This article examines the governance challenges of human genomic data sharing. The analysis builds upon the unique characteristics that distinguish genomic data from other forms of personal data, particularly its dual nature as both uniquely identifiable to individuals and inherently collective, reflecting familial and ethnic group characteristics. This duality informs a tripartite risk taxonomy: individual privacy violations, group-level harms, and bioterrorism threats. Examining regulatory frameworks in the European Union (EU) and China, the article demonstrates how current data protection mechanisms—primarily anonymisation and informed consent—prove inadequate for genomic data governance due to the impossibility of true anonymisation and the limitations of consent-based models in addressing the risks of such sharing. Drawing on the concept of “genomic contextualism,” the article proposes a nuanced framework that incorporates interest balancing, comprehensive data lifecycle management, and tailored technical safeguards. The objective is to protect individuals and underrepresented groups while maximising the scientific and clinical value of genomic data.

We introduce a family of parsimonious network models that are intended to generalize the configuration model to temporal settings. We present consistent estimators for the model parameters and perform numerical simulations to illustrate the properties of the estimators on finite samples. We also derive analytical solutions for the basic and effective reproduction numbers for the early stage of the discrete-time SIR spreading process for our temporal configuration model (TCM). We apply three distinct TCMs to empirical student proximity networks and compare their performance.

We study how COVID-19 affected the ownership co-location network of French multinationals over 2012–2022. Using INSEE’s LiFi, we build annual country-industry co-location networks and assess robustness via topology (density, centralization, assortativity, and clustering) and edge survival (Weighted Jaccard). We then test for post-shock shifts in the determinants of dyadic co-location with multiple regression quadratic assignment procedure. Three results emerge. First, the network’s core is robust: topology shows no discontinuity and centrality persists. Second, adaptation is continuous at the margin: around one-third of edges rewire, concentrated in the periphery while core ties endure. Third, after 2020 the determinants of tie weights change, with a reduced role for gravity-like factors and greater cross-sector rebalancing. Thus the system is structurally robust with active peripheral adjustment. Rather than strict resilience in the sense of a return to the pre-COVID configuration, we observe durable strategic reweighting.

Learning has recently played a vital role in control engineering, producing numerous applications and facilitating easier control over systems; however, it has presented serious challenges in flight learning for unmanned platforms. Iterative learning control (ILC) is a practical method for cases needing repetition in control loops. This work focuses on the ILC of a quadrotor flight. An unstable flight might lead to a crash in the system and stop the iterations; hence, a base controller, the state-dependent Riccati equation (SDRE), is selected to stabilize the drone in the first loop. The ILC acts on top of the SDRE to increase the precision and force the system to learn to track trajectories better. The combination of ILC and SDRE was tested for stationary (fixed-base) systems without the risk of crashes; nonetheless, its implementation on a flying (mobile) system is reported for the first time. The gradient descent method shapes the training criteria for error reduction in the ILC. The proposed design is implemented on simulation and a real flight of a quadrotor in a series of tests, showing the effectiveness of the proposed input law. The nonlinear and optimal structure of the base controller and the complex iterative learning programming were challenges of this work, which were successfully addressed and demonstrated experimentally.

Many empirical systems contain complex interactions of arbitrary size, representing, for example, chemical reactions, social groups, co-authorship relationships, and ecological dependencies. These interactions are known as higher-order interactions, and the collection of these interactions comprise a higher-order network, or hypergraph. Hypergraphs have established themselves as a popular and versatile mathematical representation of such systems, and a number of software packages written in various programming languages have been designed to analyze these networks. However, the ecosystem of higher-order network analysis software is fragmented due to specialization of each software’s programming interface and compatible data representations. To enable seamless data exchange between higher-order network analysis software packages, we introduce the Hypergraph Interchange Format (HIF), a standardized format for storing higher-order network data. HIF supports multiple types of higher-order networks, including undirected hypergraphs, directed hypergraphs, and abstract simplicial complexes, while actively exploring extensions to represent multiplex hypergraphs, temporal hypergraphs, and ordered hypergraphs. To accommodate the wide variety of metadata used in different contexts, HIF also includes support for attributes associated with nodes, edges, and incidences. This initiative is a collaborative effort involving authors, maintainers, and contributors from prominent hypergraph software packages. This project introduces a JSON schema with corresponding documentation and unit tests, example HIF-compliant datasets, and tutorials demonstrating the use of HIF with several popular higher-order network analysis software packages.

Fix integers $r \ge 2$ and $1\le s_1\le \cdots \le s_{r-1}\le t$ and set $s=\prod _{i=1}^{r-1}s_i$. Let $K=K(s_1, \ldots , s_{r-1}, t)$ denote the complete $r$-partite $r$-uniform hypergraph with parts of size $s_1, \ldots , s_{r-1}, t$. We prove that the Zarankiewicz number $z(n, K)= n^{r-1/s-o(1)}$ provided $t\gt 3^{s+o(s)}$. Previously this was known only for $t \gt ((r-1)(s-1))!$ due to Pohoata and Zakharov. Our novel approach, which uses Behrend’s construction of sets with no 3-term arithmetic progression, also applies for small values of $s_i$, for example, it gives $z(n, K(2,2,7))=n^{11/4-o(1)}$ where the exponent 11/4 is optimal, whereas previously this was only known with 7 replaced by 721.

This article addresses the question of experiential dimensions of space in sound, in electroacoustic music and sound arts practices in particular. We suggest that these practices are limited by the generalised way that spatial audio techniques are communicated, and we attempt to develop a tentative method that would enable discussion and sharing of spatial aspects in sonic environments. These modes of articulation would permit a translation of the experience of space in sound into other modalities. Reporting from a series of workshops, we outline a three-phase method that moves through the stages of listening, describing, recreating and imagining the sonic spaces. In the final stage, a speculative design approach shows that shared sonic spatial experiences are essentially relational. Topics relating to expectations, biases and language – such as memory and imagination – and the methods of mapping and speculative design are addressed in the discussion. Through the explorations presented in this article it becomes evident that different artistic musical practices still show the same need to develop articulations that enable the integration and communication of spatial relationships. The divide between the development of new technologies for spatial audio and the conceptual frameworks for understanding and communicating spatial sonic knowledge can be bridged, and eventually the development of spatial audio should be fuelled by the dynamics between these two poles.

In this paper, a novel series–parallel stable platform is proposed, and its kinematic and dynamic models are established. The relationship between the length, speed, and acceleration of rolling and pitching electric push rods is analyzed. The workspace of the series–parallel stable platform is determined, and the singularity and interference are analyzed. The state-machine-based control system of the stable platform is designed. An experimental environment of the principle of the real-time control system based on dSPACE was built. A position–speed double closed-loop experiment, simulating mounting carrier of the random signal tracking, and system comprehensive performance experiment were conducted to verify the accuracy of the kinematics and dynamics model of the series–parallel stable platform and the rationality and stability of the control system.

The famous Sidorenko’s conjecture asserts that for every bipartite graph $H$, the number of homomorphisms from $H$ to a graph $G$ with given edge density is minimised when $G$ is pseudorandom. We prove that for any graph $H$, a graph obtained from replacing edges of $H$ by generalised theta graphs consisting of even paths satisfies Sidorenko’s conjecture, provided a certain divisibility condition on the number of paths. To achieve this, we prove unconditionally that bipartite graphs obtained from replacing each edge of a complete graph with a generalised theta graph satisfy Sidorenko’s conjecture, which extends a result of Conlon, Kim, Lee and Lee [J. Lond. Math. Soc., 2018].

This paper aims to theorise how virtual reality (VR) can contribute to the development of contextual architecture. We start by considering how an architectural context may translate into a virtual domain, introducing preliminary definitions of what a virtual design context (VDC) could entail. We then discuss a proposed taxonomy that guides the creation of such a VDC, anchored in principles drawn from virtual realism in art philosophy and contextualism within architecture. This taxonomy is envisioned as a preliminary framework for developing VR-driven design environments with a focus on context. Next, we conducted expert user-testing with 24 architects using two VDCs developed according to the taxonomy. The goal of this step was to gain insights regarding the cognitive load of designers and their user experience while engaged in different types of VDCs. Results suggest that designing in these virtual environments enhanced contextual learning, supported conceptual and creative insight and helped maintain manageable cognitive load. The paper concludes by underscoring the real-world applicability of this taxonomy, highlighting how VR can breathe new life into contextual design, not by reducing context into a digital replica, but by opening new dimensions through which its richness can be explored, interpreted and reimagined.

In aerospace, automated assembly line, and precision engineering, asymmetric multi-robot systems comprising serial and parallel robots leverage the complementary strengths of these configurations to address the conflicting demands of high load capacity, extensive range, and flexibility in assembly tasks. However, the relatively small workspace of the parallel robot limits the full potential of the collaborative system functionality. This paper centers on a collaborative assembly system involving serial-parallel robots, whose collaborative workspace is determined by using a combination of the Monte Carlo method and lattice method. Additionally, a multi-objective optimization model is developed to holistically evaluate the collaborative workspace performance. The optimization problem is solved by an enhanced NSGA-II algorithm, which yields a Pareto optimal solution set. This result offers valuable technical insights for designing collaborative systems tailored to diverse task requirements.

Large language models (LLMs) are increasingly used to address real-world design problems, especially during the design ideation phase. Although LLMs hold substantial promise for concept generation, the understanding of how they can effectively assist designers in enhancing the diversity of design concepts is still limited. In this study, we set up different strategies for prompting multiple professional personas to the LLM for design concept generation, including (1) multiple prompts for concept generation in parallel, each with a professional persona, (2) a single prompt for concept generation with multiple professional personas, and (3) a sequence of prompts for concept generation and update, each with a professional persona. We formulate and test several hypotheses on the effectiveness of different strategies. All hypotheses are tested by constructing professional knowledge bases, selecting design problems and personas, and designing the prompts. The results suggest that LLMs can facilitate the design ideation process and provide more diverse design concepts when they are given multiple prompts in parallel, each with a professional persona, or given a sequence of prompts with multiple professional personas to generate and update design concepts gradually.

This paper responds to Rosolini’s suggestion to use the ultracompletion of a category as a way to understand versions of conceptual completeness. Over 50 years ago, Kock and Mikkelsen observed in effect that one obtains ultracompletions of the category of sets by factorising ultrapower functors. They gave a concrete description of the factorisation under what they recognised were special conditions. In parallel work, Volger obtained a different description using categorical logic. Here, I revisit these ideas using Tripos Theory and show in particular that any left exact functor of toposes admits a Kock–Mikkelsen factorisation. In this reading, the ultracompletion appears amongst the various regular and exact completions which have been studied in particular by members of the Italian Category Theory School.

We show that for any integer $k\ge 1$ there exists an integer $t_0(k)$ such that, for integers $t, k_1, \ldots , k_{t+1}, n$ with $t\gt t_0(k)$, $\max \{k_1, \ldots , k_{t+1}\}\le k$, and $n \gt 2k(t+1)$, the following holds: If $F_i$ is a $k_i$-uniform hypergraph with vertex set $[n]$ and more than $ \binom{n}{k_i}-\binom{n-t}{k_i} - \binom{n-t-k}{k_i-1} + 1$ edges for all $i \in [t+1]$, then either $\{F_1,\ldots , F_{t+1}\}$ admits a rainbow matching of size $t+1$ or there exists $W\in \binom{[n]}{t}$ such that $W$ intersects $F_i$ for all $i\in [t+1]$. This may be viewed as a rainbow non-uniform extension of the classical Hilton-Milner theorem. We also show that the same holds for every $t$ and $n \gt 2k^3t$, generalizing a recent stability result of Frankl and Kupavskii on matchings to rainbow matchings.

We present a new way to control the unfolding of definitions in dependent type theory. Traditionally, proof assistants require users to fix whether each definition will or will not be unfolded in the remainder of a development; unfolding definitions is often necessary in order to reason about them, but an excess of unfolding can result in brittle proofs and intractably large proof goals. In our system, definitions are by default not unfolded, but users can selectively unfold them in a local manner. We justify our mechanism by means of elaboration to a core theory with extension types – a connective first introduced in the context of homotopy type theory – and by establishing a normalization theorem for our core calculus. We have implemented controlled unfolding in the proof assistant, inspiring an independent implementation in Agda.

The author’s primary goal in this paper is to characterize $\omega$-Rudin sets and $\omega$-Rudin spaces via sequence convergence and give some important applications of such characterizations. For an irreducible closed set $A$ of a $T_0$-space $X$, we prove that the following four conditions are equivalent: (1) $A$ is an $\omega$-Rudin set; (2) there is $\{a_n : n\in \mathbb{N}\}\subseteq A$ such that the sequence $(a_n)_{n\in \mathbb{N}}$ simultaneously converges to all points of $A$; (3) there is $\{a_n : n\in \mathbb{N}\}\subseteq A$ such that the sequence $(\overline {\{a_n\}})_{n\in \mathbb{N}}$ converges to $A$ in the Hoare power space of $X$; (4) there is $\{a_n : n\in \mathbb{N}\}\subseteq A$ such that the sequence $(\overline {\{a_n\}})_{n\in \mathbb{N}}$ converges to $A$ in the sobrification of $X$. Based on these characterizations, we obtain some characterizations of $\omega$-Rudin spaces and sober spaces. In particular, we show that for a complete lattice $L$, its Scott space $\Sigma L$ is sober iff for any nonempty Scott irreducible closed set $A$ of $L$, there is $\{a_n : n\in \mathbb{N}\}\subseteq A$ such that the sequence $(a_n)_{n\in \mathbb{N}}$ simultaneously Scott converges to all points of $A$ or, equivalently, the sequence $(\overline {\{a_n\}})_{n\in \mathbb{N}}$ converges to $A$ in the sobrification of $\Sigma L$. Several related examples are presented. We also investigate some basic properties of $\omega$-Rudin spaces. It is proved that the property of being an $\omega$-Rudin space is retractive, productive, and closed-hereditary. We give two examples to show that it is not saturated-hereditary and the category $\boldsymbol{\omega }$-$\mathbf{Rud}$ of $\omega$-Rudin spaces does not have equalizers, and hence, $\boldsymbol{\omega }$-$\mathbf{Rud}$ is not reflective in the category $\mathbf{Top}_{0}$ of all $T_0$-spaces. Finally, we discuss the Smyth power spaces of $\omega$-Rudin spaces. It is shown that if the Smyth power space of a $T_0$-space $X$ is an $\omega$-Rudin space, then $X$ is an $\omega$-Rudin space. The question naturally arises whether the Smyth power space of an $\omega$-Rudin space is still an $\omega$-Rudin space.

We study generalised automata (in the sense of Adámek and Trnková) in Joyal’s category of (set-valued) combinatorial species, and as an important preliminary step, we study coalgebras for its derivative endofunctor $\partial$ and for the ‘Euler homogeneity operator’ $L\circ \partial$ arising from the adjunction $L\dashv \partial \dashv R$. The theory is connected with, and in fact provides relatively nontrivial examples of, differential 2-rigs, a notion recently introduced by the author putting combinatorial species on the same relation a generic (differential) semiring $(R,d)$ has with the (differential) semiring $\mathbb{N}[\![ X]\!]$ of power series with natural coefficients. The desire to study categories of ‘state machines’ valued in an ambient monoidal category $(\mathcal{K},\otimes )$ gives a pretext to further develop the abstract theory of differential 2-rigs, proving lifting theorems of a differential 2-rig structure from $(\mathcal{R},\partial )$ to the category of $\partial$-algebras on objects of $\mathcal{R}$ and to categories of Mealy automata valued in $(\mathcal{R},\otimes )$, as well as various constructions inspired by differential algebra such as jet spaces and modules of differential operators. These theorems adapt to various ‘species-like’ categories such as coloured species, $k$-vector species (both used in operad theory), linear species (introduced by Leroux to study combinatorial differential equations), Möbius species and others.

The traditional ant colony optimisation (ACO) algorithm, when applied to mobile robot path planning, faces several challenges: slow convergence, susceptibility to local optima, and the generation of paths with excessive turning points, all of which reduce the robot’s operational efficiency. To overcome these shortcomings, this paper proposes a targeted set of improvements designed to enhance algorithm performance and increase the practicality and efficiency of path planning. First, we introduce an initial pheromone enhancement mechanism based on the Bresenham algorithm. By augmenting pheromone concentration along the approximate straight-line path from the start to the goal, ants are guided to explore in the optimal direction, thereby significantly accelerating convergence. Second, we integrate a directional continuity factor into the path selection probability: by using vector dot products to strengthen the bias toward consistent directions and by coupling this with a curvature-based pheromone reward that favours straighter segments, we ensure smoother, more direct paths. Finally, we apply a spring-model-based smoothing strategy as a post-processing step to the paths generated by the ant colony, reducing path complexity and the number of turns to guarantee efficient and reliable robot motion. To validate the performance of the improved algorithm, we conduct comparative experiments on a MATLAB platform against other enhanced ACO variants reported in the literature. The results demonstrate that our proposed algorithm significantly outperforms these existing methods across all performance metrics, exhibiting superior path planning capabilities.

The article is concerned with realizability in abstract argumentation. It provides characterization theorems for the most basic types of labelling-based semantics, namely conflict-free and naive labellings. It turns out that existing characterizations for extension-based semantics are of little help in characterizing labelling-based semantics. To this end, we introduce several new criteria like L-tightness, reject-witnessing, reject-compositionality as well as the new construct of a labelling-downward-closure, which help determine whether a given set of labellings is realizable regarding conflict-free or naive semantics. Moreover, we present standard constructions and analyse their uniqueness status. Further classical concepts like ordinary and strong equivalence are studied too. Last but not least, we delve into the characterization of stable labellings. It turns out that this endeavour is a highly non-trivial task with many parallels to so-called compact realizability, an open problem for stable semantics in abstract argumentation.