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1. Generalization of the two-point-source resolution criterion in the presence of noise

   https://doi.org/10.1364/OL.494910  

   Wani, Pranav; Usmani, Kashif; Javidi, Bahram (July 2023, Optics Letters)

   The two-point-source resolution criterion is widely used to quantify the performance of imaging systems. The two main approaches for the computation of the two-point-source resolution are the detection theoretic and visual analyses. The first assumes a shift-invariant system and lacks the ability to incorporate two different point spread functions (PSFs), which may be required in certain situations like computing axial resolution. The latter approach, which includes the Rayleigh criterion, relies on the peak-to-valley ratio and does not properly account for the presence of noise. We present a heuristic generalization of the visual two-point-source resolution criterion using Gaussian processes (GP). This heuristic criterion is applicable to both shift-invariant and shift-variant imaging modalities. This criterion can also incorporate different definitions of resolution expressed in terms of varying peak-to-valley ratios. Our approach implicitly incorporates information about noise statistics such as the variance or signal-to-noise ratio by making assumptions about the spatial correlation of PSFs in the form of kernel functions. Also, it does not rely on an analytic form of the PSF. 

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2. Dynamics and Persistence of a Generalized Multi-strain SIS Model

   https://doi.org/10.1007/s11538-025-01516-z  

   Greenhalgh, Scott; Henriquez, Tabitha; Frutschy, Michael; Leonard, Rebecah (September 2025, Bulletin of Mathematical Biology)

   Abstract Autonomous differential equation compartmental models hold broad utility in epidemiology and public health. However, these models typically cannot account explicitly for myriad factors that affect the trajectory of infectious diseases, with seasonal variations in host behavior and environmental conditions as noteworthy examples. Fortunately, using non-autonomous differential equation compartmental models can mitigate some of these deficiencies, as the inclusion of time-varying parameters can account for temporally varying factors. The inclusion of these temporally varying factors does come at a cost though, as many analysis techniques, such as the use of Poincaré maps and Floquet theory, on non-autonomous differential equation compartmental models are typically only tractable numerically. Here, we illustrate a rare$$n$$ $n$-strain generalized Susceptible-Infectious-Susceptible (SIS) compartmental model, with a general time-varying recovery rate, which features Floquet exponents that are algebraic expressions. We completely characterize the persistence and stability properties of our$$n$$ $n$-strain generalized SIS model for$$n\ge 1$$ $n\ge 1$. We also derive a closed-form solution in terms of elementary functions for the single-strain SIS model, which is capable of incorporating almost any infectious period distribution. Finally, to demonstrate the applicability of our work, we apply it to recent syphilis incidence data from the United States, utilizing Akaike Information Criteria and Forecast Skill Scores to inform on the model’s goodness of fit relative to complexity and the model’s capacity to predict future trends. 

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3. The Power of the Hybrid Model for Mean Estimation

   https://doi.org/10.2478/popets-2020-0062  

   Avent, Brendan; Dubey, Yatharth; Korolova, Aleksandra (August 2020, Proceedings on Privacy Enhancing Technologies)

   null (Ed.)

   Abstract We explore the power of the hybrid model of differential privacy (DP), in which some users desire the guarantees of the local model of DP and others are content with receiving the trusted-curator model guarantees. In particular, we study the utility of hybrid model estimators that compute the mean of arbitrary realvalued distributions with bounded support. When the curator knows the distribution’s variance, we design a hybrid estimator that, for realistic datasets and parameter settings, achieves a constant factor improvement over natural baselines.We then analytically characterize how the estimator’s utility is parameterized by the problem setting and parameter choices. When the distribution’s variance is unknown, we design a heuristic hybrid estimator and analyze how it compares to the baselines. We find that it often performs better than the baselines, and sometimes almost as well as the known-variance estimator. We then answer the question of how our estimator’s utility is affected when users’ data are not drawn from the same distribution, but rather from distributions dependent on their trust model preference. Concretely, we examine the implications of the two groups’ distributions diverging and show that in some cases, our estimators maintain fairly high utility. We then demonstrate how our hybrid estimator can be incorporated as a sub-component in more complex, higher-dimensional applications. Finally, we propose a new privacy amplification notion for the hybrid model that emerges due to interaction between the groups, and derive corresponding amplification results for our hybrid estimators. 

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4. Privacy-Preserving Policy Synthesis in Markov Decision Processes

   https://doi.org/10.1109/CDC42340.2020.9304015  

   Gohari, Parham; Hale, Matthew; Topcu, Ufuk (December 2020, Proceedings of the 2020 59th IEEE Conference on Decision and Control (CDC))

   null (Ed.)

   In decision-making problems, the actions of an agent may reveal sensitive information that drives its decisions. For instance, a corporation’s investment decisions may reveal its sensitive knowledge about market dynamics. To prevent this type of information leakage, we introduce a policy synthesis algorithm that protects the privacy of the transition probabilities in a Markov decision process. We use differential privacy as the mathematical definition of privacy. The algorithm first perturbs the transition probabilities using a mechanism that provides differential privacy. Then, based on the privatized transition probabilities, we synthesize a policy using dynamic programming. Our main contribution is to bound the "cost of privacy," i.e., the difference between the expected total rewards with privacy and the expected total rewards without privacy. We also show that computing the cost of privacy has time complexity that is polynomial in the parameters of the problem. Moreover, we establish that the cost of privacy increases with the strength of differential privacy protections, and we quantify this increase. Finally, numerical experiments on two example environments validate the established relationship between the cost of privacy and the strength of data privacy protections. 

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5. Registered Replication Report: A Large Multilab Cross-Cultural Conceptual Replication of Turri et al. (2015)

   https://doi.org/10.1177/25152459241267902  

   Hall, Braeden; Schmidt, Kathleen; Wagge, Jordan; Lewis, Savannah C; Weissgerber, Sophia C; Kiunke, Felix; Pfuhl, Gerit; Stieger, Stefan; Tran, Ulrich S; Barzykowski, Krystian; et al (October 2024, Advances in Methods and Practices in Psychological Science)

   According to the justified true belief (JTB) account of knowledge, people can truly know something only if they have a belief that is both justified and true (i.e., knowledge is JTB). This account was challenged by Gettier, who argued that JTB does not explain knowledge attributions in certain situations, later called “Gettier-type cases,” wherein protagonists are justified in believing something to be true, but their belief was correct only because of luck. Laypeople may not attribute knowledge to protagonists with justified but only luckily true beliefs. Although some research has found evidence for these so-called Gettier intuitions, Turri et al. found no evidence that participants attributed knowledge in a counterfeit-object Gettier-type case differently than in a matched case of JTB. In a large-scale, cross-cultural conceptual replication of Turri and colleagues’ Experiment 1 ( N = 4,724) using a within-participants design and three vignettes across 19 geopolitical regions, we did find evidence for Gettier intuitions; participants were 1.86 times more likely to attribute knowledge to protagonists in standard cases of JTB than to protagonists in Gettier-type cases. These results suggest that Gettier intuitions may be detectable across different scenarios and cultural contexts. However, the size of the Gettier intuition effect did vary by vignette, and the Turri et al. vignette produced the smallest effect, which was similar in size to that observed in the original study. Differences across vignettes suggest that epistemic intuitions may also depend on contextual factors unrelated to the criteria of knowledge, such as the characteristics of the protagonist being evaluated. 

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