has been developed into two components: developing an offline sentiment analysis and modeling an online prediction pipeline. The system has two components: the offline and the online components. For the offline component of the system, the historical tweets’ dataset was collected in duration 23/01/2020 and 01/06/2020 and filtered by #COVID-19 and #Coronavirus hashtags. Two feature extraction methods of textual data analysis were used, n-gram and TF-ID, to extract the dataset’s essential features, collected using coronavirus hashtags. Then, five regular machine learning algorithms were performed and compared: decision tree, logistic regression, k-nearest neighbors, random forest, and support vector machine to select the best model for the online prediction component. The online prediction pipeline was developed using Twitter Streaming API, Apache Kafka, and Apache Spark. The experimental results indicate that the RF model using the unigram feature extraction method has achieved the best performance, and it is used for sentiment prediction on Twitter streaming data for coronavirus. (shrink)

For a large natural class of forcing notions, we prove general equivalence theorems between forcing absoluteness statements, regularity properties, and transcendence properties over and the core model . We use our results to answer open questions from set theory of the reals.

In a professional learning community, teachers are organized into teams, committed to meeting on a regular basis to study their teaching strategies and the effects of those strategies on the students in their classrooms. Whatever the organizational structure, the teams have one goal, that is to improve teaching so that student learning is improved.

We investigate the behavior of cardinal characteristics of the reals under extensions that do not add new [Formula: see text]-sequences (for some regular [Formula: see text]). As an application, we show that consistently the following cardinal characteristics can be different: The (“independent”) characteristics in Cichoń’s diagram, plus [Formula: see text]. (So we get thirteen different values, including [Formula: see text] and continuum). We also give constructions to alternatively separate other MA-numbers (instead of [Formula: see text]), namely: MA for (...) [Formula: see text]-Knaster from MA for [Formula: see text]-Knaster; and MA for the union of all [Formula: see text]-Knaster forcings from MA for precaliber. (shrink)

My task here is the first one. I do present a consistent formal system and claim that it provides a perfect model of natural languages such as English, but this system involves no surprises. It is none other than the standard framework of classical logic and model theory. The real weight of the argument lies in the claim that the classical framework—without alteration or addition—contains the resources to model what happens when we say in English ‘This sentence is not true’.

School physical education has the potential to contribute to public-health promotion and well-being, but oftentimes students' lack of motivation toward PE or physical activity in general, especially during adolescence, diminishes, or eradicates the positive effects associated with PE. Therefore, practical approaches are required that help teachers to increase or awake students intrinsic motivation toward PE, for which self-determination theory may provide the conceptual framework. In that regard, the purpose of the present study was to examine whether the use of real-time, (...) heart rate feedback during regular PE lessons has the potential to increase students' autonomous motivation and physical effort. To achieve this, we had forty healthy adolescents between 16 and 17 years of age run for 30 min either with or without real-time, individualized heart rate feedback during a regular PE class and compared physical and perceived exertion as well as joy of running between the two groups. Participants were randomly assigned to the groups. Our data revealed that participants in the EG enjoyed running more than participants in the CG despite a higher physical and perceived exertion. That means, running with real-time, individualized heart rate feedback apparently increased participants' motivation to run and to enjoy running at higher levels of exertion. In that regard, real-time, individualized activity feedback should be implemented in regular PE classes systematically and repeatedly to create a controllable and attainable situation that allows students to actively adjust their own behavior to achieve appealing and realistic goals. (shrink)

Received approaches to a unified phenomenon called “language” are firmly committed to a Cartesian view of distinct unobservable minds. Questioning this commitment leads us to recognize that the boundaries conventionally separating the linguistic from the non-linguistic can appear arbitrary, omitting much that is regularly present during vocal communication. The thesis is put forward that uttering, or voicing, is a much older phenomenon than the formal structures studied by the linguist, and that the voice has found elaborations and codifications in other (...) domains too, such as in systems of ritual and rite. Voice, it is suggested, necessarily gives rise to a temporally bound subjectivity, whether it is in inner speech (Descartes' “cogito”), in conversation, or in the synchronized utterances of collective speech found in prayer, protest, and sports arenas world wide. The notion of a fleeting subjective pole tied to dynamically entwined participants who exert reciprocal influence upon each other in real time provides an insightful way to understand notions of common ground, or socially shared cognition. It suggests that the remarkable capacity to construct a shared world that is so characteristic of Homo sapiens may be grounded in this ability to become dynamically entangled as seen, e.g., in the centrality of joint attention in human interaction. Empirical evidence of dynamic entanglement in joint speaking is found in behavioral and neuroimaging studies. A convergent theoretical vocabulary is now available in the concept of participatory sense-making, leading to the development of a rich scientific agenda liberated from a stifling metaphysics that obscures, rather than illuminates, the means by which we come to inhabit a shared world. (shrink)

Argumentation theorists know that their work has real-life application, and similarly, they draw inspiration for that work from real-life experiences. Sometimes, it comes from some public medium – the newspaper, a blog, a debate stage. But we also draw from more private reason-exchanges – a conversation with a neighbor, small-talk with a colleague, or a lovers’ spat. A few worries about publicly theorizing about those more private cases arise. We may be making public something that was unguarded, and so betray (...) a trust. Our theoretical reflections may themselves warp the relationship we’d originally savored, particularly when our partners know about the possibility of them being publicly scrutinized. Novelists and poets regularly struggle with this challenge with their work, and we argumentation theorists should, too. Les théoriciens de l’argumentation savent que leur travail a des applications concrètes et, de la même manière, ils s’inspirent d’expériences réelles. Parfois, ces idées proviennent d’un média public – un journal, un blog, une tribune de débat. Mais nous nous inspirons aussi d’échanges de raisonnement plus privés – une conversation avec un voisin, une petite conversation avec un collègue ou une dispute amoureuse. Nous craignons de théoriser publiquement sur ces cas plus privés. Nous pouvons rendre public des commentaires irréfléchis et ainsi trahir une confiance. Nos réflexions théoriques peuvent déformer la relation que nous avions initialement très appréciée, en particulier lorsque nos partenaires savent qu’ils peuvent être scrutés publiquement. Les romanciers et les poètes sont régulièrement confrontés à ce défi dans leur travail, et nous, les théoriciens de l’argumentation, devrions également le faire. (shrink)

In language learning, learners engage with their environment, incorporating cues from different sources. However, in lab‐based experiments, using artificial languages, many of the cues and features that are part of real‐world language learning are stripped away. In three experiments, we investigated the role of positive, negative, and mixed feedback on the gradual learning of language‐like statistical regularities within an active guessing game paradigm. In Experiment 1, participants received deterministic feedback (100%), whereas probabilistic feedback (i.e., 75% or 50%) was introduced in (...) Experiment 2. Finally, Experiment 3 explored the impact of mixed probabilistic feedback (33% positive, 33% negative, 33% no feedback). The results showed that cross‐situational learning of words was observed without feedback, but participants were able to learn structural regularities of the miniature language only when feedback was provided. Interestingly, the presence of positive feedback was particularly helpful for the learner, promoting more in‐depth learning of the artificial language. (shrink)

Let be an o-minimal structure expanding a real closed field R. We show that any definable set in Rn can be stratified into cells, whose defining functions are smooth Lipschitz continuous functions with constant 2n3/2, which have additional regularity conditions on the derivatives of higher order.

The first part of this paper explores the general issues in using Artificial Life techniques to program actual mobile robots. In particular it explores the difficulties inherent in transferring programs evolved in a simulated environment to run on an actual robot. It examines the dual evolution of organism morphology and nervous systems in biology. It proposes techniques to capture some of the search space pruning that dual evolution offers in the domain of robot programming. It explores the relationship between robot (...) morphology and program structure, and techniques for capturing regularities across this mapping. (shrink)

Topic modelling is a popular unsupervised method for text processing that provides interpretable document representation. One of the most high-level approaches is additively regularized topic models (ARTM). This method features better quality than other methods due to its flexibility and advanced regularization abilities. However, it is challenging to find an optimal learning strategy to create high-quality topics because a user needs to select the regularizers with their values and determine the order of application. Moreover, it may require many real runs (...) or model training which makes this task time consuming. At the current moment, there is a lack of research on parameter optimization for ARTM-based models. Our work proposes an approach that formalizes the learning strategy into a vector of parameters which can be solved with evolutionary approach. We also propose a surrogate-based modification which utilizes machine learning methods that makes the approach for parameters search time efficient. We investigate different optimization algorithms (evolutionary and Bayesian) and their modifications with surrogates in application to topic modelling optimization using the proposed learning strategy approach. An experimental study conducted on English and Russian datasets indicates that the proposed approaches are able to find high-quality parameter solutions for ARTM and substantially reduce the execution time of the search. (shrink)

There is broad agreement among social researchers and social ontologists that the project of dividing humans into social kinds should be guided by at least two methodological commitments. First, a commitment to what best serves moral and political interests, and second, a commitment to describing accurately the causal structures of social reality. However, researchers have not sufficiently analyzed how these two commitments interact and constrain one another. In the absence of that analysis, several confusions have set in, threatening to undermine (...) shared goals for the responsible modeling of social kinds of humans. This essay first explains the source and substance of these confusions. Then, by distinguishing different value-laden investigative questions into the classification of social kinds of humans, it sets out specific relations of dependence and constraint between empirically-driven investigations and value-driven investigations into social kinds of humans. The result is a more detailed and fruitful framework for thinking about the classification of social kinds that respects both normative interests and mind-independent causal regularities. (shrink)

We prove that the only implications between four notions for Σ 1 2 -sets of reals are $\Sigma^1_2-\text{measurability} \Rightarrow \Sigma^1_2-\text{categoricity} \big\downarrow \Sigma^1_2-\text{Ramsey} \Rightarrow \Sigma^1_2-K_\sigma-\text{regular}$.

Let ${\mathbb{B}}$ and ${\mathbb{C}}$ be Boolean algebras and ${e: \mathbb{B}\rightarrow \mathbb{C}}$ an embedding. We examine the hierarchy of ideals on ${\mathbb{C}}$ for which ${ \bar{e}: \mathbb{B}\rightarrow \mathbb{C} / \fancyscript{I}}$ is a regular (i.e. complete) embedding. As an application we deal with the interrelationship between ${\fancyscript{P}(\omega)/{{\rm fin}}}$ in the ground model and in its extension. If M is an extension of V containing a new subset of ω, then in M there is an almost disjoint refinement of the family ([ω]ω) (...) V . Moreover, there is, in M, exactly one ideal ${\fancyscript{I}}$ on ω such that ${(\fancyscript{P}(\omega)/{{\rm fin}})^V}$ is a dense subalgebra of ${(\fancyscript{P}(\omega)/\fancyscript{I})^M}$ if and only if M does not contain an independent (splitting) real. We show that for a generic extension V[G], the canonical embedding $$\fancyscript{P}^V(\omega){/}{\rm fin}\hookrightarrow \fancyscript{P}(\omega){/}(U(Os)(\mathbb{B}))^G$$ is a regular one, where ${U(Os)(\mathbb{B})}$ is the Urysohn closure of the zero-convergence structure on ${\mathbb{B}}$. (shrink)

��This paper investigates how an evolutionary al- gorithm with an indirect encoding exploits the property of phenotypic regularity, an important design principle found in natural organisms and engineered designs. We present the first comprehensive study showing that such phenotypic regularity enables an indirect encoding to outperform direct encoding con- trols as problem regularity increases. Such an ability to produce regular solutions that can exploit the regularity of problems is an important prerequisite if evolutionary algorithms are to scale to high-dimensional (...) real-world problems, which typically contain many regularities, both known and unrecognized. The indirect encoding in this case study is HyperNEAT, which evolves artificial neural networks (ANNs) in a manner inspired by concepts from biological development. We demonstrate that, in contrast to two direct encoding controls, HyperNEAT produces both regular behaviors and regular ANNs, which enables HyperNEAT to significantly outperform the direct encodings as regularity increases in three problem domains. We also show that the types of regularities HyperNEAT produces can be biased, allowing domain knowledge and preferences to be injected into the search. Finally, we examine the downside of a bias toward regularity. Even when a solution is mainly regular, some irregularity may be needed to perfect its functionality. This insight is illustrated by a new algorithm called HybrID that hybridizes indirect and direct encodings, which matched HyperNEAT’s performance on regular problems yet outperformed it on problems with some irregularity. HybrID’s ability to improve upon the performance of HyperNEAT raises the question of whether indirect encodings may ultimately excel not as stand-alone algorithms, but by being hybridized with a further process of refinement, wherein the indirect encoding produces patterns that exploit problem regu-. (shrink)

This study has proven that the economic system is determined by various components, in particular, it includes the real sector of the economy, which is formed on mega-, macro, meso-, micro-and nano-levels. In addition, it was proved that the nano-level is determined by the activities of individuals whose economic activity begins with the birth and attitude of parents, attending various educational and upbringing institutions, and studying at university. A separate segment of the nano-level of the economic system is the baby (...) industry responsible for the production of goods and services for children and future parents. All these aspects are indicators of the development of the baby economy. Such an economic category as the baby economy was separated and defined. The study uses the following methods: analysis, synthesis, structural analysis, systemic approach, observation, comparison, multifactor regression. These methods made it possible to achieve the results, which involve isolation of the baby economy as a component of nanoeconomy and definition of such components of the baby economic segment of nanoeconomy as a family or household economy, the baby industry, the economy of the educational process and upbringing. For this purpose, the value-institutional approach was applied. In addition, multifactorial analysis of the impact of indicators of the baby economy development on the population of a country with a transitive economy with incomes below the subsistence minimum was performed. This analysis identified a direct but minor relationship between these phenomena, which demonstrates the need to intensify and create a policy for the baby economy in similar states. The theoretical significance of the obtained results is determined by the introduction of a new economic category of "the baby economy" for the formation of a nano economic component within socio-economic systems. (shrink)

We investigate some versions of amoeba for tree-forcings in the generalized Cantor and Baire spaces. This answers [10, Question 3.20] and generalizes a line of research that in the standard case has been studied in [11], [13], and [7]. Moreover, we also answer questions posed in [3] by Friedman, Khomskii, and Kulikov, about the relationships between regularity properties at uncountable cardinals. We show ${\bf{\Sigma }}_1^1$-counterexamples to some regularity properties related to trees without club splitting. In particular we prove a strong (...) relationship between the Ramsey and the Baire properties, in slight contrast with the standard case. (shrink)

We give a direct and elementary proof of the fact that every real-valued probability measure can be approximated—up to an infinitesimal—by a hyperreal-valued one which is regular and defined on the whole powerset of the sample space.

This thesis divides naturally into two parts, each concerned with the extent to which the theory of $L$ can be changed by forcing.The first part focuses primarily on applying generic-absoluteness principles to how that definable sets of reals enjoy regularity properties. The work in Part I is joint with Itay Neeman and is adapted from our paper Happy and mad families in $L$, JSL, 2018. The project was motivated by questions about mad families, maximal families of infinite subsets of (...) $\omega $ of which any two have only finitely many members in common. We begin, in the spirit of Mathias, by establishing a strong Ramsey property for sets of reals in the Solovay model, giving a new proof of Törnquist’s theorem that there are no infinite mad families in the Solovay model.In Chapter 3 we stray from the main line of inquiry to briefly study a game-theoretic characterization of filters with the Baire Property.Neeman and Zapletal showed, assuming roughly the existence of a proper class of Woodin cardinals, that the boldface theory of $L$ cannot be changed by proper forcing. They call their result the Embedding Theorem, because they conclude that in fact there is an elementary embedding from the $L$ of the ground model to that of the proper forcing extension. With a view toward analyzing mad families under $\mathsf {AD}^+$ and in $L$ under large-cardinal hypotheses, in Chapter 4 we establish triangular versions of the Embedding Theorem. These are enough for us to use Mathias’s methods to show that there are no infinite mad families in $L$ under large cardinals and that $\mathsf {AD}^+$ implies that there are no infinite mad families. These are again corollaries of theorems about strong Ramsey properties under large-cardinal assumptions and $\mathsf {AD}^+$, respectively. Our first theorem improves the large-cardinal assumption under which Todorcevic established the nonexistence of infinite mad families in $L$. Part I concludes with Chapter 5, a short list of open questions.In the second part of the thesis, we undertake a finer analysis of the Embedding Theorem and its consistency strength. Schindler found that the the Embedding Theorem is consistent relative to much weaker assumptions than the existence of Woodin cardinals. He defined remarkable cardinals, which can exist even in L, and showed that the Embedding Theorem is equiconsistent with the existence of a remarkable cardinal. His theorem resembles a theorem of Harrington–Shelah and Kunen from the 1980s: the absoluteness of the theory of $L$ to ccc forcing extensions is equiconsistent with a weakly compact cardinal. Joint with Itay Neeman, we improve Schindler’s theorem by showing that absoluteness for $\sigma $ -closed $\ast $ ccc posets—instead of the larger class of proper posets—implies the remarkability of $\aleph _1^V$ in L. This requires a fundamental change in the proof, since Schindler’s lower-bound argument uses Jensen’s reshaping forcing, which, though proper, need not be $\sigma $ -closed $\ast $ ccc in that context. Our proof bears more resemblance to that of Harrington–Shelah than to Schindler’s.The proof of Theorem 6.2 splits naturally into two arguments. In Chapter 7 we extend the Harrington–Shelah method of coding reals into a specializing function to allow for trees with uncountable levels that may not belong to L. This culminates in Theorem 7.4, which asserts that if there are $X\subseteq \omega _1$ and a tree $T\subseteq \omega _1$ of height $\omega _1$ such that X is codable along T, then $L$ -absoluteness for ccc posets must fail.We complete the argument in Chapter 8, where we show that if in any $\sigma $ -closed extension of V there is no $X\subseteq \omega _1$ codable along a tree T, then $\aleph _1^V$ must be remarkable in L.In Chapter 9 we review Schindler’s proof of generic absoluteness from a remarkable cardinal to show that the argument gives a level-by-level upper bound: a strongly $\lambda ^+$ -remarkable cardinal is enough to get $L$ -absoluteness for $\lambda $ -linked proper posets.Chapter 10 is devoted to partially reversing the level-by-level upper bound of Chapter 9. Adapting the methods of Neeman, Hierarchies of forcing axioms II, we are able to show that $L$ -absoluteness for $\left |\mathbf {R}\right |\cdot \left |\lambda \right |$ -linked posets implies that the interval $[\aleph _1^V,\lambda ]$ is $\Sigma ^2_1$ -remarkable in L.prepared by Zach Norwood.E-mail: [email protected]. (shrink)

Many prepared actions have to be withheld for a certain amount of time in order to have the most beneficial outcome. Therefore, keeping track of time accurately is vital to using temporal regularities in our environment. Traditional theories assume that time is tracked by means of a clock and an “attentional gate” (AG) that modulates subjective time if not enough attentional resources are directed toward the temporal process. According to the AG theory, the moment of distraction does not have an (...) influence on the subjective modulation. Here, we show, based on an analysis of 28,354 datasets, that highly motivated players of the online multiplayer real‐time strategy game StarCraft2 indeed respond later to timed events when they are distracted by other tasks during the interval. However, transient periods of distraction during the interval influence the response time to a lesser degree than distraction just before the required response. We extend the work of Taatgen, van Rijn, and Anderson (2007) and propose an alternative active check theory that postulates that distracted attention prevents people from checking their internal clock; we demonstrate that this account better predicts variance observed in response time. By analyzing StarCraft2 data, we assessed the role of attention in a naturalistic setting that more directly generalizes to real‐world settings than typical laboratory studies. (shrink)

Many prepared actions have to be withheld for a certain amount of time in order to have the most beneficial outcome. Therefore, keeping track of time accurately is vital to using temporal regularities in our environment. Traditional theories assume that time is tracked by means of a clock and an “attentional gate” (AG) that modulates subjective time if not enough attentional resources are directed toward the temporal process. According to the AG theory, the moment of distraction does not have an (...) influence on the subjective modulation. Here, we show, based on an analysis of 28,354 datasets, that highly motivated players of the online multiplayer real‐time strategy game StarCraft2 indeed respond later to timed events when they are distracted by other tasks during the interval. However, transient periods of distraction during the interval influence the response time to a lesser degree than distraction just before the required response. We extend the work of Taatgen, van Rijn, and Anderson (2007) and propose an alternative active check theory that postulates that distracted attention prevents people from checking their internal clock; we demonstrate that this account better predicts variance observed in response time. By analyzing StarCraft2 data, we assessed the role of attention in a naturalistic setting that more directly generalizes to real‐world settings than typical laboratory studies. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Virginia Woolf, Time, and the RealJane DuranCritical appraisal of the work of Virginia Woolf has tended to focus on feminist concerns, or on issues revolving around the actual facts of her upbringing and the extent to which she might have been thought to be a victim of abuse. Although some commentators have noted that Woolf's high modernist style lends itself to a number of readings with respect to sense (...) of self, the passage of time, and a sort of phenomenological reflection, philosophical concerns have, in general, not played a large role in Woolf scholarship to date.In this article I shall argue that some of Woolf's best known work—especially To the Lighthouse—exemplifies a concern for time, reality and a sense of interior life-as-lived that is overtly philosophical in its construction, and even somewhat didactic. Furthermore, I will claim, it is part and parcel of modernism as it is ordinarily conceived to address these issues in some fashion, even if, in many cases, they are not addressed as thoroughly as they are in Woolf's work. Even if we can be certain that a great deal of Woolf's mental disturbance, or mental illness, was the result of childhood abuse, or even inherited tendencies, it still does not detract from the power with which she was able to use depictions of inner turmoil to give us a sense of the fleeting and transitory nature of the real. Indeed, such a sense is one of the hallmarks of Woolf's work and is acknowledged by most of her critics, even if it is not termed a philosophical concern. I will analyze constructs of time and the chronological through a view of To the Lighthouse.IA number of philosophers have offered conceptions of time; these efforts range from those of antiquity to the more technical articulations [End Page 300] of the twentieth century. One of the most haunting evocations of the power of time is in the work of one whose thought is seldom cited in this regard, Simone de Beauvoir. In Old Age, she offers a phenomenological account of the passage of time that reflects an emphasis on the internally-felt disparity between the past and the present that is a frequently-remarked upon aspect of old age.1 There is a paucity of experience-of-the-present among the very elderly, and a reliance upon the past. Concomitantly, there is a foreshortening of the future. As Beauvoir writes: "How far does memory allow us to retrieve our lives? The images... are far from possessing the richness of their original object. An image is the seeing of an absent object by means of an organic and affective analogue" (p. 147). Despite the fact that these images may lack the richness of the original, the somewhat paradoxical effect of being older is that these images predominate.In To the Lighthouse, Woolf plays with time in a way that allows for a development of the internally-sensed structure of time on the parts of the various characters. Although many have remarked upon the well-known middle section, "Time Passes," this aspect of the felt sensation of time as an internal phenomenon, and one on which her characters seem to draw at regular intervals, is a somewhat little remarked feature of the rest of the book. It is present from the outset: James's first thoughts about the trip to the lighthouse highlight time in a sort of reversal of the way that Beauvoir has indicated for the elderly; James's conception of the passing of time is altered in another sense, since he is only six. He has projected himself forward so intently to the trip to the lighthouse that everything else has seemed somewhat unreal. As Woolf writes, "he had looked forward, for years and years it seemed...."2Although the differences between the felt constructions of time between, for example, childhood and old age might seem to partake of the commonplace, Beauvoir is among those philosophers who have used the notion of the truncation of time and the foreshortening of the future among the elderly to make philosophical commentary. By the same token... (shrink)

Most e-commerce platforms allow consumers to post product reviews, causing more and more consumers to get into the habit of reading reviews before they buy. These online reviews serve as an emotional feedback of consumers’ product experience and contain a lot of important information, but inevitably there are malicious or irrelevant reviews. It is especially important to discover and identify the real sentiment tendency in online reviews in a timely manner. Therefore, a deep learning-based real online consumer sentiment classification model (...) is proposed. First, the mapping relationship between online reviews of goods and sentiment features is established based on expert knowledge and using fuzzy mathematics, thus mapping the high-dimensional original text data into a continuous low-dimensional space. Secondly, after obtaining local contextual features using convolutional operations, the long-term dependencies between features are fully considered by a bidirectional long- and short-term memory network. Then, the degree of contribution of different words to the text is considered by introducing an attention mechanism, and a regular term constraint is introduced in the objective function. The experimental results show that the proposed convolutional attention–long and short-term memory network model has a higher test accuracy of 83.3% compared with other models, indicating that the model has better classification performance. (shrink)

In this paper we analyse some questions concerning trees on κ, both for the countable and the uncountable case, and the connections with Cohen reals. In particular, we provide a proof for one of the implications left open in [6, Question 5.2] about the diagram for regularity properties.

This section discusses mostly some unsolved problems. . . .I hope that some mathematicians who are interested in a classification of sets of real numbers, in particular sets with Lebesgue measure zero, will read it and try to find solutions for the problems here outlined.

Rational agents seem more confident in any possible event than in an impossible event. But if rational credences are real-valued, then there are some possible events that are assigned 0 credence nonetheless. How do we differentiate these events from impossible events then when we order events? de Finetti (1975), Hájek (2012) and Easwaran (2014) suggest that when ordering events, conditional credences and subset relations are as relevant as unconditional credences. I present a counterexample to all their proposals in this paper. (...) While their proposals order possible and impossible events correctly, they deliver the wrong verdict for disjoint possible events assigned equal positive credence. (shrink)

Clustering algorithm is one of the important research topics in the field of machine learning. Neutrosophic clustering is the generalization of fuzzy clustering and has been applied to many fields. This paper presents a new neutrosophic clustering algorithm with the help of regularization. Firstly, the regularization term is introduced into the FC-PFS algorithm to generate sparsity, which can reduce the complexity of the algorithm on large data sets. Secondly, we propose a method to simplify the process of determining regularization parameters. (...) Finally, experiments show that the clustering results of this algorithm on artificial data sets and real data sets are mostly better than other clustering algorithms. Our clustering algorithm is effective in most cases. (shrink)

We present a uniform version of Di Nola Theorem, this enables to embed all MV-algebras of a bounded cardinality in an algebra of functions with values in a single non-standard ultrapower of the real interval [0,1]. This result also implies the existence, for any cardinal α, of a single MV-algebra in which all infinite MV-algebras of cardinality at most α embed. Recasting the above construction with iterated ultrapowers, we show how to construct such an algebra of values in a definable (...) way, thus providing a sort of “canonical” set of values for the functional representation. (shrink)

We improve a theorem of Raisonnier by showing that Cons(ZFC+every Σ 2 1 -set of reals in Lebesgue measurable+every Π 2 1 -set of reals isK σ-regular) implies Cons(ZFC+there exists an inaccessible cardinal). We construct, fromL, a model where every Δ 3 1 -sets of reals is Lebesgue measurable, has the property of Baire, and every Σ 2 1 -set of reals isK σ-regular. We prove that if there exists a Σ n+1 1 unbounded (...) filter on ω, then there exists a nonK σ-regular Π 2 1 -subset. (shrink)