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This chapter traces how networks of global connectivity came together in emporia through the changing flows of goods and ideas. With a point of departure in globalization theory, it asks to what extent the economic exchanges between strangers in emporia were able to convey economic, cultural, and political causes and effects between societies and across geographic spaces. Zooming in on the evidence of small finds, along with isotopic and biomolecular data, I show how refined chronologies and high-definition methods have altered the terms of the debate between archaeology and history. With a focus on early contacts between the Islamic world and Northern Europe from the eighth to the eleventh centuries, it demonstrates how the organization of networks could be of critical importance for their ability to link societies across geographical distances and make large worlds ‘small’ and navigable by those who were active in exchange. I propose that the organization of ‘weak ties’ between distantly related people was a key aspect of what made urban networks urban.
A central empirical fact about natural language expressions is that they involve, at some level of mental representation, arrangements of nested constituents that enter into relations of various kinds by virtue of being so arranged. Any natural language theory must specify a subtheory of constituency incorporating a recursive generative procedure. A theory of phrase structure (PS) in the most general sense is a set of hypotheses about how this internal organization of expressions and the dependencies it supports are mentally represented as part of the speaker’s knowledge of language. Hierarchical organization (empirical fact) is formalized in terms of PS (theory), such that properties of the atoms of syntactic computation determine properties of complex expressions constructed from them. Specific implementations of PS theory vary dramatically across the different frameworks that have emerged in the development of Generative Grammar. This vignette focuses on the limits of PS theory. It demarcates, generally, its analytical purview then gives examples of constructions that have resisted a coherent description in PS terms, which suggests that they fall altogether outside its scope.
The Trans-Mexican Volcanic Belt is a biogeographical province, and its eastern sub-province faces intense pressures from land-use and land-cover change (LULCC). This study integrates a systematic conservation planning approach, species distribution models and LULCC projections to identify areas that facilitate the conservation of endemic biodiversity under a dynamic conceptual framework. We selected 13 species of amphibians and mammals as surrogates, obtained their geographical distributions and analysed the distributional patterns of species richness and rarity, which showed significant concentrations in volcanic mountain systems. Historical and future LULCC models indicated a continued expansion of rainfed agriculture, potentially reaching 70% of the study area by 2050, alongside a severe reduction in temperate forest. Currently, 65% of the potential habitat of endemic species and 43% of the potential habitat of geographically rare species are affected. Under pessimistic future scenarios, losses could exceed 95%. Although the priority conservation areas identified are relatively continuous core areas at present, future projections showed considerable fragmentation. We propose a possible dynamic conservation network linking permanent nodes with dynamic nodes and temporary ecological corridors according to ecological, seasonal or anthropogenic pressures. Furthermore, this approach integrates ecological, socioeconomic and governance dimensions to reconcile conservation with sustainable practices in highly transformed landscapes.
We develop a toric topological framework for studying the cohomology of Vietoris–Rips complexes $VR(Q_n;r)$ of hypercube graphs. Using total domination invariants and spectral methods, we establish general lower bounds on connectivity, which lead to infinite families of counterexamples to Shukla’s conjecture, and derive first global upper bounds on coconnectivity. Our approach interprets Vietoris–Rips complexes via Stanley–Reisner rings, moment-angle complexes, and Tor algebras, allowing global topological information to be extracted from combinatorial data. In a second direction, we construct explicit cohomology classes using the Koszul resolution and show that they are decomposable products of $1$-dimensional classes, and that their representatives can be combinatorially realized as the boundary of cross polytopes, positively answering the question posed by Adams and Virk. We introduce ghost vertices as a new tool for detecting, extending, and proving linear independence of cohomology classes.
Abstract: The history of Egypt has always had strong Mediterranean characteristics. Traditionally, however, scholars have neglected or set apart the Mediterranean face of Egyptian society. The aim of this article, therefore, is to illustrate and analyse their entangled historical development. To that end we provide a longue durée overview of the relations between Egypt and the Mediterranean, from the Bronze Age to the Roman period. A history of approximately two millennia has been divided into seven different periods that appear meaningful in terms of the changes that occurred in these mutual relations and influences. Linking with recent debates on the impact of increasing connectivity, or globalization, in the ancient world, our Braudelian overview shows how the ecology of connectivity patterned socio-cultural and political history, throughout this entire period, as a history of joining up.
Hypoxic–ischemic encephalopathy (HIE) is a form of brain damage in infants caused by reduced blood and oxygen supply to the brain, occurring in about 1–3 infants per 1,000 live term births in America and Western Europe. Damage can be mild, moderate, or severe and can cause death or long-term neurological, cognitive, and behavioral disabilities. Worldwide nearly 1 million infants die each year from HIE after perinatal asphyxia. Hypothermia (HT) is the only approved treatment for neonatal HIE in western countries. However, about one third of the infants who receive whole-body or head cooling still have moderate-to-severe impairments in executive, visuospatial, and motor functions, language, and emotional maturity years later. A better understanding of the process of neonatal brain degeneration and the mechanisms of HT neuroprotection and persistence of injury will help to develop additional therapeutics. We explore four key mechanistic aspects of neonatal brain injury to potentially catalyze progress: connectivity or connectomics; proteinopathy; cell death; and the proteasome. In this chapter we discuss these four aspects of neonatal brain injury and their possible interrelations.
As the opening chapter of and introduction to the volume, this chapter serves three main purposes. First, it sets out the conceptual and intellectual background of the book as a whole and outlines the rationale for the core aim, which is to foreground local communities and their practices – locality and agency. Second, it outlines three broad topics that organize the case studies and thus provide an overall structure. Third, it briefly introduces the specific local contexts investigated in each chapter and clarifies how these engage with the overall theme and objective of the volume.
This chapter examines what the designs of coins may tell us about the communities that commissioned them. Religious designs featured predominantly, often the presiding deity of a city or a design which referred to it. Mythology and topography also played an important role, often rooting coinages in their localities, and there were references to events or contemporary personalities. Comparisons can be made in relation to artistic work in other fields, such as gems, with a special reference to those who were involved in their creation – the engravers of the dies from which the coins were struck. The engraving of coin dies appears to have been regarded as an artistic exercise, and the appearance of signatures on coins offers a window onto part of the chaîne opératoire of coin production.
This chapter uses aspects of numismatic evidence (circulation and weight standards) to examine what coinage can tell us about connectivity and regionalism in Archaic Greece. Coinage spread westwards and northwards from its beginnings in around 550, first in the Aegean basin (Aegina and other islands), mainland Greece (Athens, Corinth, Boeotia, Thessaly) and further north (Thrace and Macedonia). By 480 it had been adopted by a wide range of communities, but they represented only a minority of known states. They are characterised by a number of different weight standards – principally the Euboeic, Aeginetan, Corinthian and Attic. Early Athenian coinage consisted of the so-called Wappenmünzen, but these were succeeded in the late sixth century by the famous ‘owls’. However, Aegina was probably the first place in mainland Greece to have made coins, from about 550, and its plentiful coinage circulated widely. Corinthian coinage was also influential. Northern Greece saw several zones of production, while inland tribal communities produced very large coins as a way of exporting the silver from their mines. All these coins circulated together and are found in hoards all over the eastern Mediterranean, having been used in trade and mercenary payments. A link with trireme warfare is also explored.
The explosion of Greek (and Phoenician) settlements around the shores of the Mediterranean and the Black Sea saw many of them adopt their own coinages with a rich iconographic repertoire, often religious in nature or reflecting a local activity such as viticulture. This chapter explores the evidence coinage offers for relationships between colonies and mother-cities, in some cases showing ongoing connections, in others showing the development of new regionalisms. Their coinages appeared quite soon after 550: in the east (Cyrene) and the west (mainly southern Italy, Sicily, but also southern France and Spain), while coinage in some of the cities of the Black Sea appeared early in the fifth century. Sources of silver are explored. Some nearby indigenous communities also made coins, adopting and adapting designs and weight standards.
An $[s,t]$-graph is a graph in which every induced subgraph on s vertices contains at least t edges. Li and Wang [‘Hamilton cycles in $2$-connected $[5,3]$-graphs’, J. Inn. Mong. Norm. Univ. Nat. Sci.35(3) (2006), 285–287] investigated the Hamiltonicity of $[5,3]$-graphs, and more recently, Liu and Liu [‘On the pancyclicity of $2$-connected $[5,3]$-graphs’, Discrete Applied Mathematics389 (2026), 323–334] studied their pancyclicity. In this note, we continue this line of research by studying the Hamiltonian-connectedness of $[5,3]$-graphs.
The author proposes that new attention be paid to spaces hitherto considered marginal, which should be studied for themselves and no longer in negative relation to more developed areas, which they would separate or link by playing the role of buffer zones or transition zones. The interest of the markers proposed, based on the case of the Roman Gauls, is to highlight the diversity of forms of marginality, as well as their relativity.
This chapter gives an overview of several classical topics in the study of graph theory, including perfect matchings, Hamilton cycles, Eulerian trails, proper vertex- and edge-colourings, and connectivity. We begin by proving Hall’s theorem on perfect matchings, Kőnig’s theorem on vertex-covers, and Dirac’s theorem on the minimum degree threshold for a graph to contain a Hamilton cycle. The middle third of the chapter focuses on proper colourings; in particular, we give elegant proofs of Brooks’ theorem on vertex-colourings and Vizing’s theorem on edge-colourings. To finish the chapter, we prove the famous Max-Flow Min-Cut theorem of Ford and Fulkerson, and the fundamental theorems of Menger and Mader on k-connectivity
Over the past few decades, graph theory has developed into one of the central areas of modern mathematics, with close (and growing) connections to areas of pure mathematics such as number theory, probability theory, algebra and geometry, as well as to applied areas such as the theory of networks, machine learning, statistical physics, and biology. It is a young and vibrant area, with several major breakthroughs having occurred in just the past few years. This book offers the reader a gentle introduction to the fundamental concepts and techniques of graph theory, covering classical topics such as matchings, colourings and connectivity, alongside the modern and vibrant areas of extremal graph theory, Ramsey theory, and random graphs. The focus throughout is on beautiful questions, ideas and proofs, and on illustrating simple but powerful techniques, such as the probabilistic method, that should be part of every young mathematician's toolkit.
Volume I offers a broad perspective on urban culture in the ancient European world. It begins with chronological overviews which paint in broad brushstrokes a picture that serves as a frame for the thematic chapters in the rest of the volume. Positioning ancient Europe within its wider context, it touches on Asia and Africa as regions that informed and were later influenced by urban development in Europe, with particular emphasis on the Mediterranean basin. Topics range from formal characteristics (including public space), water provision, waste disposal, urban maintenance, spaces for the dead, and border spaces; to ways of thinking about, visualising, and remembering cities in antiquity; to conflict within and between cities, economics, mobility and globalisation, intersectional urban experiences, slavery, political participation, and religion.
Volume I offers a broad perspective on urban culture in the ancient European world. It begins with chronological overviews which paint in broad brushstrokes a picture that serves as a frame for the thematic chapters in the rest of the volume. Positioning ancient Europe within its wider context, it touches on Asia and Africa as regions that informed and were later influenced by urban development in Europe, with particular emphasis on the Mediterranean basin. Topics range from formal characteristics (including public space), water provision, waste disposal, urban maintenance, spaces for the dead, and border spaces; to ways of thinking about, visualising, and remembering cities in antiquity; to conflict within and between cities, economics, mobility and globalisation, intersectional urban experiences, slavery, political participation, and religion.
The human brain can be divided by both structure and function. Brodmann maps provide a useful way of organising the complex cortical structure based on cytoarchitecture. The basic architecture of the prefrontal cortex shows nothing substantially different to other cortical regions we have a clearer understanding of. However, it remains clear that there must be something anatomically different in the prefrontal cortex for it to be able to carry out such complex functions. Despite vast differences in the functionality of brain regions, topographic connectivity is considered a hallmark feature of cortical structure. However, relatively recent research evidence shows there may be more complexity to the connectivity pattern in the prefrontal cortex when viewed on a fine scale.
Functional magnetic resonance imaging (fMRI) is a noninvasive technique widely used in research to identify and characterize the neural correlates of human cognitive and affective processes. Here we provide a brief introduction to the physical and physiological bases of fMRI, as well as a description of some of the main analysis approaches. These include traditional approaches, such as those based on univariate general linear models, as well as more recent ones, including multivariate methods and connectivity measures. We discuss how these different techniques can be used to answer different, complementary scientific questions, providing some examples to illustrate this. We end with a discussion of some of the key issues, both in terms of experimental design and data acquisition, analysis, and interpretation, that should be considered when planning an fMRI study and that can be of particular interest to those new to the technique.
Social rewards (e.g. smiles) powerfully shape human behavior, starting from early childhood. Yet, the neural architecture that enables differential processing of social and nonsocial rewards remains largely unknown. Few previous studies that directly compared social vs nonsocial stimuli have used stimuli that have low ecological validity or are not matched on low-level stimulus parameters – limiting the scope of inference. To address this gap in knowledge, social and nonsocial reward images taken from the real world were matched on valence, arousal, and key low-level stimulus properties and presented to 37 adults in a functional magnetic resonance imaging (fMRI) study. Individual self-reported preference for social images was associated with the functional connectivity between the left anterior insula (LAI) and medial orbitofrontal cortex (mOFC), as well as that between the left Fusiform Gyrus (LFG) and the Anterior Cingulate Cortex (ACC). Autistic traits negatively modulated LAI – mOFC connectivity and LFG – ACC connectivity. Reduced functional connectivity between these regions may contribute to the lower social reward responsivity in individuals with high autistic traits, as also noted from their lower valence ratings to social rewards. This study provides evidence for a new experimental paradigm to test social reward processing at a behavioral and neural level, which can contribute to potential transdiagnostic biomarkers for social cognitive processes.
Network analysis is a promising approach for elucidating the dynamics of the transition from psychopathology to well-being. Recently, symptom connectivity strength has been proposed as a measure of plasticity – the capacity to change disease severity. Yet, empirical findings remain inconsistent. We propose that this inconsistency can be resolved by recognizing that the interpretation of connectivity strength varies along the recovery process from depression, whether at baseline or during clinical change.
Methods
We analyzed 2,710 depressed patients from the STAR*D dataset, grouped by the magnitude of change in depressive score. Symptom network connectivity was estimated from QIDS-C items at three time points: (i) baseline, (ii) change – defined as when clinical change in depression score occurs, (iii) post-change - corresponding to when the maximum clinical change is achieved.
Results
At baseline, connectivity strength predicts the maximum clinical change, inversely correlating with its magnitude (ρ = −0.95, p = 0.001). At the change time point, connectivity strength parallels clinical change (ρ = 0.92, p = 0.002). A direct and significant association between connectivity strength and depression severity emerges only at the change (ρ = 0.98, p = 0.0003) and post-change (ρ = 0.95, p = 0.001) time points.
Conclusions
The interpretation of connectivity strength for predicting depression trajectories varies by timepoint: at baseline, it measures plasticity -- the capacity for change -- whereas during clinical change, it indicates the magnitude of change in symptom severity. This framework supports the reliability of this prognostic marker for designing personalized therapeutic interventions in psychiatry.