Exact multi-parameter persistent homology of time-series data: one-dimensional reduction of multi-parameter persistence theory

In various applications of data classification and clustering problems, multi-parameter analysis is effective and crucial because data are usually defined in multi-parametric space. Multi-parameter persistent homology, an extension of persistent homology of one-parameter data analysis, has been developed for topological data analysis (TDA). Although it is conceptually attractive, multi-parameter persistent homology still has challenges in theory and practical applications. In this study, we consider time-series data and its classification and clustering problems using multi-parameter persistent homology. We develop a multi-parameter filtration method based on Fourier decomposition and provide an exact formula and its interpretation of one-dimensional reduction of multi-parameter persistent homology. The exact formula implies that the one-dimensional reduction of multi-parameter persistent homology of the given time-series data is equivalent to choosing diagonal ray (standard ray) in the multi-parameter filtration space. For this, we first consider the continuousization of time-series data based on Fourier decomposition towards the construction of the exact persistent barcode formula for the Vietoris-Rips complex of the point cloud generated by sliding window embedding. The proposed method is highly efficient even if the sliding window embedding dimension and the length of time-series data are large because the method precomputes the exact barcode and the computational complexity is as low as the fast Fourier transformation of $O(N \log N)$. Further the proposed method provides a way of finding different topological inferences by trying different rays in the filtration space in no time.Comment: 29 page

Supervised low-rank semi-nonnegative matrix factorization with frequency regularization for forecasting spatio-temporal data

We propose a novel methodology for forecasting spatio-temporal data using supervised semi-nonnegative matrix factorization (SSNMF) with frequency regularization. Matrix factorization is employed to decompose spatio-temporal data into spatial and temporal components. To improve clarity in the temporal patterns, we introduce a nonnegativity constraint on the time domain along with regularization in the frequency domain. Specifically, regularization in the frequency domain involves selecting features in the frequency space, making an interpretation in the frequency domain more convenient. We propose two methods in the frequency domain: soft and hard regularizations, and provide convergence guarantees to first-order stationary points of the corresponding constrained optimization problem. While our primary motivation stems from geophysical data analysis based on GRACE (Gravity Recovery and Climate Experiment) data, our methodology has the potential for wider application. Consequently, when applying our methodology to GRACE data, we find that the results with the proposed methodology are comparable to previous research in the field of geophysical sciences but offer clearer interpretability.Comment: 34 page

Rotting infinitely many-armed bandits

We consider the infinitely many-armed bandit problem with rotting rewards, where the mean reward of an arm decreases at each pull of the arm according to an arbitrary trend with maximum rotting rate ϱ=o(1). We show that this learning problem has an Ω(max{ϱ1/3T,T−−√}) worst-case regret lower bound where T is the time horizon. We show that a matching upper bound O~(max{ϱ1/3T,T−−√}), up to a poly-logarithmic factor, can be achieved by an algorithm that uses a UCB index for each arm and a threshold value to decide whether to continue pulling an arm or remove the arm from further consideration, when the algorithm knows the value of the maximum rotting rate ϱ. We also show that an O~(max{ϱ1/3T,T3/4}) regret upper bound can be achieved by an algorithm that does not know the value of ϱ, by using an adaptive UCB index along with an adaptive threshold value

Contextual Linear Bandits under Noisy Features: Towards Bayesian Oracles

We study contextual linear bandit problems under uncertainty on features; they are noisy with missing entries. To address the challenges from the noise, we analyze Bayesian oracles given observed noisy features. Our Bayesian analysis finds that the optimal hypothesis can be far from the underlying realizability function, depending on noise characteristics, which is highly non-intuitive and does not occur for classical noiseless setups. This implies that classical approaches cannot guarantee a non-trivial regret bound. We thus propose an algorithm aiming at the Bayesian oracle from observed information under this model, achieving $\tilde{O}(d\sqrt{T})$ regret bound with respect to feature dimension $d$ and time horizon $T$. We demonstrate the proposed algorithm using synthetic and real-world datasets.Comment: 30 page

Are Histrionic Personality Traits Associated with Irritability during Conscious Sedation Endoscopy?

Aim. We aimed to evaluate whether histrionic personality traits are associated with irritability during conscious sedation endoscopy (CSE). Materials and Methods. A prospective cross-sectional study was planned. Irritability during CSE was classified into five grades: 0, no response; I, minimal movement; II, moderate movement; III, severe movement; IV, fighting against procedure. Patients in grades III and IV were defined as the irritable group. Participants were required to complete questionnaire sheet assessing the extent of histrionic personality traits, extraversion-introversion, and current psychological status. The present authors also collected basic sociodemographic data including alcohol use history. Results. A total of 32 irritable patients and 32 stable patients were analyzed. The histrionic personality trait score of the irritable group was higher than that of the stable group (9.5 ± 3.1 versus 6.9 ± 2.9; P = 0.001), as was the anxiety score (52.8 ± 8.6 versus 46.1 ± 9.6; P = 0.004). Heavy alcohol use was more frequently observed in the irritable group (65.6% versus 28.1%; P = 0.003). In multivariate analysis, all these three factors were independently correlated with irritability during CSE. Conclusion. This study revealed that histrionic personality traits, anxiety, and heavy alcohol use can affect irritability during CSE

Primary Candida guilliermondii Infection of the Knee in a Patient without Predisposing Factors

Isolated primary candidal infection of joint is extremely rare, with only a few reported cases. It occurs as a result of accidental implantations of fungus during traumatic procedures, such as surgery, and is usually reported in patients with predisposing factors such as immunosuppression, malignancy, and drug abuse. If left untreated, irreversible deformity and pain with severe osteoarticular destruction occur. Thus, early diagnosis and treatment are important. This paper presents a case of 72-year-old man with primary C. guilliermondii infection of knee joint without predisposing factors and previous traumatic procedures, who was misdiagnosed with advanced degenerative osteoarthritis. Our case is the second case of primary C. guilliermondii arthritis of knee to be reported in the English-language literature and the first to be successfully treated with total knee arthroplasty following IV amphotericin B and oral fluconazole. Primary candidal infection of joint is generally asymptomatic or involves only mild pain and swelling in the affected knee. Thus, although the majority of knee joint infections are of a pyogenic or tuberculous origin, if a patient complains of mild pain and swelling in the knee and has mild signs of infection, the possibility of fungal infection should be considered