Background: Some patients present clinical features of both asthma and chronic obstructive pulmonary disease (COPD), which has led to the recent proposal of asthma-COPD overlap (ACO) as a diagnosis. Fractional exhaled nitric oxide (FeNO) is a candidate biomarker to diagnose ACO. We assessed the effect of an add-on treatment with budesonide/formoterol (BUD/FM) combination in patients with ACO, which was diagnosed by FeNO. Methods: This was a prospective, single-arm, open-label, before and after comparison study. Subjects included 83 patients with COPD who attended outpatient clinics for routine checkups at Shizuoka General Hospital between June and November 2016. All patients fulfilled the GOLD definition of COPD and were receiving long-acting muscarinic antagonist (LAMA) or LAMA/long-acting β_{2} agonist (LABA) combinations. After an 8-week run-in period, BUD/FM was added to the patients with FeNO levels of ≥35 ppb, defined as having ACO. For patients receiving LAMA/LABA, BUD/FM was added after the discontinuation of LABA. The modified British Medical Research Council (mMRC) score, COPD assessment test (CAT) score, spirometric indices, forced oscillation parameters, and FeNO were assessed before and after 8 weeks of BUD/ FM add-on treatment. Results: Twenty-four patients (28.9%) had FeNO levels ≥ 35 ppb, and 17 patients completed the study (mean age: 73 years and GOLD I/II/III/IV, 5/10/1/1). The mean CAT scores significantly improved (9.2 to 5.4, p = 0.015) and 10 patients (58.8%) showed ≥2 points improvement, a minimal clinically important difference. The mean FeNO levels significantly decreased from 63.0 to 34.3 ppb (p < 0.006). However, there were no changes in mMRC scores, spirometric indices, or forced oscillation parameters. Conclusions: FeNO-guided treatment with BUD/FM improves symptoms in patients with ACO.

Abstract:
A one-dimensional dynamical system with a marginal quasiperiodic gradient is presented as a mathematical extension of a nonuniform oscillator. The system exhibits a nonchaotic stagnant motion, which is reminiscent of intermittent chaos. In fact, the density function of residence times near stagnation points obeys an inverse-square law, due to a mechanism similar to type-I intermittency. However, unlike intermittent chaos, in which the alternation between long stagnant phases and rapid moving phases occurs in a random manner, here the alternation occurs in a quasiperiodic manner. In particular, in case of a gradient with the golden ratio, the renewal of the largest residence time occurs at positions corresponding to the Fibonacci sequence. Finally, the asymptotic long-time behavior, in the form of a nested logarithm, is theoretically derived. Compared with the Pomeau-Manneville intermittency, a significant difference in the relaxation property of the long-time average of the dynamical variable is found.

Abstract:
A finite element approximation of the Stokes equations under a certain nonlinear boundary condition, namely, the slip or leak boundary condition of friction type, is considered. We propose an approximate problem formulated by a variational inequality, prove an existence and uniqueness result, present an error estimate, and discuss a numerical realization using an iterative Uzawa-type method. Several numerical examples are provided to support our theoretical results.

Abstract:
F\'{e}lix and Thomas developed string topology of Chas and Sullivan on simply-connected Gorenstein spaces. In this paper, we prove that the degree shifted homology of the free loop space of a simply-connected ${\mathbb Q}$-Gorenstein space with rational coefficient is a non-unital and non-counital Frobenius algebra by solving the up to constant problem. We also investigate triviality or non-triviality of the loop product and coproduct of particular Gorenstein spaces.

Abstract:
Samuel J. Lomonaco Jr and Louis H. Kauffman conjectured that tame knot theory and knot mosaic theory are equivalent. We give a proof of the Lomonaco-Kauffman conjecture.

Abstract:
We give a proof of the LMO conjecture which say that for any simply connectd simple Lie group $G$, the LMO invariant of rational homology 3-spheres recovers the perturvative invariant $\tau^{PG}$. By Habiro-Le theorem, this implies that the LMO invariant is the universal quantum invariant of integral homology 3-spheres.

Abstract:
We investigate the moduli sets of central extensions of H-spaces enjoying inversivity, power associativity and Moufang properties. By considering rational H-extensions, it turns out that there is no relationship between the first and the second properties in general.

Abstract:
We describe the Whitehead products in the rational homotopy group of a connected component of a mapping space in terms of the Andr\'{e}-Quillen cohomology. As a consequence, an upper bound for the Whitehead length of a mapping space is given.

Abstract:
Strong solutions of the non-stationary Navier-Stokes equations under non-linearized slip or leak boundary conditions are investigated. We show that the problems are formulated by a variational inequality of parabolic type, to which uniqueness is established. Using Galerkin's method and deriving a priori estimates, we prove global and local existence for 2D and 3D slip problems respectively. For leak problems, under no-leak assumption at $t=0$ we prove local existence in 2D and 3D cases. Compatibility conditions for initial states play a significant role in the estimates.

Abstract:
Objective. The aim of this study is to develop a prognostic model capable of predicting the probability of significant upgrading among Japanese patients. Methods. The study cohort comprised 508 men treated with RP, with available prostate-specific antigen levels, biopsy, and RP Gleason sum values. Clinical and pathological data from 258 patients were obtained from another Japanese institution for validation. Results. Significant Gleason sum upgrading was recorded in 92 patients (18.1%) at RP. The accuracy of the nomogram predicting the probability of significant Gleason sum upgrading between biopsy and RP specimens was 88.9%. Overall AUC was 0.872 when applied to the validation data set. Nomogram predictions of significant upgrading were within 7.5% of an ideal nomogram. Conclusions. Nearly one-fifth of Japanese patients with prostate cancer will be significantly upgraded. Our nomogram seems to provide considerably accurate predictions regardless of minor variations in pathological assessment when applied to Japanese patient populations. 1. Introduction Pretreatment prostate-specific antigen (PSA) level, Gleason score, and pathological stage are generally recognized as significant predictors of biochemical recurrence in patients with clinically localized prostate cancer treated by radical prostatectomy (RP) [1]. A finding of high-grade disease in RP specimens is an adverse prognostic factor, and such tumors are significantly more likely to progress than organ-confined cancers. In addition, this finding is associated with a greater risk of positive surgical margins, further decreasing the likelihood of long-term cancer control. Determining whether a patient has high-grade disease is thus important for treatment selection and prognosis [2]. Chun et al. developed and validated a model predicting Gleason sum upgrading from biopsy to final pathology using clinical variables (PSA level, clinical stage, and biopsy Gleason sum) [3]. That model relies on three readily available clinical variables, all of which are significant uni- and multivariate predictors of biopsy Gleason sum upgrading. Based on the importance of the concept of Gleason sum upgrading in decision making for prostate cancer, we previously performed a formal external validation using a fully independent data set in a contemporary cohort of two Japanese institutions [4]. Unfortunately, our results did not suggest that accurate predictions may be expected when using this nomogram across different racial patient populations. Development of a nomogram predicting the probability of biopsy Gleason sum