Codes for Correcting Asymmetric Adjacent Transpositions and Deletions

Codes in the Damerau--Levenshtein metric have been extensively studied recently owing to their applications in DNA-based data storage. In particular, Gabrys, Yaakobi, and Milenkovic (2017) designed a length-$n$ code correcting a single deletion and $s$ adjacent transpositions with at most $(1+2s)\log n$ bits of redundancy. In this work, we consider a new setting where both asymmetric adjacent transpositions (also known as right-shifts or left-shifts) and deletions may occur. We present several constructions of the codes correcting these errors in various cases. In particular, we design a code correcting a single deletion, $s^+$ right-shift, and $s^-$ left-shift errors with at most $(1+s)\log (n+s+1)+1$ bits of redundancy where $s=s^{+}+s^{-}$. In addition, we investigate codes correcting $t$ $0$-deletions, $s^+$ right-shift, and $s^-$ left-shift errors with both uniquely-decoding and list-decoding algorithms. Our main contribution here is the construction of a list-decodable code with list size $O(n^{\min\{s+1,t\}})$ and with at most $(\max \{t,s+1\}) \log n+O(1)$ bits of redundancy, where $s=s^{+}+s^{-}$. Finally, we construct both non-systematic and systematic codes for correcting blocks of $0$-deletions with $\ell$-limited-magnitude and $s$ adjacent transpositions

Achieving the Pareto Frontier of Regret Minimization and Best Arm Identification in Multi-Armed Bandits

We study the Pareto frontier of two archetypal objectives in multi-armed bandits, namely, regret minimization (RM) and best arm identification (BAI) with a fixed horizon. It is folklore that the balance between exploitation and exploration is crucial for both RM and BAI, but exploration is more critical in achieving the optimal performance for the latter objective. To this end, we design and analyze the BoBW-lil'UCB$(\gamma)$ algorithm. Complementarily, by establishing lower bounds on the regret achievable by any algorithm with a given BAI failure probability, we show that (i) no algorithm can simultaneously perform optimally for both the RM and BAI objectives, and (ii) BoBW-lil'UCB$(\gamma)$ achieves order-wise optimal performance for RM or BAI under different values of $\gamma$. Our work elucidates the trade-off more precisely by showing how the constants in previous works depend on certain hardness parameters. Finally, we show that BoBW-lil'UCB outperforms a close competitor UCB$_\alpha$ (Degenne et al., 2019) in terms of the time complexity and the regret on diverse datasets such as MovieLens and Published Kinase Inhibitor Set.Comment: 43 pages, 10 figure

Learning Regularized Graphon Mean-Field Games with Unknown Graphons

We design and analyze reinforcement learning algorithms for Graphon Mean-Field Games (GMFGs). In contrast to previous works that require the precise values of the graphons, we aim to learn the Nash Equilibrium (NE) of the regularized GMFGs when the graphons are unknown. Our contributions are threefold. First, we propose the Proximal Policy Optimization for GMFG (GMFG-PPO) algorithm and show that it converges at a rate of $O(T^{-1/3})$ after $T$ iterations with an estimation oracle, improving on a previous work by Xie et al. (ICML, 2021). Second, using kernel embedding of distributions, we design efficient algorithms to estimate the transition kernels, reward functions, and graphons from sampled agents. Convergence rates are then derived when the positions of the agents are either known or unknown. Results for the combination of the optimization algorithm GMFG-PPO and the estimation algorithm are then provided. These algorithms are the first specifically designed for learning graphons from sampled agents. Finally, the efficacy of the proposed algorithms are corroborated through simulations. These simulations demonstrate that learning the unknown graphons reduces the exploitability effectively

Designing and Optimizing a Healthcare Kiosk for the Community

Investigating new ways to deliver care, such as the use of self-service kiosks to collect and monitor signs of wellness, supports healthcare efficiency and inclusivity. Self-service kiosks offer this potential, but there is a need for solutions to meet acceptable standards, e.g., provision of accurate measurements. This study investigates the design and optimization of a prototype healthcare kiosk to collect vital signs measures. The design problem was decomposed, formalized, focused and used to generate multiple solutions. Systematic implementation and evaluation allowed for the optimization of measurement accuracy, first for individuals and then for a population. The optimized solution was tested independently to check the suitability of the methods, and quality of the solution. The process resulted in a reduction of measurement noise and an optimal fit, in terms of the positioning of measurement devices. This guaranteed the accuracy of the solution and provides a general methodology for similar design problems

Free-hand thoracic pedicle screws placed by neurosurgery residents: a CT analysis

Free-hand thoracic pedicle screw placement is becoming more prevalent within neurosurgery residency training programs. This technique implements anatomic landmarks and tactile palpation without fluoroscopy or navigation to place thoracic pedicle screws. Because this technique is performed by surgeons in training, we wished to analyze the rate at which these screws were properly placed by residents by retrospectively reviewing the accuracy of resident-placed free-hand thoracic pedicle screws using computed tomography imaging. A total of 268 resident-placed thoracic pedicle screws was analyzed using axial computed tomography by an independent attending neuroradiologist. Eighty-five percent of the screws were completely within the pedicle and that 15% of the screws violated the pedicle cortex. The majority of the breaches were lateral breaches between 2 and 4 mm (46%). There was no clinical evidence of neurovascular injury or injury to the esophagus. There were no re-operations for screw replacement. We concluded that under appropriate supervision, neurosurgery residents can safely place free-hand thoracic pedicle screws with an acceptable breach rate