In this paper, the notion of locally algebraic intersection structure is introduced for algebraic L-domains. Essentially, every locally algebraic intersection structure is a family of sets, which forms an algebraic L-domain ordered by inclusion. It is shown that there is a locally algebraic intersection structure which is order-isomorphic to a given algebraic L-domain. This result extends the classic Stone’s representation theorem for Boolean algebras to the case of algebraic L-domains. In addition, it can be seen that many well-known representations of algebraic L-domains, such as logical algebras, information systems, closure spaces, and formal concept analysis, can be analyzed in the framework of locally algebraic intersection structures. Then, a set-theoretic uniformity across different representations of algebraic L-domains is established.

Compressible anisothermal flows, which are commonly found in industrial settings such as combustion chambers and heat exchangers, are characterized by significant variations in density, viscosity, and heat conductivity with temperature. These variations lead to a strong interaction between the temperature and velocity fields that impacts the near-wall profiles of both quantities. Wall-modeled large-eddy simulations (LESs) rely on a wall model to provide a boundary condition, for example, the shear stress and the heat flux that accurately represents this interaction despite the use of coarse cells near the wall, and thereby achieve a good balance between computational cost and accuracy. In this article, the use of graph neural networks for wall modeling in LES is assessed for compressible anisothermal flow. Graph neural networks are a type of machine learning model that can learn from data and operate directly on complex unstructured meshes. Previous work has shown the effectiveness of graph neural network wall modeling for isothermal incompressible flows. This article develops the graph neural network architecture and training to extend their applicability to compressible anisothermal flows. The model is trained and tested a priori using a database of both incompressible isothermal and compressible anisothermal flows. The model is finally tested a posteriori for the wall-modeled LES of a channel flow and a turbine blade, both of which were not seen during training.

This paper examines the potential role of network analysis in understanding the powerful elites that pose a significant threat to peace and state-building within post-conflict contexts. This paper makes a threefold contribution. First, it identifies a caveat in the scholarship surrounding international interventions, shedding light on shortcomings in their design and implementation strategies, and elucidating the influence these elites wield in the political and economic realms. Next, it delineates the essentials of the network analysis approach, addressing the information and data requirements and limitations inherent in its application in conflict environments. Finally, the paper provides valuable insights gleaned from the international operation in Guatemala known as the International Commission for Impunity in Guatemala, which specifically targeted illicit networks. The argument asserts that network analysis functions as a dual-purpose tool—serving as both a descriptive instrument to reveal, identify, and address the root causes of conflict and a predictive tool to enhance peace agreement implementation and improve decision-making. Simultaneously, it underscores the challenge of data analysis and translating network interventions into tangible real-life consequences for long-lasting results.

We introduce a novel preferential attachment model using the draw variables of a modified Pólya urn with an expanding number of colors, notably capable of modeling influential opinions (in terms of vertices of high degree) as the graph evolves. Similar to the Barabási-Albert model, the generated graph grows in size by one vertex at each time instance; in contrast however, each vertex of the graph is uniquely characterized by a color, which is represented by a ball color in the Pólya urn. More specifically at each time step, we draw a ball from the urn and return it to the urn along with a number of reinforcing balls of the same color; we also add another ball of a new color to the urn. We then construct an edge between the new vertex (corresponding to the new color) and the existing vertex whose color ball is drawn. Using color-coded vertices in conjunction with the time-varying reinforcing parameter allows for vertices added (born) later in the process to potentially attain a high degree in a way that is not captured in the Barabási-Albert model. We study the degree count of the vertices by analyzing the draw vectors of the underlying stochastic process. In particular, we establish the probability distribution of the random variable counting the number of draws of a given color which determines the degree of the vertex corresponding to that color in the graph. We further provide simulation results presenting a comparison between our model and the Barabási-Albert network.

Design education prepares novice designers to solve complex and challenging problems requiring diverse skill sets and an interdisciplinary approach. Hackathons, for example, offer a hands-on, collaborative learning approach in a limited time frame to gain practical experience and develop problem-solving skills quickly. They enable collaboration, prototyping and testing among interdisciplinary teams. Typically, hackathons strongly focus on the solution, assuming that this will support learning. However, building the best product and achieving a strong learning effect may not be related. This paper presents the results of an empirical study that examines the relationship between product quality, learning effect and effort spent in an academic 2-week hackathon. Thirty teams identified user problems in this course and developed hardware and mechatronic products. This study collected the following data: (1) effort spent during the hackathon through task tracking, (2) learning effect through self-assessment by the participants and (3) product quality after the hackathon by an external jury. The study found that the team effort spent has a statistically significant but moderate correlation with product quality. The correlation between product quality and learning effect is statistically insignificant, suggesting that for this setting, there is no relevant association.

We give algorithms for approximating the partition function of the ferromagnetic $q$-color Potts model on graphs of maximum degree $d$. Our primary contribution is a fully polynomial-time approximation scheme for $d$-regular graphs with an expansion condition at low temperatures (that is, bounded away from the order-disorder threshold). The expansion condition is much weaker than in previous works; for example, the expansion exhibited by the hypercube suffices. The main improvements come from a significantly sharper analysis of standard polymer models; we use extremal graph theory and applications of Karger’s algorithm to count cuts that may be of independent interest. It is #BIS-hard to approximate the partition function at low temperatures on bounded-degree graphs, so our algorithm can be seen as evidence that hard instances of #BIS are rare. We also obtain efficient algorithms in the Gibbs uniqueness region for bounded-degree graphs. While our high-temperature proof follows more standard polymer model analysis, our result holds in the largest-known range of parameters $d$ and $q$.

We study a fundamental efficiency benefit afforded by delimited control, showing that for certain higher-order functions, a language with advanced control features offers an asymptotic improvement in runtime over a language without them. Specifically, we consider the generic count problem in the context of a pure functional base language ${\lambda_{\textrm{b}}}$ and an extension ${\lambda_{\textrm{h}}}$ with general effect handlers. We prove that ${\lambda_{\textrm{h}}}$ admits an asymptotically more efficient implementation of generic count than any implementation in ${\lambda_{\textrm{b}}}$. We also show that this gap remains even when ${\lambda_{\textrm{b}}}$ is extended to a language ${{{{{{\lambda_{\textrm{a}}}}}}}}$ with affine effect handlers, which is strong enough to encode exceptions, local state, coroutines and single-shot continuations. This locates the efficiency difference in the gap between ‘single-shot’ and ‘multi-shot’ versions of delimited control.

To our knowledge, these results are the first of their kind for control operators.