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In this paper, without requiring any constraint qualifications, we establish tight error bounds for the log-determinant cone, which is the closure of the hypograph of the perspective function of the log-determinant function. This error bound is obtained using the recently developed framework based on one-step facial residual functions.

In this paper, we harness a result in point process theory, specifically the expectation of the weighted $K$-function, where the weighting is done by the true first-order intensity function. This theoretical result can be employed as an estimation method to derive parameter estimates for a particular model assumed for the data. The underlying motivation is to avoid the difficulties associated with dealing with complex likelihoods in point process models and their maximization. The exploited result makes our method theoretically applicable to any model specification. In this paper, we restrict our study to Poisson models, whose likelihood represents the base for many more complex point process models. In this context, our proposed method can estimate the vector of local parameters that correspond to the points within the analyzed point pattern without introducing any additional complexity compared to the global estimation. We illustrate the method through simulation studies for both purely spatial and spatio-temporal point processes and show complex scenarios based on the Poisson model through the analysis of two real datasets concerning environmental problems.

Most businesses impose a supervisory hierarchy on employees to facilitate management, decision-making, and collaboration, yet routine inter-employee communication patterns within workplaces tend to emerge more naturally as a consequence of both supervisory relationships and the needs of the organization. What then is the relationship between a formal organizational structure and the emergent communications between its employees? Understanding the nature of this relationship is critical for the successful management of an organization. While scholars of organizational management have proposed theories relating organizational trees to communication dynamics, and separately, network scientists have studied the topological structure of communication patterns in different types of organizations, existing empirical analyses are both lacking in representativeness and limited in size. In fact, much of the methodology used to study the relationship between organizational hierarchy and communication patterns comes from analyses of the Enron email corpus, reflecting a uniquely dysfunctional corporate environment. In this paper, we develop new methodology for assessing the relationship between organizational hierarchy and communication dynamics and apply it to Microsoft Corporation, currently the highest valued company in the world, consisting of approximately 200,000 employees divided into 88 teams. This reveals distinct communication network structures within and between teams. We then characterize the relationship of routine employee communication patterns to these team supervisory hierarchies, while empirically evaluating several theories of organizational management and performance. To do so, we propose new measures of communication reciprocity and new shortest-path distances for trees to track the frequency of messages passed up, down, and across the organizational hierarchy.

In decision-making, maxitive functions are used for worst-case and best-case evaluations. Maxitivity gives rise to a rich structure that is well-studied in the context of the pointwise order. In this article, we investigate maxitivity with respect to general preorders and provide a representation theorem for such functionals. The results are illustrated for different stochastic orders in the literature, including the usual stochastic order, the increasing convex/concave order, and the dispersive order.

The purpose of anonymizing structured data is to protect the privacy of individuals in the data while retaining the statistical properties of the data. There is a large body of work that examines anonymization vulnerabilities. Focusing on strong anonymization mechanisms, this paper examines a number of prominent attack papers and finds several problems, all of which lead to overstating risk. First, some papers fail to establish a correct statistical inference baseline (or any at all), leading to incorrect measures. Notably, the reconstruction attack from the US Census Bureau that led to a redesign of its disclosure method made this mistake. We propose the non-member framework, an improved method for how to compute a more accurate inference baseline, and give examples of its operation. Second, some papers don't use a realistic membership base rate, leading to incorrect precision measures if precision is reported. Third, some papers unnecessarily report measures in such a way that it is difficult or impossible to assess risk. Virtually the entire literature on membership inference attacks, dozens of papers, make one or both of these errors. We propose that membership inference papers report precision/recall values using a representative range of base rates.

Charts, figures, and text derived from data play an important role in decision making, from data-driven policy development to day-to-day choices informed by online articles. Making sense of, or fact-checking, outputs means understanding how they relate to the underlying data. Even for domain experts with access to the source code and data sets, this poses a significant challenge. In this paper we introduce a new program analysis framework which supports interactive exploration of fine-grained I/O relationships directly through computed outputs, making use of dynamic dependence graphs. Our main contribution is a novel notion in data provenance which we call related inputs, a relation of mutual relevance or "cognacy" which arises between inputs when they contribute to common features of the output. Queries of this form allow readers to ask questions like "What outputs use this data element, and what other data elements are used along with it?". We show how Jonsson and Tarski's concept of conjugate operators on Boolean algebras appropriately characterises the notion of cognacy in a dependence graph, and give a procedure for computing related inputs over such a graph.

In this letter, we give a characterization for a generic construction of bent functions. This characterization enables us to obtain another efficient construction of bent functions and to give a positive answer on a problem of bent functions.

For the ground state of the Gross-Pitaevskii (GP) eigenvalue problem, we consider a fully discretized Sobolev gradient flow, which can be regarded as the Riemannian gradient descent on the sphere under a metric induced by a modified $H^1$-norm. We prove its global convergence to a critical point of the discrete GP energy and its local exponential convergence to the ground state of the discrete GP energy. The local exponential convergence rate depends on the eigengap of the discrete GP energy. When the discretization is the classical second-order finite difference in two dimensions, such an eigengap can be further proven to be mesh independent, i.e., it has a uniform positive lower bound, thus the local exponential convergence rate is mesh independent. Numerical experiments with discretization by high order $Q^k$ spectral element methods in two and three dimensions are provided to validate the efficiency of the proposed method.

We investigate personalizing the explanations that an Intelligent Tutoring System generates to justify the hints it provides to students to foster their learning. The personalization targets students with low levels of two traits, Need for Cognition and Conscientiousness, and aims to enhance these students' engagement with the explanations, based on prior findings that these students do not naturally engage with the explanations but they would benefit from them if they do. To evaluate the effectiveness of the personalization, we conducted a user study where we found that our proposed personalization significantly increases our target users' interaction with the hint explanations, their understanding of the hints and their learning. Hence, this work provides valuable insights into effectively personalizing AI-driven explanations for cognitively demanding tasks such as learning.