Understanding how AI will represent and reason about geography should be a key concern for all of us, as the broader public increasingly interacts with spaces and places through these systems. Similarly, in line with the nature of foundation models, our own research often relies on pre-trained models. Hence, understanding what world AI systems construct is as important as evaluating their accuracy, including factual recall. To motivate the need for such studies, we provide three illustrative vignettes, i.e., exploratory probes, in the hope that they will spark lively discussions and follow-up work: (1) Do models form strong defaults, and how brittle are model outputs to minute syntactic variations? (2) Can distributional shifts resurface from the composition of individually benign tasks, e.g., when using AI systems to create personas? (3) Do we overlook deeper questions of understanding when solely focusing on the ability of systems to recall facts such as geographic principles?
We study the behavior of toric Landau-Ginzburg models under extremal contraction and minimal model program. We also establish a relation between the moduli space of toric Landau-Ginzburg models and the geography of central models. We conjecture that there is a correspondence between extremal contractions and minimal model program on Fano varieties, and degenerations of their associated toric Landau-Ginzburg models written explicitly. We prove the conjectures for smooth toric varieties, as well as general smooth Fano varieties in dimensions 2 and 3. As an application, we compute the elementary syzygies for smooth Fano threefolds.
Road network representation learning aims to learn compressed and effective vectorized representations for road segments that are applicable to numerous tasks. In this paper, we identify the limitations of existing methods, particularly their overemphasis on the distance effect as outlined in the First Law of Geography. In response, we propose to endow road network representation with the principles of the recent Third Law of Geography. To this end, we propose a novel graph contrastive learning framework that employs geographic configuration-aware graph augmentation and spectral negative sampling, ensuring that road segments with similar geographic configurations yield similar representations, and vice versa, aligning with the principles stated in the Third Law. The framework further fuses the Third Law with the First Law through a dual contrastive learning objective to effectively balance the implications of both laws. We evaluate our framework on two real-world datasets across three downstream tasks. The results show that the integration of the Third Law significantly improves the performance of road segment representations in downstream tasks.
This survey focuses on the geometric problem of log-surfaces, which are pairs consisting of a smooth projective surface and a reduced non-empty boundary divisor. In the first part, we focus on the geography problem for complex log-surfaces associated with pairs of the form $(\mathbb{P}^{2}, C)$, where $C$ is an arrangement of smooth plane curves admitting ordinary singularities. Specifically, we focus on the case in which $C$ is an arrangement consisting of smooth rational curves as its irreducible components. In the second part, containing original new results, we study log-surfaces constructed as pairs consisting of a complex projective $K3$ surface and a rational curve arrangement. In particular, we provide some combinatorial conditions for such pairs to have the log-Chern slope equal to $3$. Our survey is illustrated with many explicit examples of log-surfaces.
Simon Scheider, Harm Bartholomeus, Judith Verstegen
The recent success of large language models and AI chatbots such as ChatGPT in various knowledge domains has a severe impact on teaching and learning Geography and GIScience. The underlying revolution is often compared to the introduction of pocket calculators, suggesting analogous adaptations that prioritize higher-level skills over other learning content. However, using ChatGPT can be fraudulent because it threatens the validity of assessments. The success of such a strategy therefore rests on the assumption that lower-level learning goals are substitutable by AI, and supervision and assessments can be refocused on higher-level goals. Based on a preliminary survey on ChatGPT's quality in answering questions in Geography and GIScience, we demonstrate that this assumption might be fairly naive, and effective control in assessments and supervision is required.
In this short note, we provide a criterion for DGA-homotopy of augmentations of Chekanov-Eliashberg algebra of disconnected Legendrian submanifolds. We apply the criterion to obtain the extension of geography results of Bourgeois and Galant concerning bilinearized Legendrian contact homology to the case of disconnected Legendrian submanifolds.
Katherine Van Koevering, Yiquan Hong, Jon Kleinberg
The COVID-19 pandemic has been a global health crisis playing out in the age of social media. Even though the virtual environment makes interaction possible regardless of physical location, many of the most pressing issues during the pandemic -- case counts, lockdown policies, vaccine availability -- have played out in an intensely local fashion. Reflecting this locality, many of the online COVID communities that formed have been closely tied to physical location, at different spatial scales ranging from cities to countries to entire global platforms. This provides an opportunity to study how the real-world geography of the pandemic translates into a virtual landscape. By analyzing almost 300 geographically-linked COVID discussion communities on Reddit, we show how these discussions were organized geographically and temporally in three aspects: what were people talking about, who were they talking about it with, and how did they self-organize these conversations?
We discuss the geography problem of closed oriented 4-manifolds that admit a Riemannian metric of positive scalar curvature, and use it to survey mathematical work employed to address Gromov's observation that manifolds with positive scalar curvature tend to be inessential by focusing on the four-dimensional case. We also point out an strengthening of a result of Carr and its extension to the non-orientable realm.
The nonorientable 4-genus is an invariant of knots which has been studied by many authors, including Gilmer and Livingston, Batson, and Ozsváth, Stipsicz, and Szabó. Given a nonorientable surface $F \subset B^4$ with $\partial F = K\subset S^3$ a knot, an analysis of the existing methods for bounding and computing the nonorientable 4-genus reveals relationships between the first Betti number $β_1$ of $F$ and the normal Euler class $e$ of $F$. This relationship yields a geography problem: given a knot $K$, what is the set of realizable pairs $(e(F), β_1(F))$ where $F\subset B^4$ is a nonorientable surface bounded by $K$? We explore this problem for families of torus knots. In addition, we use the Ozsváth-Szabó $d$-invariant of two-fold branched covers to give finer information on the geography problem. We present an infinite family of knots where this information provides an improvement upon the bound given by Ozsváth, Stipsicz, and Szabó using the Upsilon invariant.
Olga Bondarenko, Olena Pakhomova, Wlodzimierz Lewoniewski
The article clarifies the concept of "virtual information educational environment" (VIEE) and examines the researchers' views on its meaning exposed in the scientific literature. The article determines the didactic potential of the virtual information educational environment for the geography students training based on the analysis of the authors' experience of blended learning by means of the Google Classroom. It also specifies the features (immersion, interactivity, and dynamism, sense of presence, continuity, and causality). The authors highlighted the advantages of virtual information educational environment implementation, such as: increase of the efficiency of the educational process by intensifying the process of cognition and interpersonal interactive communication; continuous access to multimedia content both in Google Classroom and beyond; saving student time due to the absence of necessity to work out the training material "manually"; availability of virtual pages of the virtual class; individualization of the educational process; formation of informational culture of the geography students ; and more productive learning of the educational material at the expense of IT educational facilities. Among the disadvantages the article mentions low level of computerization, insignificant quantity and low quality of software products, underestimation of the role of VIEE in the professional training of geography students, and the lack of economic stimuli, etc.
In this short note we reply to a comment by Callegaro et al. [1] (arXiv:2009.11709) that points out some weakness of the model of indeterministic physics that we proposed in Ref. [2] (Physical Review A, 100(6), p.062107), based on what we named "finite information quantities" (FIQs). While we acknowledge the merit of their criticism, we maintain that it applies only to a concrete example that we discussed in [2], whereas the main concept of FIQ remains valid and suitable for describing indeterministic physical models. We hint at a more sophisticated way to define FIQs which, taking inspiration from intuitionistic mathematics, would allow to overcome the criticisms in [1].
We study the geography of bilinearized Legendrian contact homology for closed, connected Legendrian submanifolds with vanishing Maslov class in 1-jet spaces. We show that this invariant detects whether the two augmentations used to define it are DGA homotopic or not. We describe a collection of graded vector spaces containing all possible values for bilinearized Legendrian contact homology and then show that all these vector spaces can be realized.
Scenario-based question answering (SQA) has attracted increasing research attention. It typically requires retrieving and integrating knowledge from multiple sources, and applying general knowledge to a specific case described by a scenario. SQA widely exists in the medical, geography, and legal domains---both in practice and in the exams. In this paper, we introduce the GeoSQA dataset. It consists of 1,981 scenarios and 4,110 multiple-choice questions in the geography domain at high school level, where diagrams (e.g., maps, charts) have been manually annotated with natural language descriptions to benefit NLP research. Benchmark results on a variety of state-of-the-art methods for question answering, textual entailment, and reading comprehension demonstrate the unique challenges presented by SQA for future research.