Let $\mathbf{G}=\{G_1,\dots,G_{s}\}$ be a collection of $s$ bipartite graphs with the same bipartition $V=(X,Y)$. For a path $P$ with $V(P)=V$ and $|E(P)|=s$, if there exists an injection $φ$: $E(P)\rightarrow [s]$ such that $e\in E(G_{φ(e)})$ for each $e\in E(P)$, then we say that the Hamiltonian path $P$ is a $\mathbf{G}$-transversal. A bipartite graph collection $\mathbf{G}$ is called Hamiltonian connected if for any two vertices $x\in X$ and $y\in Y$, there exists a $\mathbf{G}$-transversal isomorphic to a Hamiltonian path between $x$ and $y$. In this paper, we give the minimum degree conditions that ensure the existence of a $\mathbf{G}$-transversal isomorphic to a Hamiltonian path and the Hamiltonian connectivity of a balanced bipartite graph collection $\mathbf{G}$, which improve the results of [Hu, Li, Li and Xu, Discrete Math., 2024]. Moreover, we also provide a minimum degree condition that guarantees a nearly balanced bipartite graph collection $\mathbf{G}$ contains a $\mathbf{G}$-transversal isomorphic to a Hamiltonian path.
Derek G. Corneil, Feodor F. Dragan, Ekkehard Köhler
et al.
In this paper we present various lower bound results on collective tree spanners and on spanners of bounded treewidth. A graph $G$ is said to admit a system of $μ$ collective additive tree $c$-spanners if there is a system $\cal{T}$$(G)$ of at most $μ$ spanning trees of $G$ such that for any two vertices $u,v$ of $G$ a tree $T\in \cal{T}$$(G)$ exists such that the distance in $T$ between $u$ and $v$ is at most $c$ plus their distance in $G$. A graph $G$ is said to admit an additive $k$-treewidth $c$-spanner if there is a spanning subgraph $H$ of $G$ with treewidth $k$ such that for any pair of vertices $u$ and $v$ their distance in $H$ is at most $c$ plus their distance in $G$. Among other results, we show that: $\bullet$ Any system of collective additive tree $1$ -- spanners must have $Ω(\sqrt[3]{\log n})$ spanning trees for some unit interval graphs; $\bullet$ No system of a constant number of collective additive tree $2$-spanners can exist for strongly chordal graphs; $\bullet$ No system of a constant number of collective additive tree $3$-spanners can exist for chordal graphs; $\bullet$ No system of a constant number of collective additive tree $c$-spanners can exist for weakly chordal graphs as well as for outerplanar graphs for any constant $c\geq 0$; $\bullet$ For any constants $k \ge 2$ and $c \ge 1$ there are graphs of treewidth $k$ such that no spanning subgraph of treewidth $k-1$ can be an additive $c$-spanner of such a graph. All these lower bound results apply also to general graphs. Furthermore, they %results complement known upper bound results with tight lower bound results.
We study model theoretic characterizations of various collection schemes over $\mathbf{PA}^-$ from the viewpoint of Gaifman's splitting theorem. Among other things, we prove that for any $n \geq 0$ and $M \models \mathbf{PA}^-$, the following are equivalent: 1. $M$ satisfies the collection scheme for $Σ_{n+1}$ formulas. 2. For any $K, N \models \mathbf{PA}^-$, if $M \subseteq_{\mathrm{cof}} K$, $M \prec_{Δ_0} K$ and $M \prec N$, then $M \prec_{Σ_{n+2}} K$ and $\sup_N(M) \prec_{Σ_n} N$. 3. For any $N \models \mathbf{PA}^-$, if $M \prec N$, then $M \prec_{Σ_{n+2}} \sup_N(M) \prec_{Σ_{n}} N$. Here, $\sup_N(M)$ is the unique $K$ satisfying $M \subseteq_{\mathrm{cof}} K \subseteq_{\mathrm{end}} N$. We also investigate strong collection schemes and parameter-free collection schemes from the similar perspective.
Nikolos Gurney, Fred Morstatter, David V. Pynadath
et al.
We explore the use of aggregative crowdsourced forecasting (ACF) as a mechanism to help operationalize ``collective intelligence'' of human-machine teams for coordinated actions. We adopt the definition for Collective Intelligence as: ``A property of groups that emerges from synergies among data-information-knowledge, software-hardware, and individuals (those with new insights as well as recognized authorities) that enables just-in-time knowledge for better decisions than these three elements acting alone.'' Collective Intelligence emerges from new ways of connecting humans and AI to enable decision-advantage, in part by creating and leveraging additional sources of information that might otherwise not be included. Aggregative crowdsourced forecasting (ACF) is a recent key advancement towards Collective Intelligence wherein predictions (X\% probability that Y will happen) and rationales (why I believe it is this probability that X will happen) are elicited independently from a diverse crowd, aggregated, and then used to inform higher-level decision-making. This research asks whether ACF, as a key way to enable Operational Collective Intelligence, could be brought to bear on operational scenarios (i.e., sequences of events with defined agents, components, and interactions) and decision-making, and considers whether such a capability could provide novel operational capabilities to enable new forms of decision-advantage.
The youngest daughter of one of the northwest of England’s largest cotton magnates, Annie Barlow, was a well-educated and passionate woman. At the time of studying English Literature and History in London in 1880 to 1882 she became involved with the newly formed Egypt Exploration Fund, and at just nineteen years old became one of the first, and youngest, Honorary Local Secretaries for Bolton and the surrounding area—a roll she held for almost sixty years up to her death in 1941. The social circles opened to her by her father and brothers included world business leaders, academics and royalty. Through lectures, exhibitions and many cups of tea, Annie proclaimed the work of the fund across the United Kingdom, while modestly keeping her own efforts unannounced. Her fundraising surpassed that of many other local secretaries and led to the amassing of the largest collection of Egyptology in a local authority museum in the UK at Bolton Museum. Her travels took her far and wide, and she too built a sizeable collection of antiquities. Her passion for history, driven by a desire for educational development and religious devotion, was transmitted to those whom she met. It was through her influence and intimate knowledge of textile production that Bolton and its first curators became a renowned center for textile analysis, with excavators sending material to Bolton to aid their interpretations. During the First World War, Annie and her family homed European refugees. Her support for one girl in particular, Raymonde Frin, became a life-long friendship. Growing up under the wing of Annie, and surrounded by private collections of ancient material, Raymonde developed a passion for archaeology. Annie’s financial legacy directly supported the development of Raymonde’s life. Eventually achieving formal archaeological qualifications, she went on to be an integral part of the newly formed UNESCO museums and monuments division, becoming its first editor for Museums International Magazine, and involved in projects to save Egyptian heritage. This paper will look at the two women, Annie and Raymonde, within the context of women collecting and museum work, and their legacy for collections, in particular Egyptology, to the current day.
Macarena Cuenca-Amigo, Eloísa Pérez Santos, María Jesús Monteagudo
Over the last 20 years, there has been a growing interest in the analysis of museum experiences. Different authors have approached this subject from various perspectives, but only a few have focused on the idea of satisfactory experiences. This study sheds light on this field of knowledge, exploring the factors involved in satisfactory museum experiences. It clarifies how subjective factors (experience dimensions) and the museum environment (contextual components) are related and play a role in shaping those visitor experiences. For this purpose, a quantitative methodology was selected. In 2019 a questionnaire was administered to a sample of 685 visitors to 16 Spanish museums, which confirmed that their museum experience was the result of their interaction with the museum, its characteristics, and its contents. The visitor experience was satisfactory when their interaction had an impact on some dimensions of their experience. This varied according to each visitor's profile and what they valued most. The results showed that, despite the subjective nature of the experience, museums play an essential role as facilitators of satisfactory experiences. They can modulate the role played by the various components of the museum context in their visits, depending on the profiles of their visitors and their orientation toward one type of experience or another.
In this article, I consider the Khanenko Museum as noble and double-wounded, a concept that emerges from two trains of thought. The first pertains to the attack on Kyiv on 10 October 2022, which destroyed the Khanenko Museum, famous for owning the largest collection of global art in Ukraine. The second stream of thought is related to theories of wounding as a specific condition, an aesthetic mode, a way of experiencing time and space. These theories allow us to conceive of the grief and pain caused by destruction, but not necessarily to surmount it.
We consider the relevance of a collective field theory description for the AdS/CFT correspondence. Collective field theory performs a systematic reorganization of the degrees of freedom of a (non-gravitational) field theory, replacing the original loop expansion parameter $\hbar$ with $1/N$. Collective fields are over complete signalling a redundancy inherent in the theory. We propose that this over completeness is the mechanism by which one arrives at a holographic description, to be identified with the gravity dual. We find evidence for this by studying the redundancy of the collective field theory, showing that degrees of freedom in the bulk can be expressed as a linear combination of degrees of freedom contained in an arbitrarily small neighbourhood of the boundary.
A total of 47 species belonging to 46 genera, 34 subfamilies, 23 families and 7 orders of predator and parasitoid insects were collected and identified. The survey was conducted throughout the program held by the General Directorate of Agriculture-Duhok, in cooperating with the College of Agricultural Engineering Sciences in Duhok Province, Kurdistan Region, Iraq from May 2013 to April 2014.
The species hosts, collecting date, locality and distributions are given. The current checklist also included some species previously collected by other researchers in Duhok Province.
Museums. Collectors and collecting, Natural history (General)
Current tasks and methods in Document Understanding aims to process documents as single elements. However, documents are usually organized in collections (historical records, purchase invoices), that provide context useful for their interpretation. To address this problem, we introduce Document Collection Visual Question Answering (DocCVQA) a new dataset and related task, where questions are posed over a whole collection of document images and the goal is not only to provide the answer to the given question, but also to retrieve the set of documents that contain the information needed to infer the answer. Along with the dataset we propose a new evaluation metric and baselines which provide further insights to the new dataset and task.
We introduce a concept called a collective: an interface with a protocol for aggregating contributions and distributing returns. Through such a protocol, many members may participate in a mutual endeavor. We present a variety of real-world examples of collectives to explore the many kinds of things that members can contribute (such as time, work, ideas, or resources) as well as the many ways these contributions can be aggregated and returns distributed. In addition, we illustrate several ways in which new collectives can be constructed from old, alluding to the fact that all these constructions have a natural mathematical description within the category of polynomial functors equipped with a certain monoidal structure.
Nathan van Beusekom, Wouter Meulemans, Bettina Speckmann
Undirected graphs are frequently used to model networks. The topology of an undirected graph G can be captured by an adjacency matrix; this matrix in turn can be visualized directly to give insight into the graph structure. Which visual patterns appear in such a matrix visualization depends on the ordering of its rows and columns. Formally defining the quality of an ordering and then automatically computing a high-quality ordering are both challenging problems; however, effective heuristics exist and are used in practice. Often, graphs exist as part of a collection of graphs on the same set of vertices. To visualize such graph collections, we need a single ordering that works well for all matrices simultaneously. The current state-of-the-art solves this problem by taking a (weighted) union over all graphs and applying existing heuristics. However, this union leads to a loss of information, specifically in those parts of the graphs which are different. We propose a collection-aware approach to avoid this loss of information and apply it to two popular heuristic methods: leaf order and barycenter. The de-facto standard computational quality metrics for matrix ordering capture only block-diagonal patterns (cliques). Instead, we propose to use Moran's I, a spatial auto-correlation metric, which captures the full range of established patterns. The popular leaf order method heuristically optimizes a similar measure which supports the use of Moran's I in this context. We evaluated our methods for simultaneous orderings on real-world datasets using Moran's I as the quality metric. Our results show that our collection-aware approach matches or improves performance compared to the union approach, depending on the similarity of the graphs in the collection. Specifically, our Moran's I-based collection-aware leaf order implementation consistently outperforms other implementations.
This paper approaches the problem of understanding collective agency from a logical and game-theoretical perspective. Instead of collective intentionality, our analysis highlights the role of Pareto optimality. To facilitate the analysis, we propose a logic of preference and functional dependence by extending the logic of functional dependence. In this logic, we can express Pareto optimality and thus reason about collective agency.
Motivations and drives for collecting have varied through time. From amassing as many examples of different species or artefacts in the sixteenth century to highlighting the importance and strength of the British Empire in the eighteenth century. General trends are seen across historic collections in museums. In an attempt to understand the motivations behind individual collectors, this paper reviews the lives of four mineral collectors from the collections in The Box, Plymouth: Sir John St. Aubyn (175801839), Colonel Sir William Serjeant (1857–1930), René Gallant (1906–1985), and Richard Barstow (1947–1986). Combined they acquired over 4,000 minerals, mostly from the South West of the British Isles. Through examining their lives and collections we may gain insight into their motivations, presenting an opportunity to exhibit new narrative and story-telling alongside the specimens, and in doing so, enriching the visitor experience.
Arkady Arkhangorodsky, Amittai Axelrod, Christopher Chu
et al.
We create a new task-oriented dialog platform (MEEP) where agents are given considerable freedom in terms of utterances and API calls, but are constrained to work within a push-button environment. We include facilities for collecting human-human dialog corpora, and for training automatic agents in an end-to-end fashion. We demonstrate MEEP with a dialog assistant that lets users specify trip destinations.
We prove the existence of a full exceptional collection for the derived category of equivariant matrix factorizations of an invertible polynomial with its maximal symmetry group. This proves a conjecture of Hirano--Ouchi. In the Gorenstein case, we also prove a stronger version of this conjecture due to Takahashi. Namely, that the full exceptional collection is strong.
David Wellnitz, Stefan Schütz, Shannon Whitlock
et al.
We propose a mechanism to realize high-yield molecular formation from ultracold atoms. Atom pairs are continuously excited by a laser, and a collective decay into the molecular ground state is induced by a coupling to a lossy cavity mode. Using a combination of analytical and numerical techniques, we demonstrate that the molecular yield can be improved by simply increasing the number of atoms, and can overcome efficiencies of state-of-the-art association schemes. We discuss realistic experimental setups for diatomic polar and nonpolar molecules, opening up collective light matter interactions as a tool for quantum state engineering, enhanced molecule formation, collective dynamics, and cavity mediated chemistry.