Search

The fundamental property of Cranfield-style evaluations, that system rankings are stable even when assessors disagree on individual relevance decisions, was validated on traditional test collections. However, the paradigm shift towards neural retrieval models affected the characteristics of modern test collections, e.g., documents are short, judged with four grades of relevance, and information needs have no descriptions or narratives. Under these changes, it is unclear whether assessor disagreement remains negligible for system comparisons. We investigate this aspect under the additional condition that the few modern test collections are heavily re-used. Given more possible query interpretations due to less formalized information needs, an ''expiration date'' for test collections might be needed if top-effectiveness requires overfitting to a single interpretation of relevance. We run a reproducibility study and re-annotate the relevance judgments of the 2019 TREC Deep Learning track. We can reproduce prior work in the neural retrieval setting, showing that assessor disagreement does not affect system rankings. However, we observe that some models substantially degrade with our new relevance judgments, and some have already reached the effectiveness of humans as rankers, providing evidence that test collections can expire., Comment: 11 pages, 6 tables, 5 figures

In this paper, we present a geometric framework for the reachability analysis of attitude control systems. We model the attitude dynamics on the product manifold $\mathrm{SO}(3) \times \mathbb{R}^3$ and introduce a novel parametrized family of Riemannian metrics on this space. Using contraction theory on manifolds, we establish reliable upper bounds on the Riemannian distance between nearby trajectories of the attitude control systems. By combining these trajectory bounds with numerical simulations, we provide a simulation-based algorithm to over-approximate the reachable sets of attitude systems. We show that the search for optimal metrics for distance bounds can be efficiently performed using semidefinite programming. Additionally, we introduce a practical and effective representation of these over-approximations on manifolds, enabling their integration with existing Euclidean tools and software. Numerical experiments validate the effectiveness of the proposed approach.

Digital individual participant data (IPD) from clinical trials are increasingly distributed for potential scientific reuse. The identification of available IPD, however, requires interpretations of textual data-sharing statements (DSS) in large databases. Recent advancements in computational linguistics include pre-trained language models that promise to simplify the implementation of effective classifiers based on textual inputs. In a subset of 5,000 textual DSS from ClinicalTrials.gov, we evaluate how well classifiers based on domain-specific pre-trained language models reproduce original availability categories as well as manually annotated labels. Typical metrics indicate that classifiers that predicted manual annotations outperformed those that learned to output the original availability categories. This suggests that the textual DSS descriptions contain applicable information that the availability categories do not, and that such classifiers could thus aid the automatic identification of available IPD in large trial databases., Comment: Published in Proceedings of MIE 2024, IOS Press eBooks. Studies in Health Technology and Informatics, Vol. 316, pp. 834-838. Conference held in Athens, Greece

The Schwarzian derivative plays a fundamental role in complex analysis, differential equations, and modular forms. In this paper, we investigate its higher-order generalizations, known as higher Schwarzians, and their connections to quasimodular forms and equivariant functions. We prove that a meromorphic function is equivariant if and only if its higher Schwarzians are quasimodular forms of prescribed weight and depth, thereby extending classical results and linking projective differential operators to the structure of modular and quasimodular forms., Comment: 11 pages

Markov chains are one of the well-known tools for modeling and analyzing stochastic systems. At the same time, they are used for constructing random walks that can achieve a given stationary distribution. This paper is concerned with determining the transition probabilities that optimize the mixing time of the reversible Markov chains towards a given equilibrium distribution. This problem is referred to as the Fastest Mixing Reversible Markov Chain (FMRMC) problem. It is shown that for a given base graph and its clique lifted graph, the FMRMC problem over the clique lifted graph is reducible to the FMRMC problem over the base graph, while the optimal mixing times on both graphs are identical. Based on this result and the solution of the semidefinite programming formulation of the FMRMC problem, the problem has been addressed over a wide variety of topologies with the same base graph. Second, the general form of the FMRMC problem is addressed on stand-alone topologies as well as subgraphs of an arbitrary graph. For subgraphs, it is shown that the optimal transition probabilities over edges of the subgraph can be determined independent of rest of the topology., Comment: 38 pages, 7 figures

A long-standing goal of social network research has been to alter the properties of network to achieve the desired outcome. In doing so, DeGroot's consensus model has served as the popular choice for modeling the information diffusion and opinion formation in social networks. Achieving a trade-off between the cost associated with modifications made to the network and the speed of convergence to the desired state has shown to be a critical factor. This has been treated as the Fastest Mixing Markov Chain (FMMC) problem over a graph with given transition probabilities over a subset of edges. Addressing this multi-objective optimization problem over the friendship graph, this paper has provided the corresponding Pareto optimal points or the Pareto frontier. In the case of friendship graph with at least three blades, it is shown that the Pareto frontier is reduced to a global minimum point which is same as the optimal point corresponding to the minimum spanning tree of the friendship graph, i.e., the star topology. Furthermore, a lower limit for transition probabilities among friends has been provided, where values higher than this limit do not have any impact on the convergence rate., Comment: 24 pages, 3 figures

The complementary second Zagreb index of a graph $G$ is defined as $cM_2(G)=\sum_{uv\in E(G)}|(d_u(G))^2-(d_v(G))^2|$, where $d_u(G)$ denotes the degree of a vertex $u$ in $G$ and $E(G)$ represents the edge set of $G$. Let $G^*$ be a graph having the maximum value of $cM_2$ among all connected graphs of order $n$. Furtula and Oz [MATCH Commun. Math. Comput. Chem. 93 (2025) 247--263] conjectured that $G^*$ is the join $K_k+\overline{K}_{n-k}$ of the complete graph $K_k$ of order $k$ and the complement $\overline{K}_{n-k}$ of the complete graph $K_{n-k}$ such that the inequality $k<\lceil n/2 \rceil$ holds. We prove that (i) the maximum degree of $G^*$ is $n-1$ and (ii) no two vertices of minimum degree in $G^*$ are adjacent; both of these results support the aforementioned conjecture. We also prove that the number of vertices of maximum degree in $G^*$, say $k$, is at most $-\frac{2}{3}n+\frac{3}{2}+\frac{1}{6}\sqrt{52n^2-132n+81}$, which implies that $k<5352n/10000$. Furthermore, we establish results that support the conjecture under consideration for certain bidegreed and tridegreed graphs. In the aforesaid paper, it was also mentioned that determining the $k$ as a function of the $n$ is far from being an easy task; we obtain the values of $k$ for $5\le n\le 149$ in the case of certain bidegreed graphs by using computer software and found that the resulting sequence of the values of $k$ does not exist in "The On-Line Encyclopedia of Integer Sequences" (an online database of integer sequences)., Comment: 13 pages, 1 figure