Noisy population recovery in polynomial time

In the noisy population recovery problem of Dvir et al., the goal is to learn an unknown distribution $f$ on binary strings of length $n$ from noisy samples. For some parameter $\mu \in [0,1]$, a noisy sample is generated by flipping each coordinate of a sample from $f$ independently with probability $(1-\mu)/2$. We assume an upper bound $k$ on the size of the support of the distribution, and the goal is to estimate the probability of any string to within some given error $\varepsilon$. It is known that the algorithmic complexity and sample complexity of this problem are polynomially related to each other. We show that for $\mu > 0$, the sample complexity (and hence the algorithmic complexity) is bounded by a polynomial in $k$, $n$ and $1/\varepsilon$ improving upon the previous best result of $\mathsf{poly}(k^{\log\log k},n,1/\varepsilon)$ due to Lovett and Zhang. Our proof combines ideas from Lovett and Zhang with a \emph{noise attenuated} version of M\"{o}bius inversion. In turn, the latter crucially uses the construction of \emph{robust local inverse} due to Moitra and Saks

Research trends of ferroptosis and pyroptosis in Parkinson’s disease: a bibliometric analysis

ObjectiveThis study aims to visualize the trends and hotspots in the research of “ferroptosis in PD” and “pyroptosis in PD” through bibliometric analysis from the past to 2024.MethodsLiterature was retrieved from the Web of Science Core Collection (WoSCC) from the past to February 16, 2024, and bibliometric analysis was conducted using Vosviewer and Citespace.Results283 and 542 papers were collected in the field of “ferroptosis in PD” and “pyroptosis in PD.” The number of publications in both fields has increased yearly, especially in “ferroptosis in PD,” which will become the focus of PD research. China, the United States and England had extensive exchanges and collaborations in both fields, and more than 60% of the top 10 institutions were from China. In the fields of “ferroptosis in PD” and “pyroptosis in PD,” the University of Melbourne and Nanjing Medical University stood out in terms of publication numbers, citation frequency, and centrality, and the most influential journals were Cell and Nature, respectively. The keyword time zone map showed that molecular mechanisms and neurons were the research hotspots of “ferroptosis in PD” in 2023, while memory and receptor 2 were the research hotspots of “pyroptosis in PD” in 2023, which may predict the future research direction.ConclusionThis study provides insights into the development, collaborations, research themes, hotspots, and tendencies of “ferroptosis in PD” and “pyroptosis in PD.” Overall situation of these fields is available for researchers to further explore the underlying mechanisms and potential treatments