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1. Language measures correlate with other measures used to study emotion

   https://doi.org/10.1038/s44271-025-00212-x  

   Munin, Shaina; Ong, Desmond_C; Okland, Sydney; Freedman, Gili; Beer, Jennifer_S (February 2025, Communications Psychology)

   Abstract Researchers are increasingly using language measures to study emotion, yet less is known about whether language relates to other measures often used to study emotion. Building on previous work which focuses on associations between language and self-report, we test associations between language and a broader range of measures (self-report, observer report, facial cues, vocal cues). Furthermore, we examine associations across different dictionaries (LIWC-22, NRC, Lexical Suite, ANEW, VADER) used to estimate valence (i.e., positive versus negative emotion) or discrete emotions (i.e., anger, fear, sadness) in language. Associations were tested in three large, multimodal datasets (Ns = 193–1856; average word count = 316.7–2782.8). Language consistently related to observer report and consistently related to self-report in two of the three datasets. Statistically significant associations between language and facial cues emerged for language measures of valence but not for language measures of discrete emotions. Language did not consistently show significant associations with vocal cues. Results did not tend to significantly vary across dictionaries. The current research suggests that language measures (in particular, language measures of valence) are correlated with a range of other measures used to study emotion. Therefore, researchers may wish to use language to study emotion when other measures are unavailable or impractical for their research question. 

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2. Dynamical Coherence Measures

   Vershynina, Anna (January 2024, arXivorg)

   We present several measures of the dynamic coherence of channels and investigate their properties. 

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3. Noncommutative rational Clark measures

   https://doi.org/10.4153/S0008414X22000384  

   Jury, Michael T.; Martin, Robert T.W.; Shamovich, Eli (July 2022, Canadian Journal of Mathematics)

   Abstract We characterize the noncommutative Aleksandrov–Clark measures and the minimal realization formulas of contractive and, in particular, isometric noncommutative rational multipliers of the Fock space. Here, the full Fock space over $$\mathbb {C} ^d$$ is defined as the Hilbert space of square-summable power series in several noncommuting (NC) formal variables, and we interpret this space as the noncommutative and multivariable analogue of the Hardy space of square-summable Taylor series in the complex unit disk. We further obtain analogues of several classical results in Aleksandrov–Clark measure theory for noncommutative and contractive rational multipliers. Noncommutative measures are defined as positive linear functionals on a certain self-adjoint subspace of the Cuntz–Toeplitz algebra, the unital $C^*$ -algebra generated by the left creation operators on the full Fock space. Our results demonstrate that there is a fundamental relationship between NC Hardy space theory, representation theory of the Cuntz–Toeplitz and Cuntz algebras, and the emerging field of noncommutative rational functions. 

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4. Centrality measures in networks

   https://doi.org/10.1007/s00355-023-01456-4  

   Bloch, Francis; Jackson, Matthew O.; Tebaldi, Pietro (April 2023, Social Choice and Welfare)
5. Truthfulness of Calibration Measures

   Haghtalab, Nika; Qiao, Mingda; Yang, Kunhe; Zhao, Eric (December 2024, Advances in Neural Information Processing Systems)

   We study calibration measures in a sequential prediction setup. In addition to rewarding accurate predictions (completeness) and penalizing incorrect ones (soundness), an important desideratum of calibration measures is truthfulness, a minimal condition for the forecaster not to be incentivized to exploit the system. Formally, a calibration measure is truthful if the forecaster (approximately) minimizes the expected penalty by predicting the conditional expectation of the next outcome, given the prior distribution of outcomes. We conduct a taxonomy of existing calibration measures. Perhaps surprisingly, all of them are far from being truthful. We introduce a new calibration measure termed the Subsampled Smooth Calibration Error (SSCE), which is complete and sound, and under which truthful prediction is optimal up to a constant multiplicative factor. In contrast, under existing calibration measures, there are simple distributions on which a polylogarithmic (or even zero) penalty is achievable, while truthful prediction leads to a polynomial penalty. 

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