In this letter we demonstrate that the fermionic zero modes on a superconducting domain wall can be associated to an one dimensional \ supersymmetry that contains non-trivial topological charges. In addition, the system also possesses three distinct \ supersymmetries with non-trivial topological charges and we also study some duality transformations of the supersymmetric algebras.

Deletions, duplications, insertions, inversions, and translocations, collectively called structural variations (SVs), affect more base pairs of the genome than any other sequence variant. The recent technological advancements in genome sequencing have enabled the discovery of tens of thousands of SVs per human genome. These SVs primarily affect non‐coding DNA sequences, but the difficulties in interpreting their impact limit our understanding of human disease etiology. The functional annotation of non‐coding DNA sequences and methodologies to characterize their three‐dimensional (3D) organization in the (...) nucleus have greatly expanded our understanding of the basic mechanisms underlying gene regulation, thereby improving the interpretation of SVs for their pathogenic impact. Here, we discuss the various mechanisms by which SVs can result in altered gene regulation and how these mechanisms can result in rare genetic disorders. Beyond changing gene expression, SVs can produce novel gene‐intergenic fusion transcripts at the SV breakpoints. (shrink)

The organization of the genome into topologically associated domains (TADs) appears to be a fundamental process occurring across a wide range of eukaryote organisms, and it likely plays an important role in providing an architectural foundation for gene regulation. Initial studies emphasized the remarkable parallels between TAD organization in organisms as diverse as Drosophila and mammals. However, whereas CCCTC‐binding factor (CTCF)/cohesin loop extrusion is emerging as a key mechanism for the formation of mammalian topological domains, the (...) genome organization in Drosophila appears to depend primarily on the partitioning of chromatin state domains. Recent work suggesting a fundamental conserved role of chromatin state in building domain architecture is discussed and insights into genome organization from recent studies in Drosophila are considered. (shrink)

Recent investigations have revealed 1) that the isochores of the human genome group into two super‐families characterized by two different long‐range 3D structures, and 2) that these structures, essentially based on the distribution and topology of short sequences, mold primary chromatin domains (and define nucleosome binding). More specifically, GC‐poor, gene‐poor isochores are low‐heterogeneity sequences with oligo‐A spikes that mold the lamina‐associated domains (LADs), whereas GC‐rich, gene‐rich isochores are characterized by single or multiple GC peaks that mold the (...) topologically associating domains (TADs). The formation of these “primary TADs” may be followed by extrusion under the action of cohesin and CTCF. Finally, the genomic code, which is responsible for the pervasive encoding and molding of primary chromatin domains (LADs and primary TADs, namely the “gene spaces”/“spatial compartments”) resolves the longstanding problems of “non‐coding DNA,” “junk DNA,” and “selfish DNA” leading to a new vision of the genome as shaped by DNA sequences. (shrink)

Théologien, historien, philosophe, sociologue et homme politique libéral, Ernst Troeltsch (1865-1923) fait partie du groupe des théologiens protestants allemands appelé " Ecole de l'histoire des religions ". Revendiquant l'héritage de Kant et de Schleiermacher, proche de Max Weber et du néo-kantisme de l'Ecole de Bade, Troeltsch est le théoricien classique du néo-protestantisme. Surtout connu en France comme sociologue de la religion, il est redécouvert aujourd'hui comme philosophe et théologien, éclipsé un temps par Barth, l'existentialisme et Heidegger. Les huit essais rassemblés (...) ici sont écrits à l'horizon d'une réflexion sur le religieux marquée par les sciences humaines et sociales et par une conscience accusée de la pluralité des formes de la religion. Troeltsch y dessine un programme qui inscrit délibérément la théologie dans une perspective historique, tout en s'efforçant d'articuler approche empirique et interrogation touchant les jugements de valeur. Il récuse ainsi toute tentative pour faire valoir un domaine théologique réservé : non seulement le christianisme n'est pas la religion dans sa forme achevée ou " absolue ", mais les tentatives pour déterminer une " essence " du christianisme par-delà ses inscriptions socioculturelles diverses devront également être refusées. En désenclavant la réflexion théologique, Troeltsch oblige à redéfinir son objet et son statut : elle ne sera plus explicitation du croire, mais devra esquisser une théorie du christianisme précisant le statut, la fonction et les limites du religieux dans une modernité marquée par la diversification des instances de rationalisation et de légitimité. Ce faisant, son propos tranche avec les discours théologiques dominants dans la seconde moitié du XXe siècle, tant en protestantisme qu'en catholicisme. Et il ouvre à nouveau la question d'une pertinence sociale et culturelle du religieux et du théologique. A l'heure où les paradigmes modernes se trouvent en profonde interrogation sur eux-mêmes et où la question religieuse fait retour - peut-être pour le meilleur mais souvent pour le pire -, la lecture de Troeltsch peut apporter une contribution bienvenue à un ensemble de questions parmi les plus centrales de notre temps. Publiés pour la première fois en français, les textes présentés ici sont accompagnés d'un important appareil de commentaires historiques aidant le lecteur à reconstituer le contexte et la genèse des débats en cause. (shrink)

We discuss here a series of testable hypotheses concerning the role of chromosome folding into topologically associating domains (TADs). Several lines of evidence suggest that segmental packaging of chromosomal neighborhoods may underlie features of chromatin that span large domains, such as heterochromatin blocks, association with the nuclear lamina and replication timing. By defining which DNA elements preferentially contact each other, the segmentation of chromosomes into TADs may also underlie many properties of long‐range transcriptional regulation. Several observations suggest (...) that TADs can indeed provide a structural basis to regulatory landscapes, by controlling enhancer sharing and allocation. We also discuss how TADs may shape the evolution of chromosomes, by causing maintenance of synteny over large chromosomal segments. Finally we suggest a series of experiments to challenge these ideas and provide concrete examples illustrating how they could be practically applied. (shrink)

Information management systems improve the retention of information in large collections. As such they act as memory prostheses, implying an ideal basis in human memory models. Since humans process information by association, and situate it in the context of space and time, systems should maximize their effectiveness by mimicking these functions. Since human attentional capacity is limited, systems should scaffold cognitive efforts in a comprehensible manner. We propose the Principles of Mnemonic Associative Knowledge (P-MAK), which describes a framework for semantically (...) identifying, organizing, and retrieving information, and for encoding episodic events by time and stimuli. Inspired by prominent human memory models, we propose associative networks as a preferred representation. Networks are ideal for their parsimony, flexibility, and ease of inspection. Networks also possess topological properties—such as clusters, hubs, and the small world—that aid analysis and navigation in an information space. Our cognitive perspective addresses fundamental problems faced by information management systems, in particular the retrieval of related items and the representation of context. We present evidence from neuroscience and memory research in support of this approach, and discuss the implications of systems design within the constraints of P-MAK’s principles, using text documents as an illustrative semantic domain. (shrink)

Recent advances in genomic and imaging techniques have revealed the complex manner of organizing billions of base pairs of DNA necessary for maintaining their functionality and ensuring the proper expression of genetic information. The SMC proteins and cohesin complex primarily contribute to forming higher‐order chromatin structures, such as chromosomal territories, compartments, topologically associating domains (TADs) and chromatin loops anchored by CCCTC‐binding factor (CTCF) protein or other genome organizers. Cohesin plays a fundamental role in chromatin organization, gene expression and (...) regulation. This review aims to describe the current understanding of the dynamic nature of the cohesin‐DNA complex and its dependence on cohesin for genome maintenance. We discuss the current 3C technique and numerous bioinformatics pipelines used to comprehend structural genomics and epigenetics focusing on the analysis of Cohesin‐centred interactions. We also incorporate our present comprehension of Loop Extrusion (LE) and insights from stochastic modelling. (shrink)

Recent years have witnessed an explosion of the single-cell biochemical toolbox including chromosome conformation capture -based methods that provide novel insights into chromatin spatial organization in individual cells. The observations made with these techniques revealed that topologically associating domains emerge from cell population averages and do not exist as static structures in individual cells. Stochastic nature of the genome folding is likely to be biologically relevant and may reflect the ability of chromatin fibers to adopt a number of (...) alternative configurations, some of which could be transiently stabilized and serve regulatory purposes. Single-cell Hi-C approaches provide an opportunity to analyze chromatin folding in rare cell types such as stem cells, tumor progenitors, oocytes, and totipotent cells, contributing to a deeper understanding of basic mechanisms in development and disease. Here, we review key findings of single-cell Hi-C and discuss possible biological reasons and consequences of the inferred dynamic chromatin spatial organization. Single-cell Hi-C expands the molecular biology toolbox for studies of chromatin structure in individual cells. This technique allows one to analyze cell-to-cell variability in TAD and loop structure, and to capture chromosome conformation in rare cell types such as oocytes, totipotent cells, and tumor progenitors. (shrink)

Recent years have witnessed an explosion of the single-cell biochemical toolbox including chromosome conformation capture -based methods that provide novel insights into chromatin spatial organization in individual cells. The observations made with these techniques revealed that topologically associating domains emerge from cell population averages and do not exist as static structures in individual cells. Stochastic nature of the genome folding is likely to be biologically relevant and may reflect the ability of chromatin fibers to adopt a number of (...) alternative configurations, some of which could be transiently stabilized and serve regulatory purposes. Single-cell Hi-C approaches provide an opportunity to analyze chromatin folding in rare cell types such as stem cells, tumor progenitors, oocytes, and totipotent cells, contributing to a deeper understanding of basic mechanisms in development and disease. Here, we review key findings of single-cell Hi-C and discuss possible biological reasons and consequences of the inferred dynamic chromatin spatial organization. Single-cell Hi-C expands the molecular biology toolbox for studies of chromatin structure in individual cells. This technique allows one to analyze cell-to-cell variability in TAD and loop structure, and to capture chromosome conformation in rare cell types such as oocytes, totipotent cells, and tumor progenitors. (shrink)

The spatial organization of the genome is intimately linked to its biological function, yet our understanding of higher order genomic structure is coarse, fragmented and incomplete. In the nucleus of eukaryotic cells, interphase chromosomes occupy distinct.

D′ ⊆ D is a normal totality on a Scott domain D if it is upward closed and x ⊓ y ∈ D′ is an equivalence relation on D′. We prove that every topological space can be represented by a domain with norma totality.

Insulators play a central role in subdividing the chromosome into a series of discrete topologically independent domains and in ensuring that enhancers and silencers contact their appropriate target genes. In this review we first discuss the general characteristics of insulator elements and their associated protein factors. A growing collection of insulator proteins have been identified including a family of proteins whose expression is developmentally regulated. We next consider several unexpected discoveries that require us to completely rethink how (...) insulators function (and how they can best be assayed). These discoveries also require a reevaluation of how insulators might restrict or orchestrate (by preventing or promoting) interactions between regulatory elements and their target genes. We conclude by connecting these new insights into the mechanisms of insulator action to dynamic changes in the three‐dimensional topology of the chromatin fiber and the generation of specific patterns of gene activity during development and differentiation. (shrink)

The existence of singularities alerts that one of the highest priorities of a centennial perspective on general relativity should be a careful re-thinking of the validity domain of Einstein’s field equations. We address the problem of constructing distinguishable extensions of the smooth spacetime manifold model, which can incorporate singularities, while retaining the form of the field equations. The sheaf-theoretic formulation of this problem is tantamount to extending the algebra sheaf of smooth functions to a distribution-like algebra sheaf in which the (...) former may be embedded, satisfying the pertinent cohomological conditions required for the coordinatization of all of the tensorial physical quantities, such that the form of the field equations is preserved. We present in detail the construction of these distribution-like algebra sheaves in terms of residue classes of sequences of smooth functions modulo the information of singular loci encoded in suitable ideals. Finally, we consider the application of these distribution-like solution sheaves in geometrodynamics by modeling topologically-circular boundaries of singular loci in three-dimensional space in terms of topological links. It turns out that the Borromean link represents higher order wormhole solutions. (shrink)

The qualitative nature of co-deployed or “associated” metaphorical source domains in discourse has been extensively researched, often in terms of whether they share common conceptual roots. There are however few empirical studies on the strength of these associations and their implications. In mental healthcare activities like psychological interviews and counseling, for example, strongly associated sources may suggest unique “conceptual assemblages” that highlight underexplored (dis)similarities between clients or client groups, beyond the typical focus on isolated sources and frequencies. (...) Our case study compares source domain associations produced by two interviewee groups – one meeting the diagnostic threshold for acute stress disorder (ASD), the other not – relating their first-hand experiences of traumatic events during the 2019 Hong Kong social unrest. The machine learning method of association rule mining is used to extract and quantify the top association rules in both groups. Results show i) a shared rule suggesting a highly schematic construal of trauma that nevertheless varies in instantiating details, and ii) several distinct rules that corroborates and lends further insight into the “agentive vs. non-agentive” characteristics exhibited by ASD vs. non-ASD individuals. Implications and future directions, including potential extensions to other discourse contexts, are discussed. (shrink)

Cardinal number knowledge-understanding “two” refers to sets of two entities-is a critical piece of knowledge that predicts later mathematics achievement. Recent studies have shown that domain-general and domain-specific skills can influence children’s cardinal number learning. However, there has not yet been research investigating the influence of domain-specific quantifier knowledge on children’s cardinal number learning. The present study aimed to investigate the influence of domain-general and domain-specific skills on Mandarin Chinese-speaking children’s cardinal number learning after controlling for a number of family (...) background factors. Particular interest was paid to the question whether domain-specific quantifier knowledge was associated with cardinal number development. Specifically, we investigated 2–5-year-old Mandarin Chinese-speaking children’s understanding of cardinal number words as well as their general language, intelligence, approximate number system acuity, and knowledge of quantifiers. Children’s age, gender, parental education, and family income were also assessed and used as covariates. We found that domain-general abilities, including general language and intelligence, did not account for significant additional variance of cardinal number knowledge after controlling for the aforementioned covariates. We also found that domain-specific quantifier knowledge did not account for significant additional variance of cardinal number knowledge, whereas domain-specific ANS acuity accounted for significant additional variance of cardinal number knowledge, after controlling for the aforementioned covariates. In sum, the results suggest that domain-specific numerical skills seem to be more important for children’s development of cardinal number words than the more proximal domain-general abilities such as language abilities and intelligence. The results also highlight the significance of ANS acuity on children’s cardinal number word development. (shrink)

We associate a canonical unital involutive quantale to a topological groupoid. When the groupoid is also étale, this association is compatible with but independent from the theory of localic étale groupoids and their quantales [9] of P. Resende. As a motivating example, we describe the connection between the quantale and the C*-algebra that both classify Penrose tilings, which was left as an open problem in [5].

A general method for constructing a new class of topological Ramsey spaces is presented. Members of such spaces are infinite sequences of products of Fraïssé classes of finite relational structures satisfying the Ramsey property. The Product Ramsey Theorem of Sokič is extended to equivalence relations for finite products of structures from Fraïssé classes of finite relational structures satisfying the Ramsey property and the Order-Prescribed Free Amalgamation Property. This is essential to proving Ramsey-classification theorems for equivalence relations on fronts, generalizing the (...) Pudlák–Rödl Theorem to this class of topological Ramsey spaces. To each topological Ramsey space in this framework corresponds an associated ultrafilter satisfying some weak partition property. By using the correct Fraïssé classes, we construct topological Ramsey spaces which are dense in the partial orders of Baumgartner and Taylor generating p-points which are k-arrow but not \-arrow, and in a partial order of Blass producing a diamond shape in the Rudin-Keisler structure of p-points. Any space in our framework in which blocks are products of n many structures produces ultrafilters with initial Tukey structure exactly the Boolean algebra \\). If the number of Fraïssé classes on each block grows without bound, then the Tukey types of the p-points below the space’s associated ultrafilter have the structure exactly \. In contrast, the set of isomorphism types of any product of finitely many Fraïssé classes of finite relational structures satisfying the Ramsey property and the OPFAP, partially ordered by embedding, is realized as the initial Rudin-Keisler structure of some p-point generated by a space constructed from our template. (shrink)

The concept of representation has been a key element in the scientific study of mental processes, ever since such studies commenced. However, usage of the term has been all but too liberal—if one were to adhere to common use it remains unclear if there are examples of physical systems which cannot be construed in terms of representation. The problem is considered afresh, taking as the starting point the notion of activity spaces—spaces of spatiotemporal events produced by dynamical systems. It is (...) argued that representation can be analyzed in terms of the geometrical and topological properties of such spaces. Several attributes and processes associated with conceptual domains, such as logical structure, generalization and learning are considered, and given analogues in structural facets of activity spaces, as are misrepresentation and states of arousal. Based on this analysis, representational systems are defined, as is a key concept associated with such systems, the notion of representational capacity. According to the proposed theory, rather than being an all or none phenomenon, representation is in fact a matter of degree—that is can be associated with measurable quantities, as is behooving of a putative naturalistic construct. (shrink)

A growing body of research demonstrates the relevance of character strengths for flourishing in general, but also for important outcomes across different life domains. Studies have also shown that there are differences in the extent to which character strengths are applied, that is, perceived as relevant and shown in behavior in a given context, between work and private life, but they have not considered other life domains. This study aims to close this gap by examining the life (...) class='Hi'>domains of work, education, leisure, close personal relationships, and romantic relationships. The present study investigates whether strengths-related behavior across different life domains explains additional variance in flourishing beyond the trait level of each respective character strength and studies differences in the relevance of character strengths and strengths-related behavior across different life domains, and examines their relationships with flourishing. A sample of 203 German-speaking adults completed self-reports assessing flourishing and character strengths. They also indicated which of the five life domains were personally relevant to them and reported the character strengths' perceived relevance and the frequency of displaying strengths-related behavior for each of these life domains separately. The results demonstrate that strengths-related behavior averaged across all relevant life domains explained unique variance in flourishing above the trait-level of character strengths in some cases, different life domains were characterized by specific profiles of character strength—regarding both their relevance and strength-related behavior. Moreover, character strengths and strengths-related behavior in different life domains both showed substantial correlations with flourishing. In some cases, these associations were domain-specific. In conclusion, we suggest that examining strengths-related behavior across different life domains represents a worthwhile addition to research on character strengths. (shrink)

We present a way of topologizing sets of Galois types over structures in abstract elementary classes with amalgamation. In the elementary case, the topologies thus produced refine the syntactic topologies familiar from first order logic. We exhibit a number of natural correspondences between the model-theoretic properties of classes and their constituent models and the topological properties of the associated spaces. Tameness of Galois types, in particular, emerges as a topological separation principle. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, (...) Weinheim. (shrink)

In this dissertation we explore projective Fraïssé theory and its applications, as well as limitations, to the study of compact metrizable spaces. The goal of projective Fraïssé theory is to approximate spaces via classes of finite structures and glean topological or dynamical properties of a space by relating them to combinatorial features of the associated class of structures. Using the framework of compact metrixable structures, we establish general results which expand and help contextualize previous works in the field. Many (...) proofs in the domain of projective Fraïssé theory are carried out in a context dependent fashion and have thus far eluded clean generalizations. A reason is to be found in the lack of a clear understanding of which spaces are amenable to be studied via projective Fraïssé limits. We give both positive and negative results in this direction. We isolate a combinatorial condition which entails a correspondence between finite structures and regular quasi-partitions of compact metrizable spaces. This correspondence greatly aids the combinatorial-toplogical translation. We apply this machinery to study a class of one-dimensional compact metrizable spaces, which we call smooth fences. To this end, we isolate a class of finite structures—finite partial orders whose Hasse diagram is a forest—whose projective Fraïssé limit approximates a distinctive smooth fence with remarkable properties. We call it the Fraïssé fence and characterize it topologically by carefully exploiting the bridge between the combinatorial and topological worlds. We explore homogeneity and universality features of the Fraïssé fence and the properties of its spaces and endpoints, and provide some results on the dynamics of its group of homeomorphisms. The dissertation is partially based on [1, 2]. (shrink)

The domain of children's social understanding, including understanding of one's own and others’ minds and emotions, has been the topic of much research over the past few decades. Social understandi...

A three-variable biochemical prototype involving two enzymes with autocatalytic regulation proposed by Decroly and Goldbeter (1987) is analyzed using a topological approach. A two-branched manifold, a so-called template, is thus identified. For certain control parameter values, this template is a horseshoe template with a global torsion of two half-turns. This implies that the bifurcation diagram can be described using the usual sequences associated with a unimodal map with a differentiable maximum as well as exemplified by the logistic map. Moreover, (...) a type-I intermittency associated with a saddle-node bifurcation is exhibited. The dynamics from a single time series are also investigated to determine whether it is possible to investigate the dynamics of this biochemical model from the measure of a single concentration. (shrink)

(Open Access.) Quantifiers frequently figure in works of fiction. But occurrences of quantificational expressions within fictions seem no more inevitably to be associated with real domains than uses of names within fictions seem inevitably to be associated with existing referents. The paper outlines some philosophical puzzles resulting from this apparent lack of associated domains, puzzles that are broadly analogous to more familiar ones raised by the apparently nonreferential nature of many fictional names. The paper argues, (...) in the light of an important disanalogy between quantifiers and names, that the quantificational puzzles are substantive, in that they cannot be resolved merely by appealing to the possibility of empty domains. It then argues that, despite the cited parallels between occurrences of quantifiers and names within fictions, promising treatments of fictional names do not always straightforwardly generalise to provide accounts of the quantificational phenomena: the quantificational puzzles are therefore not only substantive but also distinctive. The paper provides further testament to the depth and interest of the problems involving content that are generated by fiction, by identifying a very wide range of previously neglected cases, while also helping to situate within a broader context the notoriously hard philosophical challenges posed by fictional names. (shrink)

Regular musical activity as a complex multimodal lifestyle activity is proposed to be protective against age-related cognitive decline and Alzheimer’s disease. This cross-sectional study investigated the association and interplay between musical instrument playing during life, multi-domain cognitive abilities and brain morphology in older adults from the DZNE-Longitudinal Cognitive Impairment and Dementia Study study. Participants reporting having played a musical instrument across three life periods were compared to controls without a history of musical instrument playing, well-matched for reserve proxies of education, (...) intelligence, socioeconomic status and physical activity. Participants with musical activity outperformed controls in global cognition, working memory, executive functions, language, and visuospatial abilities, with no effects seen for learning and memory. The musically active group had greater gray matter volume in the somatosensory area, but did not differ from controls in higher-order frontal, temporal, or hippocampal volumes. However, the association between gray matter volume in distributed frontal-to-temporal regions and cognitive abilities was enhanced in participants with musical activity compared to controls. We show that playing a musical instrument during life relates to better late-life cognitive abilities and greater brain capacities in OA. Musical activity may serve as a multimodal enrichment strategy that could help preserve cognitive and brain health in late life. Longitudinal and interventional studies are needed to support this notion. (shrink)

Shehtman introduced bimodal logics of the products of Kripke frames, thereby introducing frame products of unimodal logics. Van Benthem, Bezhanishvili, ten Cate and Sarenac generalize this idea to the bimodal logics of the products of topological spaces, thereby introducing topological products of unimodal logics. In particular, they show that the topological product of S4 and S4 is S4 ⊗ S4, i.e., the fusion of S4 and S4: this logic is strictly weaker than the frame product S4 × S4. In this (...) paper, we axiomatize the topological product of S4 and S5, which is strictly between S4 ⊗ S5 and S4 × S5. We also apply our techniques to (1) proving a conjecture of van Benthem et al concerning the logic of products of Alexandrov spaces with arbitrary topological spaces; and (2) solving a problem in quantified modal logic: in particular, it is known that standard quantified S4 without identity, QS4, is complete in Kripke semantics with expanding domains; we show that QS4 is complete not only in topological semantics with constant domains (which was already shown by Rasiowa and Sikorski), but wrt the topological space Q with a constant countable domain. (shrink)

Cross-domain descriptions are descriptions of features pertaining to one domain in terms of vocabulary primarily associated with another domain. Notably, we routinely describe psychological features in terms of the sensory domain and vice versa. Sorrow is said to be ‘bitter’ and fear ‘cold’. Music can be described as ‘happy’, ‘sad’, ‘mournful’, and so on. Such descriptions are rife in both everyday discourse and literary writings. What is it about psychological features that invites descriptions in sensory terms and what is (...) it about the sensory that invites descriptions in terms of the psychological? Drawing on the literature on polysemy, this paper sheds light on cross-domain descriptions pertaining to the sensory and the psychological domains. (shrink)

It is often possible to know what a speaker intends to communicate without knowing what they intend to say. In such cases, speakers need not intend to say anything at all. Stanley and Szabó's influential survey of possible analysis of quantifier domain restriction is, therefore, incomplete and the arguments made by Clapp and Buchanan against Truth Conditional Compositionality and propositional speaker-meaning are flawed. Two theories should not always be viewed as incompatible when they associate the same utterance with different propositions, (...) as there may be many ways to interpret speakers that are compatible with their intentions. (shrink)

To generalize as in [7] the constructions of [2] and [5], let L be a nondegenerate join-semilattice with unit. With A · B = {x ∨ y ∈ L : x ∈ A, y ∈ B} and A⊥ = {y ∈ L : x ∨ y = 1 for all x ∈ A}, the structure , ·,∪, ⊥ , L, ∅) is the algebra of subsets for L. Let R be the maximal ideals of L. Interpreting L as the totality (...) of elementary situations, and 1 ∈ L as the impossible one , the members of R will be called realizations, and R itself – the logical space associated with L. (shrink)

Topological indices are quantitative measurements that describe a molecule’s topology and are quantified from the molecule’s graphical representation. The significance of topological indices is linked to their use in QSPR/QSAR modelling as descriptors. Mathematical associations between a particular molecular or biological activity and one or several biochemical and/or molecular structural features are QSPRs and QSARs. In this paper, we give explicit expressions of two recently defined novel ev-degree- and ve-degree-based topological indices of two classes of benzenoid, namely, linear hexagonal chain (...) and hammer-like benzenoid. (shrink)

A topological index can be focused on uprising of a chemical structure into a real number. The degree-based topological indices have an active place among all topological indices. These topological descriptors intentionally associate certain physicochemical assets of the corresponding chemical compounds. Graph theory plays a very useful role in such type of research directions. The hex-derived networks have vast applications in computer science, physical sciences, and medical science, and these networks are constructed by hexagonal mesh networks. In this paper, we (...) determined the exact values of vertex-edge-degree-based topological descriptors for hex-derived networks HDN 1 p and HDN 2 p, which are generated by the hexagonal network of dimension p. (shrink)

Violence, as a concept, has shaped most of human history and discourse. Over the centuries, the concept has gone through dynamic evolutions and should be understood in relation to diverse agents such as nation, nostalgia, and culture. Modern society’s tendency to impede and constrain overt forms of violence has paved the way for covert forms to exist in socio-cultural spheres. Cultural violence is one such realization where aggression gets exercised covertly through heterogenous mediums such as language, regulations, mass media, and (...) most importantly cultural practices. Its topological structures can be traced in national imagination and a sense of cultural nostalgia originating out of it, that ultimately formulates cultural “otherness.” In Gandhian philosophy, the absence of physical aggression is insignificant, if not complemented with the eradication of violence from the cultural and intellectual strata. Gandhi’s critique of exclusive nationalism and narrowness is reflective of a distinct kind of cultural topology that generates structural violence and with the due course of history it gets legitimacy to exert power over the cultural binary it constructed. The fundamental questions of the paper are associated with assessing the role of national imagination and cultural imperatives in germinating the structures of violence in culture, exclusive nationalism, and Gandhian reconsideration of peace in the context of covert violence in the material and intellectual realms. (shrink)

Wulf Gaertner provides a comprehensive account of an important and complex issue within social choice theory: how to establish a social welfare function while restricting the spectrum of individual preferences in a sensible way. Gaertner's starting point is K. J. Arrow's famous 'Impossibility Theorem', which showed that no welfare function could exist if an unrestricted domain of preferences is to be satisfied together with some other appealing conditions. A number of leading economists have tried to provide avenues out of this (...) 'impossibility' by restricting the variety of preferences: here, Gaertner provides a clear and detailed account, using standardized mathematical notation, of well over forty theorems associated with domain conditions. Domain Conditions in Social Choice Theory will be an essential addition to the library of social choice theory for scholars and their advanced graduate students. (shrink)

Criteria of acceptability for mathematical proofs are field-dependent. In topology, though not in most other domains, it is sometimes acceptable to appeal to visual intuition to support inferential steps. In previous work :829–842, 2014; Lolli, Panza, Venturi From logic to practice, Springer, Berlin, 2015; Larvor Mathematical cultures, Springer, Berlin, 2016) my co-author and I aimed at spelling out how topological proofs work on their own terms, without appealing to formal proofs which might be associated with them. In this (...) article, I address two criticisms that have been raised in Tatton-Brown against our approach: that it leads to a form of relativism according to which validity is equated with social agreement and that it implies an antiformalizability thesis according to which it is not the case that all rigorous mathematical proofs can be formalized. I reject both criticisms and suggest that our previous case studies provide insight into the plausibility of two related but quite different theses. (shrink)

The endomorphism monoid of a model-theoretic structure carries two interesting topologies: on the one hand, the topology of pointwise convergence induced externally by the action of the endomorphisms on the domain via evaluation; on the other hand, the Zariski topology induced within the monoid by (non-)solutions to equations. For all concrete endomorphism monoids of $\omega $ -categorical structures on which the Zariski topology has been analysed thus far, the two topologies were shown to coincide, in turn yielding that the pointwise (...) topology is the coarsest Hausdorff semigroup topology on those endomorphism monoids. We establish two systematic reasons for the two topologies to agree, formulated in terms of the model-complete core of the structure. Further, we give an example of an $\omega $ -categorical structure on whose endomorphism monoid the topology of pointwise convergence and the Zariski topology differ, answering a question of Elliott, Jonušas, Mitchell, Péresse, and Pinsker. (shrink)

The category of Scott-domains gives a computability theory for possibly uncountable topological spaces, via representations. In particular, every separable Banach-space is representable over a separable domain. A large class of topological spaces, including all Banach-spaces, is representable by domains, and in domain theory, there is a well-understood notion of parametrizations over a domain. We explore the link with parameter-dependent collections of spaces in e. g. functional analysis through a case study of "Lp" -spaces. We show that a well-known (...) domain representation of "Lp" as a metric space can be made uniform in the sense of parametrizations of domains. The uniform representations admit lifting of continuous functions and are effective in p. Dependent type constructions apply, and through the study of the sum and product spaces, we clarify the notions of uniformity and uniform computability. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim). (shrink)