We consider the problem of functional decomposition of univariate sparse polynomials. Suppose \(f\in {\mathsf {F}}[x]\) is a polynomial over a field \({\mathsf {F}}\) which has a non-trivial decomposition into \(g,h\in {\mathsf {F}}[x]\) such that f(x) = g(h(x)). Given f and \(\deg g\), our algorithm produces both decomposition factors \(g,h\in {\mathsf {F}}[x]\) in polynomial time in the number of nonzero terms in f, h, the degree of g, and \(\log \deg f\). Work by Zannier implies that \(\deg g\) is typically bounded quadratically by the number of non-zero terms of f, so that we can say the algorithm runs in polynomial time in the sparse sizes of the inputs and outputs. Our algorithm works when the characteristic of \({\mathsf {F}}\) is 0 or does not divide \(\deg g\). We also develop a heuristic and probabilistic classifier, based on random sampling of evaluations in a finite field, which can (on average) distinguish whether a given polynomial is decomposable or not, in sub-linear time in \(\deg f\). Finally, we give a generalization to sparse systems of linear differential equations.

We propose Adaptive Randomized Smoothing (ARS) to certify the predictions of our test-time adaptive models against adversarial examples. ARS extends the analysis of randomized smoothing using $f$-Differential Privacy to certify the adaptive composition of multiple steps. For the first time, our theory covers the sound adaptive composition of general and high-dimensional functions of noisy inputs. We instantiate ARS on deep image classification to certify predictions against adversarial examples of bounded $L_{\infty}$ norm. In the $L_{\infty}$ threat model, ARS enables flexible adaptation through high-dimensional input-dependent masking. We design adaptivity benchmarks, based on CIFAR-10 and CelebA, and show that ARS improves standard test accuracy by 1 to 15\% points. On ImageNet, ARS improves certified test accuracy by up to 1.6% points over standard RS without adaptivity. Our code is available at [https://github.com/ubc-systopia/adaptive-randomized-smoothing](https://github.com/ubc-systopia/adaptive-randomized-smoothing).

The 2011 Fukushima Daiichi nuclear disaster has led to worldwide disruptive discussions related to crisis. In April 2021, the news that the Japanese Cabinet decided to discharge the stored wastewater into the Pacific Ocean drew global attention once again. Social media platforms like Twitter are ubiquitously used to gain information and exchange opinions during and after a crisis. Analyzing crisis-related tweets can help capture insights for public situational awareness development, crisis global response coordination, and post-disaster policy-making. We examined corresponding Twitter discourse in different languages about the nuclear disaster in 2011 and the follow-up discharge of the stored water until 2021. We utilized NLP techniques including topic modeling and sentiment analysis to identify the dominant topics related to the nuclear disaster, the post-disaster discourses, and the public attitudes towards these topics in different time phases. Our work revealed multilingual disparities of post-disaster discourse dynamics and the regional public attitudes towards the post-disaster management in the long run.