This article began as a review of a conference, organized by Gerhard Schlosser, entitled “Modularity in Development and Evolution.” The conference was held at, and sponsored by, the Hanse Wissenschaftskolleg in Delmenhorst, Germany in May, 2000. The article subsequently metamorphosed into a literature and concept review as well as an analysis of the differences in current perspectives on modularity. Consequently, I refer to general aspects of the conference but do not review particular presentations. I divide modules into three kinds: (...) structural, developmental, and physiological. Every module fulfills none, one, or multiple functional roles. Two further orthogonal distinctions are important in this context: module-kinds versus module-variants-of-a-kind and reproducer versus nonreproducer modules. I review criteria for individuation of modules and mechanisms for the phylogenetic origin of modularity. I discuss conceptual and methodological differences between developmental and evolutionary biologists, in particular the difference between integration and competition perspectives on individualization and modular behavior. The variety in views regarding modularity presents challenges that require resolution in order to attain a comprehensive, rather than a piecemeal and fragmentary, evolutionary developmental biology. (shrink)

We show that certain classes of modules have universal models with respect to pure embeddings: Let R be a ring, T a first‐order theory with an infinite model extending the theory of R‐modules and (where ⩽pp stands for “pure submodule”). Assume has the joint embedding and amalgamation properties. If or, then has a universal model of cardinality λ. As a special case, we get a recent result of Shelah [28, 1.2] concerning the existence of universal reduced torsion‐free abelian (...) groups with respect to pure embeddings.We begin the study of limit models for classes of R‐modules with joint embedding and amalgamation. We show that limit models with chains of long cofinality are pure‐injective and we characterize limit models with chains of countable cofinality. This can be used to answer [18, Question 4.25].As this paper is aimed at model theorists and algebraists an effort was made to provide the background for both. (shrink)

Embedding ethics modules within computer science courses has become a popular response to the growing recognition that CS programs need to better equip their students to navigate the ethical dimensions of computing technologies like AI, machine learning, and big data analytics. However, the popularity of this approach has outpaced the evidence of its positive outcomes. To help close that gap, this empirical study reports positive results from Northeastern’s program that embeds values analysis modules into CS courses. The resulting (...) data suggest that such modules have a positive effect on students’ moral attitudes and that students leave the modules believing they are more prepared to navigate the ethical dimensions they’ll likely face in their eventual careers. Importantly, these gains were accomplished at an institution without a philosophy doctoral program, suggesting this strategy can be effectively employed by a wider range of institutions than many have thought. (shrink)

This paper studies two dual notions in module theory—namely, radicals and socles—from the standpoint of reverse mathematics. We first consider radicals of Z-modules, where the radical of a Z-module M is defined as the intersection of pM={px:x∈M} with p taken from all primes. It shows that ACA0 is equivalent to the existence of radicals of Z-modules over RCA0. We then study socles of modules over commutative rings with identity. The socle of an R-module M is the largest (...) semisimple submodule of M. We show that the existence of socles of modules over a commutative ring with identity is equivalent to ACA0 over RCA0. Vector spaces are semisimple modules over fields. In general, semisimple modules possess nice properties of vector spaces. Lastly, we study characterizations of semisimple modules over commutative rings using techniques of reverse mathematics. (shrink)

The Architecture of Mind is an ambitious and informative work, surveying an impressive range of empirical literature and arguing that the mind is massively modular. However, it suffers from two major theoretical flaws. First, Carruthers’ concept of a module is weak, so much so that it robs his thesis of massive modularity of any real substance. Second, his conception of how the mind’s modules evolved ignores the role of niche construction and cultural evolution to its detriment.

We define a first-order extension LK(CP) of the cutting planes proof system CP as the first-order sequent calculus LK whose atomic formulas are CP-inequalities ∑ i a i · x i ≥ b (x i 's variables, a i 's and b constants). We prove an interpolation theorem for LK(CP) yielding as a corollary a conditional lower bound for LK(CP)-proofs. For a subsystem R(CP) of LK(CP), essentially resolution working with clauses formed by CP- inequalities, we prove a monotone interpolation theorem (...) obtaining thus an unconditional lower bound (depending on the maximum size of coefficients in proofs and on the maximum number of CP-inequalities in clauses). We also give an interpolation theorem for polynomial calculus working with sparse polynomials. The proof relies on a universal interpolation theorem for semantic derivations [16, Theorem 5.1]. LK(CP) can be viewed as a two-sorted first-order theory of Z considered itself as a discretely ordered Z-module. One sort of variables are module elements, another sort are scalars. The quantification is allowed only over the former sort. We shall give a construction of a theory LK(M) for any discretely ordered module M (e.g., LK(Z) extends LK(CP)). The interpolation theorem generalizes to these theories obtained from discretely ordered Z-modules. We shall also discuss a connection to quantifier elimination for such theories. We formulate a communication complexity problem whose (suitable) solution would allow to improve the monotone interpolation theorem and the lower bound for R(CP). (shrink)

Quantum B‐algebras are partially ordered algebras characterizing the residuated structure of a quantale. Examples arise in algebraic logic, non‐commutative arithmetic, and quantum theory. A quantum B‐algebra with trivial partial order is equivalent to a group. The paper introduces a corresponding analogue of quantale modules. It is proved that every quantum B‐module admits an injective envelope which is a quantale module. The injective envelope is constructed explicitly as a completion, a multi‐poset version of the completion of Dedekind and MacNeille.

We characterize rings over which every cotorsion module is pure injective in terms of certain descending chain conditions and the Ziegler spectrum, which renders the classes of von Neumann regular rings and of pure semisimple rings as two possible extremes. As preparation, descriptions of pure projective and Mittag–Leffler preenvelopes with respect to so-called definable subcategories and of pure generation for such are derived, which may be of interest on their own. Infinitary axiomatizations lead to coherence results previously known for the (...) special case of flat modules. Along with pseudoflat modules we introduce quasiflat modules, which arise naturally in the model-theoretic and the category-theoretic contexts. (shrink)

We use the Drozd-Warfield structure theorem for finitely presented modules over a serial ring to investigate the model theory of modules over a serial ring, in particular, to give a simple description of pp-formulas and to classify the pure-injective indecomposable modules. We also study the question of whether every pure-injective indecomposable module over a valuation ring is the hull of a uniserial module.

We prove the elimination of Magidor-Malitz quantifiers for R-modules relative to certain Q 2 α -core sentences and positive primitive formulas. For complete extensions of the elementary theory of R-modules it follows that all Ramsey quantifiers (ℵ 0 -interpretation) are eliminable. By a result of Baldwin and Kueker [1] this implies that there is no R-module having the finite cover property.

Electric-mechanical equipment manufacturing industries focus on the implementation of intelligent manufacturing systems in order to enhance customer services for highly customized machines with high-profit margins such as electric power transformers. Intelligent manufacturing consists in using supply chain data that are integrated for smart decision making during the production life cycle. This research, in cooperation with a large electric power transformer manufacturer, provides an overview of critical intelligent manufacturing technologies. An ontology schema forms the terminology relationships needed to build two intelligent (...) supply chain management modules for the IM system demonstration. The two core modules proposed in this research are the intelligent supplier selection and component ordering module and the product quality prediction module. The intelligent supplier selection and component ordering module dispatches orders that match the best options of suppliers based on combined analytic hierarchy process analysis and multiobjective integer optimization. In the case study, the intelligent supplier selection and component ordering module demonstrates several acceptable Pareto solutions based on strict constraints, which is a very challenging task for decision makers without assistance. The second module is the product quality prediction module which uses multivariate regression and ARIMA to predict the quality of the finished products. Results show that the R square values are very close to 1. The module shortens the time for the company to accurately judge whether the two semifinished iron cores for the product meet the quality requirements. The component supplier selection module and the finished product quality prediction module developed in this research can be extended to other IM systems for general high-end equipment manufacturers using mass customization. (shrink)

The generation of isometric force at the hand can be mediated by activating a few motor modules. Stroke induces alterations in motor modules underlying steady-state isometric force generation in the human upper extremity. However, how the altered motor modules impact task performance remains unclear as stroke survivors develop and converge to the three-dimensional target force. Thus, we tested whether stroke-specific motor modules would be activated from the onset of force generation and also examined how alterations in (...) motor modules would induce changes in force representation. During 3D isometric force development, electromyographic signals were recorded from eight major elbow and shoulder muscles in the paretic arm of 10 chronic hemispheric stroke survivors and both arms of six age-matched control participants. A non-negative matrix factorization algorithm identified motor modules in four different time windows: three “exploratory” force ramping phases and the stable force match phase. Motor module similarity and between-force coupling were examined by calculating the scalar product and Pearson correlation across the phases. To investigate the association between the end-point force representation and the activation of the motor modules, principal component analysis and multivariate multiple linear regression analyses were applied. In addition, the force components regressed on the activation profiles of motor modules were utilized to model the feasible force direction. Both stroke and control groups developed exploratory isometric forces with a non-linear relationship between EMG and force. During the force matching, only the stroke group showed abnormal between-force coupling in medial-lateral and backward-forward and medial-lateral and downward-upward directions. In each group, the same motor modules, including the abnormal deltoid module in stroke survivors, were expressed from the beginning of force development instead of emerging during the force exploration. The PCA and the multivariate multiple linear regression analyses showed that alterations in motor modules were associated with abnormal between-force coupling and limited feasible force direction after stroke. Overall, these results suggest that alterations in intermuscular coordination contribute to the abnormal end-point force control under isometric conditions in the UE after stroke. (shrink)

The main theorem characterizes Mittag-Leffler modules as ‘positively atomic’ modules . This is applied to reduced products of Mittag-Leffler modules and pure-semisimple.

Van den Dries, L. and J. Holly, Quantifier elimination for modules with scalar variables, Annals of Pure and Applied Logic 57 161–179. We consider modules as two-sorted structures with scalar variables ranging over the ring. We show that each formula in which all scalar variables are free is equivalent to a formula of a very simple form, uniformly and effectively for all torsion-free modules over gcd domains . For the case of Presburger arithmetic with scalar variables the (...) result takes a still simpler form, and we derive in this way the polynomial-time decidability of the sets defined by such formulas. (shrink)

We consider the reduct to the module language of certain theories of fields with a non surjective endomorphism. We show in some cases the existence of a model companion. We apply our results for axiomatizing the reduct to the theory of modules of non principal ultraproducts of separably closed fields of fixed but non zero imperfection degree.

We prove that the property characterizes Σ‐algebraically compact modules if is not ω‐measurable. Moreover, under a large cardinal assumption, we show that over any ring R where is not ω‐measurable, any free module M of ω‐measurable rank satisfies, hence the assumption on cannot be dropped in general (e.g., over small non‐right perfect rings). In this way, we extend results from a recent paper by Simion Breaz.

It is shown that the first-order theory Th R (A) of a countable module over an arbitrary countable ring R is ℵ 0 -categorical if and only if $A \cong \bigoplus_{t finite, n ∈ ω, κ i ≤ ω. Furthermore, Th R (A) is ℵ 0 -categorical for all R-modules A if and only if R is finite and there exist only finitely many isomorphism classes of indecomposable R-modules.

In this paper, by considering the notion of MV-module, which is the structure that naturally correspond to lu-modules over lu-rings, we study injective MV-modules and we investigate some conditions for constructing injective MV-modules. Then we define the notions of essential A-homomorphisms and essential extension of A-homomorphisms, where A is a product MV-algebra, and we get some of there properties. Finally, we prove that a maximal essential extension of any A-ideal of an injective MV-module is an injective A-module, (...) too. (shrink)

The study of pairs of modules (over a Dedekind domain) arises from two different perspectives, as a starting step in the analysis of tuples of submodules of a given module, or also as a particular case in the analysis of Abelian structures made by two modules and a morphism between them. We discuss how these two perspectives converge to pairs of modules, and we follow the latter one to obtain an alternative approach to the classification of pairs (...) of torsionfree objects. Then we restrict our attention to pairs of free modules. Our main results are that the theory of pairs of free Abelian groups is co-recursively enumerable, and that a few remarkable extensions of this theory are decidable. (shrink)

In this commentary, we support a complex, mosaic, and multimodal approach to the evolution of intelligence. Using the arcuate fasciculus as an example of discontinuity in the evolution of neurobiological architectures, we argue that the strict dichotomy of modules versus G, adopted by Burkart et al. in the target article, is insufficient to interpret the available statistical and experimental evidence.

In the past few decades, research in the psychology of emotion has benefited greatly from being located in a firm evolutionary framework. It is argued that research in the psychology of mood might attain equal rigour by taking a similar approach. An evolutionary framework for mood research would be based on evolutionary psychology, the main thesis of which is the Massive Modularity Hypothesis. Translating the folk-psychological language of moods into the scientific language of modules might clarify many theoretical questions (...) and provide a sound basis for empirical research. It is argued that such an evolutionary approach would reveal mood to be a much more heterogeneous category than emotion. While the six basic emotions identified by Paul Ekman are probably each subserved by a single module, prototypical moods such as elation, depression, anxiety and irritability are likely to be subserved by a wide range of modules. An evolutionary approach to mood might therefore lead to the elimination of the concept of mood from scientific psychology altogether. (shrink)

The composition series of Verma modules and homomorphisms between Verma modules in the case of a complex semisimple Lie algebra were studied by Verma and by Bernstein, Gelfand and Gelfand. The author studies homomorphisms between the Verma modules in characteristic p.

We fully support dissociating the subjective experience from the memory contents in recognition memory, as Bastin et al. posit in the target article. However, having two generic memory modules with qualitatively different functions is not mandatory and is in fact inconsistent with experimental evidence. We propose that quantitative differences in the properties of the memory modules can account for the apparent dissociation of recollection and familiarity along anatomical lines.

Ordered sheaves on a small quantaloid have been defined in terms of -enriched categorical structures; they form a locally ordered category . The free-cocompletion KZ-doctrine on has , the quantaloid of -modules, as its category of Eilenberg–Moore algebras. In this paper we give an intrinsic description of the Kleisli algebras: we call them the locally principally generated -modules. We deduce that is biequivalent to the 2-category of locally principally generated -modules and left adjoint module morphisms. The example (...) of locally principally generated modules on a locale X is worked out in full detail: relating X-modules to objects of the slice category , we show that ordered sheaves on X correspond with skew local homeomorphisms into X. (shrink)

Let FΛ be a finite dimensional path algebra of a quiver Λ over a field F. Let L and R denote the varieties of all left and right FΛ-modules respectively. We prove the equivalence of the following statements. • The subvariety lattice of L is a sublattice of the subquasivariety lattice of L. • The subquasivariety lattice of R is distributive. • Λ is an ordered forest.

It is proved that Vaught's conjecture is true for modules over an arbitrary countable serial ring. It follows from the structural result that every module with few models over a (countable) serial ring is ω-stable.

The hypothesis that nonhuman species, lacking verbal language, do not really integrate information from different modules, but use instead information sequentially, appears difficult to put under empirical scrutiny. Evidence is discussed showing that in nonhuman species storing of geometric information occurs spontaneously even when landmark information suffices for spatial reorientation, suggesting simultaneous encoding, if not use, of information from different modules.

We generalize to theories of modules (complete or not) a result of U. Felgner stating that a complete theory of abelian groups is a Horn theory if and only if it is closed under products. To prove this we show that a reduced product of modules $\Pi_F M_i (i \in I)$ is elementarily equivalent to a direct product of ultraproducts of the modules $M_i (i \in I)$.

We find the model completion of the theory modules over ������, where ������ is a finitely generated commutative algebra over a field K. This is done in a context where the field K and the module are represented by sorts in the theory, so that constructible sets associated with a module can be interpreted in this language. The language is expanded by additional sorts for the Grassmanians of all powers of $K^n $ , which are necessary to achieve quantifier (...) elimination. The result turns out to be that the model completion is the theory of a certain class of "big" injective modules. In particular, it is shown that the class of injective modules is itself elementary. We also obtain an explicit description of the types in this theory. (shrink)

Definitions for heterogeneous congruences and heterogeneous ideals on a Boolean module are given and the respective lattices and are presented. A characterization of the simple bijective Boolean modules is achieved differing from that given by Brink in a homogeneous approach. We construct the smallest and the greatest modular congruence having the same Boolean part. The same is established for modular ideals. The notions of kernel of a modular congruence and the congruence induced by a modular ideal are introduced to (...) describe an isomorphism between and. This isomorphism leads us to conclude that the class of the Boolean module is ideal determined. (shrink)

We investigate the issues of Diophantine definability over the non-finitely generated version of non-degenerate modules contained in the infinite algebraic extensions of the rational numbers. In particular, we show the following. Let k be a number field and let K inf be a normal algebraic, possibly infinite, extension of k such that k has a normal extension L linearly disjoint from K inf over k. Assume L is totally real and K inf is totally complex. Let M inf be (...) a non-degenerate O k -module, possibly non-finitely generated and contained in O Kinf . Then M inf contains a submodule M¯ inf such that M inf /M¯ inf is torsion and O k has a Diophantine definition over M¯ inf. (shrink)

Jane is calmly strolling through the forest one lovely day. Suddenly, a large spider drops in front of her face. She immediately freezes; her heart races; her hands tremble; her face broadcasts “fear.” She screams and runs away. Both before and after, she concedes that spiders in this forest are harmless.Jane's reaction to the spider contrasts greatly with the way she normally reacts to events. Normally, or so the story goes, Jane weighs her options thoughtfully, choosing a course of action (...) consistent with her beliefs and with the greatest benefit. Indeed, her reaction to the spider contrasts so greatly with calm, rational, deliberate, belief-consistent action that traditional folk psychology supposed two different kinds of mechanism are at work: animal-like emotion versus human reason. Her emotion explains her reaction to the spider. Her emotion made her do it. (shrink)

Using theoretical analysis of self-consciousness concept and experimental evidence on the brain default mode network (DMN) that constitutes the neural signature of self-referential processes, we hypothesized that the anterior and posterior subnets comprising the DMN should show differences in their integrity as a function of meditation training. Functional connectivity within DMN and its subnets (measured by operational synchrony) has been measured in ten novice meditators using an electroencephalogram (EEG) recording in a pre-/post-meditation intervention design. We have found that while the (...) whole DMN was clearly suppressed, different subnets of DMN responded differently after 4 months of meditation training: The strength of EEG operational synchrony in the right and left posterior modules of the DMN decreased in resting post-meditation condition compared to a pre-meditation condition, whereas the frontal DMN module on the contrary exhibited an increase in the strength of EEG operational synchrony. These findings combined with published data on functional–anatomic heterogeneity within the DMN and on trait subjective experiences commonly found following meditation allow us to propose that the first-person perspective and the sense of agency (the witnessing observer) are presented by the frontal DMN module, while the posterior modules of the DMN are generally responsible for the experience of the continuity of ‘I’ as embodied and localized within bodily space. Significance of these findings is discussed. (shrink)

Fisher [10] and Baur [6] showed independently in the seventies that if T is a complete first-order theory extending the theory of modules, then the class of models of T with pure embeddings is stable. In [25, 2.12], it is asked if the same is true for any abstract elementary class $(K, \leq _p)$ such that K is a class of modules and $\leq _p$ is the pure submodule relation. In this paper we give some instances where this (...) is true:Theorem.Assume R is an associative ring with unity. Let $(K, \leq _p)$ be an AEC such that $K \subseteq R\text {-Mod}$ and K is closed under finite direct sums, then: •If K is closed under pure-injective envelopes, then $\mathbf {K}$ is $\lambda $ -stable for every $\lambda \geq \operatorname {LS}(\mathbf {K})$ such that $\lambda ^{|R| + \aleph _0}= \lambda $.•If K is closed under pure submodules and pure epimorphic images, then $\mathbf {K}$ is $\lambda $ -stable for every $\lambda $ such that $\lambda ^{|R| + \aleph _0}= \lambda $.•Assume R is Von Neumann regular. If $\mathbf {K}$ is closed under submodules and has arbitrarily large models, then $\mathbf {K}$ is $\lambda $ -stable for every $\lambda $ such that $\lambda ^{|R| + \aleph _0}= \lambda $.As an application of these results we give new characterizations of noetherian rings, pure-semisimple rings, Dedekind domains, and fields via superstability. Moreover, we show how these results can be used to show a link between being good in the stability hierarchy and being good in the axiomatizability hierarchy.Another application is the existence of universal models with respect to pure embeddings in several classes of modules. Among them, the class of flat modules and the class of $\mathfrak {s}$ -torsion modules. (shrink)

Foundational ontologies are usually developed in powerful logical languages, while they are often implemented in applications via their formalisations in the Web Ontology language (OWL). These OWL formalisations are in fact approximations of the original theories, to cope with the well-known limited expressivity of OWL. In this paper, we propose a novel modular approach to the OWL rendering of the Descriptive Ontology for Linguistic and Cognitive Engineering ( dolce ). We start presenting two fundamental modules of dolce in OWL (...) 2: (i) a core module of dolce (termed ‘DOLCEbasic OWL ’), which provides the main taxonomy and the binary relations of the foundational ontology and (ii) an extension (termed ‘DOLCEnaryRel OWL ’) to deal with the n -ary relations of dolce (for n > 2 ). We examine how the OWL rendering requires approaching delicate and truly ontological issues to motivate the choices made to circumvent the limited expressivity. To provide a minimal justification of our approximation, we establish that the OWL 2 versions are compatible with the original version of dolce by offering an automated proof that the first-order version of dolce entails the translations into first-order logic of the OWL 2 modules. Other adequacy criteria are then discussed. Finally, we illustrate the functioning of our rendering by means of examples. We conclude by discussing a number of other modules to cope with other core concepts and specific domains. (shrink)

What are the landmarks of the cognitive revolution? What are the core topics of modern cognitive science? Where is cognitive science heading to? Leading cognitive scientists--Chomsky, Pylyshyn, Gallistel, and others--examine their own work in relation to one of cognitive science's most influential and polemical figures: Jerry Fodor.

Public “upstream engagement” and other approaches to the social control of technology are currently receiving international attention in policy discourses around emerging technologies such as nanotechnology. To the extent that such approaches hold implications for research and development (R&D) activities, the distinct participation of scientists and engineers is required. The capacity of technoscientists to broaden the influences on R&D activities, however, implies that they conduct R&D differently. This article discusses the possibility for more reflexive participation by scientists and engineers in (...) the internal governance of technology development. It reviews various historical attempts to govern technoscience and introduces the concept of midstream modulation, through which scientists and engineers, ideally in concert with others, bring societal considerations to bear on their work. (shrink)

We study the theory of a Hilbert space H as a module for a unital C*-algebra ${\mathcal{A}}$ from the point of view of continuous logic. We give an explicit axiomatization for this theory and describe the structure of all the representations which are elementary equivalent to it. Also, we show that this theory has quantifier elimination and we characterize the model companion of the incomplete theory of all non-degenerate representations of ${\mathcal{A}}$. Finally, we show that there is an homeomorphism between (...) the space of types of norm less than 1 in this model companion, and the space of quasistates of the C*-algebra ${\mathcal{A}}$. (shrink)

In response to an increasing amount of policy papers stressing the need for integrating social and ethical aspects in Research and Development (R&D) practices, science studies scholars have conducted integrative research and experiments with science and innovation actors. One widely employed integration method is Midstream Modulation (MM), in which an ‘embedded humanist’ interacts in regular meetings with researchers to engage them with the social and ethical aspects of their work. While the possibility of using MM to enhance critical reflection has (...) been demonstrated in academic settings, few attempts have been made to examine its appropriateness in industry. This paper describes the outcomes of a case study aiming to find out firstly whether MM can effectively be deployed to encourage and facilitate researchers to actively include social and ethical aspects in their daily R&D practice, and secondly to what extent the integration activities could form an integral part of the engaged industrial researchers’ professional activities. Our data show that after MM, researchers display increased reflexive awareness on the social and ethical aspects of their work and acknowledge the relevance and utility of such aspects on their daily practice. Also, all participants considered actively reflecting on social and ethical aspects to be part of their work. Future research on the role of MM in industrial settings could focus on how to embed social and ethical integration as a regular part of innovation practice. We suggest that one possibility would be through aligning social and ethical aspects with innovation Key Performance Indicators. (shrink)