a b s t r a c t Tarski's fixed point theorem guarantees the existence of a fixed point of an orderpreserving function f : L → L defined on a nonempty complete lattice (L, ) [B. Knaster, Un théorème sur les fonctions d'ensembles, Annales de la Société Polonaise de Mathématique 6 (1928) 133-134; A. Tarski, A lattice theoretical fixpoint theorem and its applications, Pacific Journal of Mathematics 5 (1955) 285-309].In this paper, we investigate several algorithmic and complexity-theoretic topics regarding Tarski's fixed point theorem. In particular, we design an algorithm that finds a fixed point of f when it is given (L, ) as input and f as an oracle. Our algorithm makes O(log | L |) queries to f when is a total order on L. We also prove that when both f and (L, ) are given as oracles, any deterministic or randomized algorithm for finding a fixed point of f makes an expected Ω(| L |) queries for some (L, ) and f .

In health care, medication errors can result in serious health risks to patients, and hospitals require a secure medication administration system to prevent such errors. This paper therefore proposes a secure medication administration method based on threshold sharing technology. When a patient visits a doctor and the doctor prescribes n medications, a photo and the personal information of the patient are encoded into n QR code transparencies that can be decoded by common QR code scanners available for smartphones. The prescription and n QR code transparencies are then stored in a hospital’s medication administration system. When the patient receives their medicine, they can scan these n QR code transparencies using a smartphone to ensure that they have all the medicines prescribed by the doctor; this function is accessible even if the patient’s phone does not have Internet access. The main purpose of the proposed system is to prevent hospitals from giving medicine to the wrong patient, or giving less than the prescribed dosage of medicine to the patient. The focus is not on the internal medicine packaging process in hospitals but on reducing the probability of counter staff giving medicine to the wrong patient. This function is of considerable importance to non-English-speaking people who are not used to reading medicine names in English.

Detecting financial fraud to profile crimes and pinpoint system vulnerabilities is an essential issue in the financial industry. Because of interpretability requirements and the lack of mass transaction data due to privacy regulations, sophisticated handcrafted features have been adopted in much of the literature for fraud detection. In addition to established recency, frequency, monetary, and anomaly features, we propose behavior-and segmentation-type features based on statistical characteristics belonging solely to (non-)fraudulent accounts informed by financial expertise. Our proposed features are difficult for automatic feature generators to synthesize, and provide transparent cause-effect relationships and good prediction results. Features with time-inhomogeneous properties cause popular boosting classifiers such as XGBoost and LGBM to produce unstable detection results. We use the Kolmogorov-Smirnov test to detect and remove these features to improve XGBoost and LGBM detection performance and robustness. The resulting performance shown in our experiments is better than that of other classifiers, such as SVM and random forests. We examine the advantage of our technique by comparing it with several feature engineering works on fraud detection and automatic feature generation methods. On the other hand, we also find that generating training/testing sets with random sampling falsely eliminates such time inhomogeneity and results in misleading assessments of the robustness of machine learning models. These time-inhomogeneous phenomena also entail various modus operandi patterns, which influence the performance of different resampling methods for addressing data imbalance in fraud detection. Improper linear interpolation of SMOTE-related approaches leads to poor performance due to varying patterns of modi operandi. However, synthesizing fraudulent samples with simple oversampling and GANs mitigates this problem.

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