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)

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)

TAD boundaries are genomic elements that separate biological processes in neighboring domains by blocking DNA loops that are formed through Cohesin‐mediated loop extrusion. Most TAD boundaries consist of arrays of binding sites for the CTCF protein, whose interaction with the Cohesin complex blocks loop extrusion. TAD boundaries are not fully impermeable though and allow a limited amount of inter‐TAD loop formation. Based on the reanalysis of Nano‐C data, a multicontact Chromosome Conformation Capture assay, we propose a model whereby (...) clustered CTCF binding sites promote the successive stalling of Cohesin and subsequent dissociation from the chromatin. A fraction of Cohesin nonetheless achieves boundary read‐through. Due to a constant rate of Cohesin dissociation elsewhere in the genome, the maximum length of inter‐TAD loops is restricted though. We speculate that the DNA‐encoded organization of stalling sites regulates TAD boundary permeability and discuss implications for enhancer–promoter loop formation and other genomic processes. (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 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)

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.

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.

Specificities associated with chromosomal linearity are not restricted to telomeres. Here, recent results obtained on fission and budding yeast are summarized and an attempt is made to define subtelomeres using chromatin features extending beyond the heterochromatin emanating from telomeres. Subtelomeres, the chromosome domains adjacent to telomeres, differ from the rest of the genome by their gene content, rapid evolution, and chromatin features that together contribute to organism adaptation. However, current definitions of subtelomeres are generally based on synteny and (...) are largely gene‐centered. Taking into consideration both the peculiar gene content and dynamics as well as the chromatin properties of those domains, it is discussed how chromatin features can contribute to subtelomeric properties and functions, and play a pivotal role in the emergence of subtelomeres. (shrink)

The chromosome passenger complex (CPC) localizes to chromosomes and microtubules, sometimes simultaneously. The CPC also has multiple domains for interacting with chromatin and microtubules. Interactions between the CPC and both the chromatin and microtubules is important for spindle assembly and error correction. Such dual chromatin‐microtubule interactions may increase the concentration of the CPC necessary for efficient kinase activity while also making it responsive to specific conditions or structures in the cell. CPC‐microtubule dependent functions are considered in the context (...) of the first meiotic division. Acentrosomal spindle assembly is a process that depends on transfer of the CPC from the chromosomes to the microtubules. Furthermore, transfer to the microtubules is not only to position the CPC for a later role in cytokinesis; metaphase I error correction and subsequent bi‐orientation of bivalents may depend on microtubule associated CPC interacting with the kinetochores. (shrink)

The human spindle and kinetochore associated complex is required for proper mitotic progression. Extensive studies have demonstrated its important functions in both stable kinetochore-microtubule interactions and spindle checkpoint silencing. We suggest a model to explain how various Ska functions might be fulfilled by distinct pools of Ska at kinetochores. The Ndc80-loop pool of Ska is recruited by the Ndc80 loop, or together with some of its flanking sequences, and the recruitment is also dependent on Cdk1-mediated Ska3 phosphorylation. This pool seems (...) to play a more important role in silencing the spindle checkpoint than stabilizing kinetochore-microtubule interactions. In contrast, the Ndc80-N-terminus pool of Ska is recruited by the N-terminal domains of Ndc80 and appears to be more important for stabilizing kinetochore-microtubule interactions. Here, we review and discuss the evidence that supports this model and suggest further experiments to test the functioning mechanisms of the Ska complex. The human spindle and kinetochore associated complex plays essential functions in proper mitotic progression by promoting stable kinetochore-microtubule interactions and spindle checkpoint silencing. We propose that “distinct pools” of Ska—the Ndc80-loop and Ndc80-N-terminus pools—might fulfill these various functions. (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 (...) class='Hi'>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)

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)

© 2014 Shapiro, Tassone, Choudhary and Simon.Chromosome 22q11.2 Deletion Syndrome is caused by the most common human microdeletion, and it is associated with cognitive impairments across many domains. While impairments in cognitive control have been described in children with 22q11.2DS, the nature and development of these impairments are not clear. Children with 22q11.2DS and typically developing children were tested on four well-validated tasks aimed at measuring specific foundational components of cognitive control: response inhibition, cognitive flexibility, and working memory. (...) Molecular assays were also conducted in order to examine genotype of catechol-O-methyltransferase, a gene located within the deleted region in 22q11.2DS and hypothesized to play a role in cognitive control. Mixed model regression analyses were used to examine group differences, as well as age-related effects on cognitive control component processes in a cross-sectional analysis. Regression models with COMT genotype were also conducted in order to examine potential effects of the different variants of the gene. Response inhibition, cognitive flexibility, and working memory were impaired in children with 22q11.2DS relative to TD children, even after accounting for global intellectual functioning. When compared with TD individuals, children with 22q11.2DS demonstrated atypical age-related patterns of response inhibition and cognitive flexibility. Both groups demonstrated typical age-related associations with working memory. The results of this cross-sectional analysis suggest a specific aberration in the development of systems mediating response inhibition in a sub-set of children with 22q11.2DS. It will be important to follow up with longitudinal analyses to directly examine these developmental trajectories, and correlate neurocognitive variables with clinical and adaptive outcome measures. (shrink)

During the eukaryotic cell cycle, chromosomes undergo large structural transitions and spatial rearrangements that are associated with the major cell functions of genome replication, transcription and chromosome condensation to metaphase chromosomes. Eukaryotic cells have evolved cell cycle dependent processes that modulate histone:DNA interactions in chromosomes. These are; (i) acetylations of lysines; (ii) phosphorylations of serines and threonines and (iii) ubiquitinations of lysines. All of these reversible modifications are contained in the well‐defined very basic N‐ and C‐ terminal domains (...) of histones. Acetylations and phosphorylations markedly affect the charge densities of these domains whereas ubiquitination adds a bulky globular protein, ubiquitin, to lysines in the C‐terminal tails of H2A and H2B. Histone acetylations are strictly associated with genome replication and transcription; histone H1 and H3 phosphorylations correlate with the process of chromosome condensation. The subunits of histone H1 kinase have now been shown to be cyclins and the p34CDC2 kinase product of the cell cycle control gene CDC2. It is probable that all of the processes that control chromosome structure:function relationships are also involved in the control of the cell cycle. (shrink)

The eukaryotic genome is organized into different domains by cis‐acting elements, such as boundaries/insulators and matrix attachment regions, and is packaged with different degrees of condensation. In the M phase, the chromatin becomes further highly condensed into chromosomes. The first step for transcriptional activation of a given gene, at a particular time during development, in any locus, is the opening of its chromatin domain. This locus needs to be kept in this state in each early G1 phase during every (...) cell cycle. Certain distal enhance elements, including locus control regions (LCRs) and enhancers, are believed to perform this target chromatin domain opening process and several models have been proposed to explain distal enhance action. But they did not explain precisely how a given chromatin domain is opened. Based on various studies, we propose a hypothesis for the mechanism of opening chromatin on a large scale. One important mechanism may involved breaking one or two DNA strands and reducing the linking numbers within chromatin domain. The topological changes can overpass some complexes formed on DNA strands and can be transmitted from specific localized points over a broad region, until boundary elements or insulators are reached. These may initiate downstream events such as propagation of histone acetylation and the binding of transcription factors to proximal promoters and may further augment the action mediated by distal enhancer elements. BioEssays 25:507–514, 2003. © 2003 Wiley Periodicals, Inc. (shrink)

t is now well accepted that defined architectural compartments within the cell nucleus can regulate the transcriptional activity of chromosomal domains within their vicinity. However, it is generally unclear how these compartments are formed. The nuclear periphery has received a great deal of attention as a repressive compartment that is implicated in many cellular functions during development and disease. The inner nuclear membrane, the nuclear lamina, and associated proteins compose the nuclear periphery and together they interact with proximal chromatin (...) creating a repressive environment. A new study by Harr et al. identifies specific protein–DNA interactions and epigenetic states necessary to re‐position chromatin to the nuclear periphery in a cell‐type specific manner. Here, we review concepts in gene positioning within the nucleus and current accepted models of dynamic gene repositioning within the nucleus during differentiation. This study highlights that myriad pathways lead to nuclear organization. (shrink)

Topologically associating domain (TAD) boundaries are the flanking edges of TADs, also known as insulated neighborhoods, within the 3D structure of genomes. A prominent feature of TAD boundaries in mammalian genomes is the enrichment of clustered CTCF sites often with mixed orientations, which can either block or facilitate enhancer–promoter (E‐P) interactions within or across distinct TADs, respectively. We will discuss recent progress in the understanding of fundamental organizing principles of the clustered CTCF insulator codes at TAD boundaries. Specifically, (...) both inward‐ and outward‐oriented CTCF sites function as topological chromatin insulators by asymmetrically blocking improper TAD‐boundary‐crossing cohesin loop extrusion. In addition, boundary stacking and enhancer clustering facilitate long‐distance E‐P interactions across multiple TADs. Finally, we provide a unified mechanism for RNA‐mediated TAD boundary function via R‐loop formation for both insulation and facilitation. This mechanism of TAD boundary formation and insulation has interesting implications not only on how the 3D genome folds in the Euclidean nuclear space but also on how the specificity of E‐P interactions is developmentally regulated. (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)

The information contained within the linear sequence of bases (the genome) must be faithfully replicated in each cell cycle, with a balance of constancy and variation taking place over the course of evolution. Recently, it has become clear that additional information important for genetic regulation is contained within the chromatin proteins associated with DNA (the epigenome). Epigenetic information also must be faithfully duplicated in each cell cycle, with a balance of constancy and variation taking place during the course of development (...) to achieve differentiation while maintaining identity within cell lineages. Both the genome and the epigenome are synthesized at the replication fork, so the events occurring during S‐phase provide a critical window of opportunity for eliciting change or maintaining existing genetic states. Cells discriminate between different states of chromatin through the activities of proteins that selectively modify the structure of chromatin. Several recent studies report the localization of certain chromatin modifying proteins to replication forks at specific times during S‐phase. Since transcriptionally active and inactive chromosome domains generally replicate at different times during S‐phase, this spatiotemporal regulation of chromatin assembly proteins may be an integral part of epigenetic inheritance. BioEssays 25:647–656, 2003. © 2003 Wiley Periodicals, Inc. (shrink)

Chromosome transmission in S. cerevisiae requires the activities of many structural and regulatory proteins required for the replication, repair, recombination and segregation of chromosomal DNA, and co‐ordination of the chromosome cycle with progression through the cell cycle. An important structural domain on each chromosome is the kinetochore (centromere DNA and associated proteins), which provides the site of attachment of chromosomes to the spindle microtubules. Stoler et al.(1) have recently reported the cloning of an essential gene CSE4, mutations (...) in which cause chromosome nondisjunction of a marked chromosome bearing a centromere DNA mutation. The cse4–1 mutation causes cells to arrest in the G2/M phase of the cell cycle with a 2N DNA content in a RAD9 checkpoint‐independent manner. The carboxyl terminus of Cse4p and the human centromere‐localized protein CENP‐A have a high degree of homology to the C‐terminal domain of histone H3. Since both CENP‐A and Cse4p also have biochemical properties similar to histones H3 and H4, it is tempting to speculate that these histone H3‐like proteins are components of specialized nucleosomes, a class of which may be unique to the centromeres. (shrink)

The ring‐shaped ATPase machine, cohesin, regulates sister chromatid cohesion, transcription, and DNA repair by topologically entrapping DNA. Here, we propose a rigid scaffold model to explain how the cohesin regulators Pds5 and Wapl release cohesin from chromosomes. Recent studies have established the Smc3‐Scc1 interface as the DNA exit gate of cohesin, revealed a requirement for ATP hydrolysis in ring opening, suggested regulation of the cohesin ATPase activity by DNA and Smc3 acetylation, and provided insights into how Pds5 and Wapl (...) open this exit gate. We hypothesize that Pds5, Wapl, and SA1/2 form a rigid scaffold that docks on Scc1 and anchors the N‐terminal domain of Scc1 (Scc1N) to the Smc1 ATPase head. Relative movements between the Smc1‐3 ATPase heads driven by ATP and Wapl disrupt the Smc3‐Scc1 interface. Pds5 binds the dissociated Scc1N and prolongs this open state of cohesin, releasing DNA. We review the evidence supporting this model and suggest experiments that can further test its key principles. (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)

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.

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)

We explore the following two cognitive questions regarding crosslinguistic variation in lexical semantic systems: Why are some linguistic categories—that is, the associations between a term and a portion of the semantic space—harder to learn than others? How does learning a language‐specific set of lexical categories affect processing in that semantic domain? Using a computational word‐learner, and the domain of color as a testbed, we investigate these questions by modeling both child acquisition of color terms and adult behavior on a non‐verbal (...) color discrimination task. A further goal is to test an approach to lexical semantic representation based on the principle that the more languages label any two situations with the same word, the more conceptually similar those two situations are. We compare such a crosslinguistically based semantic space to one based on perceptual similarity. Our computational model suggests a mechanistic explanation for the interplay between term frequency and the semantic closeness of learned categories in developmental error patterns for color terms. Our model also indicates how linguistic relativity effects could arise from an acquisition mechanism that yields language‐specific topologies for the same semantic domain. Moreover, we find that the crosslinguistically inspired semantic space supports these results at least as well as—and in some aspects better than—the purely perceptual one, thus confirming our approach as a practical and principled method for lexical semantic representation in cognitive modeling. (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)

SummaryMis‐regulation (e.g. overproduction) of the human Ndc80/Hec1 outer kinetochore protein has been associated with aneuploidy and tumourigenesis, but the genetic basis and underlying mechanisms of this phenomenon remain poorly understood. Recent studies have identified the ubiquitous Ndc80 internal loop as a protein‐protein interaction platform. Binding partners include the Ska complex, the replication licensing factor Cdt1, the Dam1 complex, TACC‐TOG microtubule‐associated proteins (MAPs) and kinesin motors. We review the field and propose that the overproduction of Ndc80 may unfavourably absorb these interactors (...) through the internal loop domain and lead to a change in the equilibrium of MAPs and motors in the cells. This sequestration will disrupt microtubule dynamics and the proper segregation of chromosomes in mitosis, leading to aneuploid formation. Further investigation of Ndc80 internal loop‐MAPs interactions will bring new insights into their roles in kinetochore‐microtubule attachment and tumourigenesis. (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)

The relationship between kinetochores and nuclear pore complexes (NPCs) is intimate but poorly understood. Several NPC components and associated proteins are relocated to mitotic kinetochores to assist in different activities that ensure faithful chromosome segregation. Such is the case of the Mad1‐c‐Mad2 complex, the catalytic core of the spindle assembly checkpoint (SAC), a surveillance pathway that delays anaphase until all kinetochores are attached to spindle microtubules. Mad1‐c‐Mad2 is recruited to discrete domains of unattached kinetochores from where it promotes (...) the rate‐limiting step in the assembly of anaphase‐inhibitory complexes. SAC proficiency further requires Mad1‐c‐Mad2 to be anchored at NPCs during interphase. However, the mechanistic relevance of this arrangement for SAC function remains ill‐defined. Recent studies uncover the molecular underpinnings that coordinate the release of Mad1‐c‐Mad2 from NPCs with its prompt recruitment to kinetochores. Here, current knowledge on Mad1‐c‐Mad2 function and spatiotemporal regulation is reviewed and the critical questions that remain unanswered are highlighted. (shrink)

This paper is concerned with certain ontological issues in the foundations of geographic representation. It sets out what these basic issues are, describes the tools needed to deal with them, and draws some implications for a general theory of spatial representation. Our approach has ramifications in the domains of mereology, topology, and the theory of location, and the question of the interaction of these three domains within a unified spatial representation theory is addressed. In the final part we (...) also consider the idea of non-standard geographies, which may be associated with geography under a classical conception in the same sense in which non-standard logics are associated with classical logic. (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)

We shall address from a conceptual perspective the duality between algebra and geometry in the framework of the refoundation of algebraic geometry associated to Grothendieck’s theory of schemes. To do so, we shall revisit scheme theory from the standpoint provided by the problem of recovering a mathematical structure A from its representations \ into other similar structures B. This vantage point will allow us to analyze the relationship between the algebra-geometry duality and the structure-semiotics duality. Whereas in classical algebraic geometry (...) a certain kind of rings can be recovered by considering their representations with respect to a unique codomain B, Grothendieck’s theory of schemes permits to reconstruct general rings by considering representations with respect to a category of codomains. The strategy to reconstruct the object from its representations remains the same in both frameworks: the elements of the ring A can be realized—by means of what we shall generally call Gelfand transform—as quantities on a topological space that parameterizes the relevant representations of A. As we shall argue, important dualities in different areas of mathematics can be understood as particular cases of this general pattern. In the wake of Majid’s analysis of the Pontryagin duality, we shall propose a Kantian-oriented interpretation of this pattern. We shall use this conceptual framework to argue that Grothendieck’s notion of functor of points can be understood as a “relativization of the a priori” that generalizes the relativization already conveyed by the notion of domain extension to more general variations of the corresponding domains. (shrink)

It has been argued within some philosophy of quantum gravity circles that endorsing Lewisian modal metaphysics is incompatible with endorsing the fundamental physical ontology of any quantum gravity theory. Speaking concisely, the unsolvable tension would be between Lewis' metaphysical commitment to the fundamentality of space and time, and the physical lesson of quantum gravity about the disappearance of space and time from the fundamental structure of the world. In this essay I argue against the idea that the tension is unsolvable. (...) The analysis does not apply to quantum gravity in general, but only to the specific perspective delivered by quantum string theory. In the first two sections I describe what I think is the general formal payoff of Lewisian possible worlds semantics, and more importantly the general metaphysical payoff generated by some Lewisian metaphysical applications of that formal framework. Lewisian possible worlds semantics is not among the topics of this essay, still a concise presentation of its basic features is required for a more accurate description of the type of modal metaphysics Lewis delivers by applying that formal machinery. The moral of the story in the first two sections is that an attempt of preserving crucial features of Lewisian modal metaphysics, although endorsing the quantum string theory lesson on spacetime non fundamentality, would be not only possible, but also philosophically worthy in a general sense. Then, section three is divided in three parts. In the first part I summarize some formal tools of the methodology used elsewhere - (Vistarini, Routledge, 2019, chapter 6)- to argue for string theory background independence. More precisely, I briefly re-describe some crucial features of a topological-vector bundle structure there defined on a "space" associated to the theory. Such structure is there shown to carry physical and dynamical information about quantum strings systems supporting the thesis of background independence of quantum strings laws (string theory background independence is not a topic of this essay, and the construction of the full formal structure as well as the full argumentative line can be found in the work cited above). The rationale behind the choice of including these formal tools is explained in the second and third parts of section three: that very same topological-fiber bundle structure associated to string theory, if read differently, is shown to also carry structural properties of the Lewisian metaphysical scheme. More precisely, in the second part of section three I attempt to show that such topological-fiber bundle structure owns a topology which qualifies as a plausible accessibility structure extending the Lewisian similarity accessibility. To avoid confusion, I will denote the extended similarity order with S*, or S*-similarity. The latter has some interesting properties. It is quantitatively describable, and even more interestingly its spectrum of variation is a countable one. Then, insofar Lewisian similarity order can be regained from the S*-similarity, one might say that the latter is a metaphysical accessibility relation underlying the former because "more fundamental". As we will see, the explanation of what "more fundamental" means in this metaphysical context mainly involves the idea that the formal nature of S*-similarity, in particular its property of having a countable spectrum of variation, calibrates a metaphysical similarity that reflects the discreteness of the fundamental quantum nature of reality. The extended modal metaphysics with accessibility structure S*-similarity is informed by quantum string physics. Within the extended scheme, the Lewisian claim "things could have been different in countless ways" (Lewis 1973) is an approximate one because only permitted by ordinary language. As soon as one refines the accessibility structure by using the formal language of quantum string theory, it appears things could have been different in countable ways. But the Lewisian variety of alternative states of affairs can be regained from the underlying countable variety via a specific interpretation of the Humean supervenience thesis, one that changes the metaphysical status of the thesis' content and restricts the thesis' domain of application. Finally, in the third part of section three I attempt to show that the same topological-fiber bundle structure used to extend Lewisian similarity has a bundle component producing the formal scheme for a tentative extension of Lewisian nomological accessibility through the lens of string dualities. This will prove to be a non trivial task, and the Lewisian accessibility structure will be regained from the extended one only partially. Finally, the essay contains two short appendices summarizing two argumentative lines outside the main topic of the essay. They briefly describe different ways in which the non fundamentality of spatiotemporal structures can be found in quantum string theory. These sections can be skipped. Nevertheless, they might contribute to understand more robustly the general view endorsed by this essay, i.e. that there isn't any unsolvable tension between Lewis' commitment to the fundamentality of spatiotemporal relations and quantum gravity's lesson about their non fundamentality. -/- . (shrink)

In this thesis, we study the complexity of some mathematical problems: in particular, those arising in computable analysis and algorithmic learning theory for algebraic structures. Our study is not limited to these two areas: indeed, in both cases, the results we obtain are tightly connected to ideas and tools coming from different areas of mathematical logic, including for example descriptive set theory and reverse mathematics.After giving the necessary preliminaries, we first study the uniform computational strength of the Cantor–Bendixson theorem in (...) the Weihrauch lattice. This work falls into the program connecting reverse mathematics and computable analysis via the framework of Weihrauch reducibility. We concentrate on problems related to perfect subsets of Polish spaces, studying the perfect set theorem, the Cantor–Bendixson theorem, and various problems arising from them. As far as we know, this is the first systematic study of problems at the level of $\mathbf {\Pi }^1_1\mathsf {-CA}_0$ in the Weihrauch lattice. We show that the strength of some of the problems we study depends on the topological properties of the Polish space under consideration, while others have the same strength once the space is rich enough.We continue considering problems related to (induced) subgraphs. We provide results on the (effective) Wadge complexity of sets of graphs, that are also used to determine the Weihrauch degree of certain decision problems. The decision problems we consider are defined for a fixed graph G, and they take as input a graph H, answering whether G is an (induced) subgraph of H: we also consider the opposite problem (i.e., answering whether H is an induced subgraph of G). We conclude this part on (induced) subgraphs considering the Weihrauch degree of “search problems.”These problems are defined for a fixed graph G, and they take as input a graph H such that G is an (induced) subgraph H: the output is a copy of G in H. In both cases, we highlight differences and analogies between the subgraph and the induced subgraph relation.We then move our attention to algorithmic learning theory, and we present the framework we use to study the learnability of families of algebraic structures: here, given a countable family of pairwise nonisomorphic structures $\mathfrak {K}$, a learner receives larger and larger pieces of an arbitrary copy of a structure in $\mathfrak {K}$ and, at each stage, is required to output a conjecture about the isomorphism type of such a structure. We say that $\mathfrak {K}$ is learnable if there exists a learner which eventually stabilizes to a correct guess. The framework was lacking a method for comparing the complexity of nonlearnable families, and so we propose a solution to this problem using tools coming from invariant descriptive set theory. To do so, we first prove that a family of structures is learnable if and only if its learning domain is continuously reducible to the relation $E_0$ of eventual agreement on infinite binary sequences and then, replacing $E_0$ with Borel equivalence relations of higher complexity, we obtain a new hierarchy of learning problems. This leads to the notion of E-learnability, where a family of structures $\mathfrak {K}$ is E-learnable, for a Borel equivalence relation E, if there is a continuous reduction from the isomorphism relation associated with $\mathfrak {K}$ to E. It is then natural to ask how the notion of E-learnability interacts with “classical” learning paradigms.Finally, we study the number of mind changes that a learner needs to learn a given family, both from a topological and a combinatorial point of view, and we consider how the complexity of a learner (in terms of Turing reducibility) affects the number of mind changes for learning a given family.Abstract prepared by Vittorio Cipriani.E-mail: vittorio.cipriani17@gmail.com.URL: https://air.uniud.it/handle/11390/1252226. (shrink)

The method of Quasi-Analysis used by Carnap in his program of theconstitution of concepts from finite observations has the following twogoals: (1) Given unsharp observations in terms of similarity relations thetrue properties of the observed objects shall be obtained by a suitablelogical construction. (2) From a single relation on a finite domain,different dimensions of qualities shall be reconstructed and identified. Inthis article I show that with a slight modification Quasi-Analysis iscapable of fulfilling the first goal for a single observable dimension. (...) Weobtain a partition of the so-called Quality Classes representing thepairwise disjoint and exhaustive extensions associated to the ``values'''' ofthe observable. On the other hand, an example demonstrates that the methodfails, as Goodman has pointed out, for a relation expressing similarity withregard to at least one out of many properties.Since it seems to be impossible in general to reconstruct more-dimensionalqualities from a single similarity relation, the constitution of at least asmany similarity relations as there are qualities have to be presumed. Thenit is possible to state adequate sufficient conditions for the dimension ofthe observable space, even if some of the similarity relations might dependon others. The concept of topological dimension cannot be used for thispurpose on finite sets of observations. We replace it by a set-algebraicalcondition on the Quality Classes. (shrink)

Gene transcription in eukaryotes is associated with conformational changes of a large area of chromatin adjacent to a gene. This rearrangement may involve the whole loop (topological domain) to which a given gene belongs.Regulatory events associated with activation or inactivation of transcription are found to act through relatively short nucleotide sequences, often located several thousand base pairs apart from gene. These sequences, termed enhancers may act independently on their distance from or orientation with respect to the gene.Both long‐range conformational rearrangements (...) of chromatin and any long distance effects of enhancers may be associated with elastic torsional strain in DNA, arising in transcriptionally active chromatin loops. Enhancer effects, in particular, may be associated with conformational transitions in DNA competing for the energy deposited in the elastic spring of the DNA. (shrink)

The great mathematician, physicist, and philosopher, Hermann Weyl, once called mathematics the “science of the infinite.” This is a fitting title: contemporary mathematics—especially Cantorian set theory—provides us with marvelous ways of taming and clarifying the infinite. Nonetheless, I believe that the epistemic significance of mathematical infinity remains poorly understood. This dissertation investigates the role of the infinite in three diverse areas of study: number theory, cosmology, and probability theory. A discovery that emerges from my work is that the epistemic role (...) of the infinite varies, often in surprising ways, across different domains of knowledge. -/- My first chapter examines the role of mathematical infinity in number theory. It is reasonable to think that theorems concerning finite patterns and structures in the natural numbers are particularly “simple” or “elementary.” Indeed, such statements are comprehensible to a wide range of investigators, regardless of their mathematical training. One might then expect proofs of these theorems to be similarly comprehensible. However, many proofs, especially those that utilize only finitary methods, are exceedingly difficult to understand. Consequently, one finds that finitary theorems are often re-proved using infinitary techniques. My claim is that this is because infinitary proofs are often explanatory, while finitary proofs are not. This chapter analyzes why this is the case. Along the way, I investigate other questions of long-standing interest in the philosophy of mathematics, e.g., the role of purity/impurity ascriptions and the nature of the content of a theorem. In particular, I diagnose the explanatory potential of the infinite by articulating a new construal of content. This new construal both saves intuitive epistemic ascriptions made in mathematical practice and explains the unexpected role of the infinite in providing explanatory proofs of finitary statements. Thus, in number theory, my claim is that the infinite often plays an explanatory role. -/- My second chapter turns to the role of the infinite in cosmology. It investigates a question much discussed by philosophers and physicists alike: is the spatial extent of the universe finite or infinite? Contemporary cosmological research has indicated that one of the essential determinants of the extent of the universe is the topology we ascribe to space. Topology is a global property, which may suggest that it is not testable through local observation. Nonetheless, some cosmologists have indicated that it may be empirically detected, thereby providing an answer to the question of spatial extent. I argue that, in fact, the epistemic status of the topology of space is extremely subtle and not well captured by any of the categories commonly employed by philosophers of science. In particular, I argue that topological properties are neither empirical nor a priori (even in suitably weakened senses). Furthermore, I claim that we should prefer topological properties that generate finite universe models (consistent with our best data) in order to avoid extremely thorny issues concerning the physics of an infinite universe. I argue for such a preference on the grounds of the simplicity and explanatory power of finite universe models. Thus, in cosmology, my claim is that the finite often plays an explanatory and simplifying role. -/- My third chapter investigates several paradoxes that arise in the foundations of infinitary probability theory: the Label Invariance Paradox, God’s Lottery, and Bertrand’s Paradox. I argue that these have been poorly understood because they do not expressly concern probability theory, but rather our intuitions about—and formal techniques for dealing with— infinite sets. The paradoxes in question are, in fact, symptoms of our complete reliance upon Cantorian cardinality and its associated criterion of sameness of “size.” That is, two sets have the same cardinality if and only if the elements of the sets can be placed in 1-1 correspondence. When applied to infinite sets, this criterion produces counterintuitive verdicts. For instance, given a fair lottery on the natural numbers, we expect that the probability of drawing an even number is 1/2, and likewise for drawing an odd number. However, one can construct “relabellings” of the naturals such that the probability of drawing an even number remains 1/2, while the probability for drawing an odd number becomes 1/4. I argue that, ultimately, it is the coarseness of Cantorian cardinality that generates the probabilistic paradoxes. I then propose that finer-grained measures of infinite sets from mathematical logic and number theory can help to dissolve the paradoxes in question. Thus, in probability theory, we find that particular kinds of infinitary techniques effectively systematize our theory, while others lead to paradox. (shrink)

Data Transfer Service (DTS) is an open-source project that is developing a document-centric message model for describing a bulk data transfer activity, with an accompanying set of loosely coupled and platform-independent components for brokering the transfer of data between a wide range of (potentially incompatible) storage resources as scheduled, fault-tolerant batch jobs. The architecture scales from small embedded deployments on a single computer to large distributed deployments through an expandable ‘worker-node pool’ controlled through message-orientated middleware. Data access and transfer efficiency (...) are maximized through the strategic placement of worker nodes at or between particular data sources/sinks. The design is inherently asynchronous, and, when third-party transfer is not available, it side-steps the bandwidth, concurrency and scalability limitations associated with buffering bytes directly through intermediary client applications. It aims to address geographical–topological deployment concerns by allowing service hosting to be either centralized (as part of a shared service) or confined to a single institution or domain. Established design patterns and open-source components are coupled with a proposal for a document-centric and open-standards-based messaging protocol. As part of the development of the message protocol, a bulk data copy activity document is proposed for the first time. (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)

The Y chromosome in the XY sex-determination system is often shorter than its X counterpart, a condition attributed to degeneration after Y recombination ceases. Contrary to the traditional view of continuous, gradual degeneration, our study reveals stabilization within large mating populations. In these populations, we demonstrate that both mutant and active alleles on the Y chromosome can reach equilibrium through a mutation-selection balance. However, the emergence of a new species, particularly through the founder effect, can disrupt this equilibrium. (...) Specifically, if the male founders of a new species carry only a mutant allele for a particular Y-linked gene, this allele becomes fixed, leading to the loss of the corresponding active gene on the Y chromosome. Our findings suggest that the rate of Y-chromosome degeneration may be linked to the frequency of speciation events associated with single-male founder events. (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)

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].

Extraordinary extended lampbrush chromosomes with thousands of transcription loops are favorable objects in chromosome biology. Chromosomes become lampbrushy due to unusually high rate of transcription during oogenesis. However, until recently, the information on the spectrum of transcribed sequences as well as genomic context of individual chromomeres was mainly limited to tandemly repetitive elements. Here we briefly outline novel findings and future directions in lampbrush chromosome studies in the post‐genomic era. We emphasize the fruitfulness of combining genome‐wide approaches with (...) microscopy imaging techniques using lampbrush chromosomes as a remarkable model object. We believe that new data on the spectrum of sequences transcribed on the lateral loops of lampbrush chromosomes and their structural organization push the boundaries in the discussion of their biological role. Also see the video abstract here: https://youtu.be/zexoHfzX9rM. (shrink)