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A partial inverse problem for non-self-adjoint Sturm-Liouville operators with a constant delay
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/125253
title: A partial inverse problem for non-self-adjoint Sturm-Liouville operators with a constant delay abstract: In this paper we study a partial inverse spectral problem for non-self-adjoint Sturm–Liouville operators with a constant delay and show that subspectra of two boundary value problems with one common boundary condition are sufficient to determine the complex potential. We developed the Horváth’s method in [M. Horváth, On the inverse spectral theory of Schrödinger and Dirac operators, Trans. Amer. Math. Soc. 353 2001, 10, 4155–4171] for the self-adjoint Sturm–Liouville operator without delay into the non-self-adjoint Sturm–Liouville differential operator with a constant delay.
<br>Convergence to traveling waves in reactiondiffusion systems with equal diffusivities
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/125143
title: Convergence to traveling waves in reactiondiffusion systems with equal diffusivities abstract: In this paper, we first derive a theorem on the convergence of solutions to traveling waves in reaction-diffusion systems with equal diffusivities. Then we apply this theorem to some specific examples of predator-prey models which were studied recently in the literature. This gives a stability result for these traveling waves in the corresponding predator-prey system under certain perturbations of initial data.
<br>Spreading dynamics for a predator-prey system with two predators and one prey in a shifting habitat
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/125142
title: Spreading dynamics for a predator-prey system with two predators and one prey in a shifting habitat abstract: We study the spreading dynamics for a three-species predator-prey system with two weak competing predators and one prey in a shifting habitat. First, we derive some extinction results for each species. Then we provide some persistence theorems for each species with moving speeds exceed the shifting speed, but less than some certain quantities. Finally, the convergence to a certain constant state is proven in each persistent regime.
<br>Prediction of human looking behavior using interest-based image representations
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/125141
title: Prediction of human looking behavior using interest-based image representations abstract: Looking behavior allows human to understand and interact with an enormous amount of information, a capacity challenging to replicate in AI systems. One of the core elements of this work is an effort to predict scan-paths from a combination of image information and past looking behavior. The success of this scan-path predication relies heavily on whether this image information can provide a sufficiently rich representation for prediction. In this paper, we show that changing representations dramatically simplifies and improves predictions of looking behavior. We introduce a representation of looking behavior that centers around interest-regions in images, defined by natural and collective looking behavior. These regions (called interest-based regions) can be used to partition images for semantic labeling and to provide a basis for shared representation across observers. Without any additional label or image information, we achieve highly accurate sequence prediction using this interest-based image representation.
<br>Forced waves for diffusive competition systems in shifting environments
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/125140
title: Forced waves for diffusive competition systems in shifting environments abstract: In this paper, we derive the existence of forced waves for diffusive competition systems in shifting environments. First, we derive two different classes of forced waves for a 3-species competition system. Then we obtain forced waves for 2-species competition systems with at least one weak competitor. In all cases, the minimal environmental shifting speeds are determined under the equal diffusivities condition.
<br>Forced waves of saturation type for Fisher–KPP equation in a shifting environment
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/125139
title: Forced waves of saturation type for Fisher–KPP equation in a shifting environment abstract: In this paper, we study the forced waves of the Fisher–KPP equation in a shifting environment. We introduce a new method to construct a sub-solution to derive the existence of forced waves without the monotonicity assumption on the shifting growth rate function. The forced waves we derived here are of the saturation type, in contrast to the extinction type in the literature
<br>Forced waves of a three species predator-prey system with a pair of weak-strong competing preys in a shifting environment
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/125098
title: Forced waves of a three species predator-prey system with a pair of weak-strong competing preys in a shifting environment abstract: In this paper, we investigate so-called forced wave solutions of a three components reaction-diffusion system from population dynamics. Our system involves three species that are respectively two competing preys and one predator; moreover, the competition between both preys is strong, i.e. in the absence of the predator, one prey is driven to extinction and the other survives. Furthermore, our problem includes a spatio-temporal heterogeneity in a moving variable that typically stands as a model for climate shift. In this context, forced waves are special stationary solutions which are expected to describe the large-time behavior of solutions, and in particular to provide criteria on the climate shift speed to allow survival of either of the three species. We will consider several types of forced waves to deal with various situations depending on which species are indigenous and which species are aboriginal.
<br>Deformation of the weighted scalar curvature
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/125097
title: Deformation of the weighted scalar curvature abstract: Inspired by the work of Fischer-Marsden [Duke Math. J. 42 (1975), 519-547], we study in this paper the deformation of the weighted scalar curvature. By studying the kernel of the formal L2ϕ
-adjoint for the linearization of the weighted scalar curvature, we prove several geometric results. In particular, we define a weighted vacuum static space, and study locally conformally flat weighted vacuum static spaces. We then prove some stability results of the weighted scalar curvature on flat spaces. Finally, we consider the prescribed weighted scalar curvature problem on closed smooth metric measure spaces.
<br>Yamabe solitons with boundary
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/124460
title: Yamabe solitons with boundary abstract: Yamabe soliton is a self-similar solution to the Yamabe flow on manifolds without boundary. In this paper, we define and study the Yamabe soliton with boundary and conformal mean curvature soliton, which are natural generalizations of the Yamabe soliton. We study these solitons from equation point of view. We also study their two-dimensional analog: the Gauss curvature soliton with boundary and geodesic curvature soliton.
<br>The weighted Yamabe flow with boundary
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/124459
title: The weighted Yamabe flow with boundaryWeighted Yamabe solitons
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/124458
title: Weighted Yamabe solitons abstract: In this paper, we first prove a Kazdan–Warner type identity for the problem of prescribing weighted scalar curvature. We then study weighted Yamabe solitons and prove some rigidity results.
<br>Sobolev inequality and isoperimetric inequality for submanifolds in a smooth metric measure space
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/124457
title: Sobolev inequality and isoperimetric inequality for submanifolds in a smooth metric measure space abstract: Brendle recently proved a sharp Sobolev inequality and logarithmic Sobolev inequality for submanifolds in Euclidean space. From the sharp Sobolev inequality, he achieved a breakthrough in the conjecture of isoperimetric inequality for minimal submanifolds. In this paper, we extend Brendle’s results to submanifolds in a smooth metric measure space. As an application, we prove some new isoperimetric-type inequalities in some smooth metric measure spaces. For example, we obtain a new isoperimetric-type inequality for self-expander.
<br>On the problem of prescribing weighted scalar curvature and the weighted Yamabe flow
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/124456
title: On the problem of prescribing weighted scalar curvature and the weighted Yamabe flow abstract: The weighted Yamabe problem introduced by Case is the generalization of the Gagliardo-Nirenberg inequalities to smooth metric measure spaces. More precisely, given a smooth metric measure space (M,g,e−ϕdVg,m) , the weighted Yamabe problem consists on finding another smooth metric measure space conformal to (M,g,e−ϕdVg,m) such that its weighted scalar curvature is equal to λ+μe−ϕ∕m for some constants μ and λ , satisfying a certain condition. In this article, we consider the problem of prescribing the weighted scalar curvature. We first prove some uniqueness and nonuniqueness results and then some existence result about prescribing the weighted scalar curvature. We also estimate the first nonzero eigenvalue of the weighted Laplacian of (M,g,e−ϕdVg,m) . On the other hand, we prove a version of the conformal Schwarz lemma on (M,g,e−ϕdVg,m) . All these results are achieved by using geometric flows related to the weighted Yamabe flow. We also prove the backward uniqueness of the weighted Yamabe flow. Finally, we consider weighted Yamabe solitons, which are the self-similar solutions of the weighted Yamabe flow.
<br>Improved Lp -Folland–Stein–Sobolev inequality under constraints
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/124455
title: Improved Lp -Folland–Stein–Sobolev inequality under constraints abstract: Hang–Wang improved the Sobolev inequality on the unit sphere under the vanishing of higher-order moments of the volume element. In this note, we improve the Folland–Stein inequality on the CR sphere under the vanishing of higher order moments of the volume element.
<br>Backward uniqueness for the inverse mean curvature flow
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/124454
title: Backward uniqueness for the inverse mean curvature flow abstract: In this paper, we prove a backward uniqueness theorem for solutions to the inverse mean curvature flow on a closed manifold. As a consequence, the isometry group of a solution cannot expand within the lifetime of the solution.
<br>OTL web interface: outlier testing in lifetime data
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/124228
title: OTL web interface: outlier testing in lifetime data abstract: A web interface, named OTL, is developed to perform outlier analysis in exponential, Weibull, lognormal, and log-Laplace samples online over the Internet through Shiny and R. It is a tool to evaluate the exact or approximate distributions of block and consecutive test statistics for testing the presence of outliers that have been discussed over the years in the literature. As it allows for identifying outliers without using the classical extensive tables, OTL can be very useful to academics, policy-makers and executives to compare and understand the results of outlier testing procedures more efficiently in the case of lifetime data.
<br>Rankin-Selberg integrals for SO(2n+1)xGL(r) attached newforms and oldforms
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/124210
title: Rankin-Selberg integrals for SO(2n+1)xGL(r) attached newforms and oldforms abstract: The conjectural newform theory for generic representations of p-adic SO2n+1
was formulated by P.-Y. Tsai in her thesis in which Tsai also verified the conjecture when the representations are supercuspidal. The main purpose of this work is to compute the Rankin–Selberg integrals for SO2n+1×GLr
with 1≤r≤n
attached to newforms and also oldforms under the validity of the conjecture.
<br>On the reconstruction of a boundary value problem from incomplete nodal data
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/124202
title: On the reconstruction of a boundary value problem from incomplete nodal data abstract: . In this paper, the reconstruction of a differential operator from
incomplete spectral characteristics is concerned. We prove that coefficients of a second-order differential equation with the eigen-parameter
appearing at the right-end boundary condition can be uniquely determined from incomplete nodal data. The new results in this paper are
unlike to the known results for the classical Sturm-Liouville operator in
[21].
<br>Spectral-Domain Optical Coherence Tomography for Early Detection of Primary Open-Angle, Angle-Closure, and Normal-Tension Glaucoma in an Asian Population
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/124201
title: Spectral-Domain Optical Coherence Tomography for Early Detection of Primary Open-Angle, Angle-Closure, and Normal-Tension Glaucoma in an Asian Population abstract: Abstract
Purpose:
We investigated the diagnostic capability of spectral-domain optical coherence tomography (SD-OCT) for different types of early glaucoma among the Chinese population in Taiwan.
Methods
One eye each was assessed from 113 individuals with healthy eyes, 125 individuals with suspected glaucoma (GS), and 156 patients with early glaucoma (primary open-angle glaucoma [POAG], 87; primary angle-closure glaucoma [PACG], 50; and normal-tension glaucoma [NTG], 19). Circumpapillary (cp) retinal nerve fiber layer (RNFL) thickness (global and sectoral); Bruch’s membrane opening-minimum rim width (BMO-MRW); and macular parameters, including the macular RNFL (mRNFL), macular ganglion cell layer (mGCL), and macular inner plexiform layer (mIPL), were assessed using SD-OCT. The areas under receiver operator characteristic curves (AUCs) were calculated to evaluate the diagnostic capacity of the parameters to differentiate between healthy and early glaucomatous eyes.
Results:
The parameters most suitable for detecting early POAG, PACG, NTG and GS were temporal inferior BMO-MRW (AUC, 0.847), inner temporal mGCL (AUC, 0.770), temporal superior cpRNFL (AUC, 0.861) and mean global BMO-MRW (AUC, 0.768), respectively. Among the macular parameters, mGCL exhibited the highest diagnostic capacity. The diagnostic capacity of mGCL was lower than that of cpRNFL and BMO-MRW for POAG and NTG but not PACG. After adjusting for confounding variables in multivariable analysis, the AUC was determined to be 0.935 for POAG and 0.787 for GS.
Conclusion:
SD-OCT facilitates the detection of early POAG, PACG and NTG. Using a combination of cpRNFL, BMO-MRW and macular parameters may enhance their diagnostic capacities. Further studies are necessary to validate these findings.
<br>The partial inverse spectral problems for a differential operator
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/124012
title: The partial inverse spectral problems for a differential operator abstract: We firstly study two partial inverse problems for a second-order differential equation with a special boundary condition and recover this operator from the known spectral data. Then we investigate the missing eigenvalue problem for this operator.
<br>Forced waves for a three-species predator-prey system with nonlocal dispersal in a shifting environment
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/124011
title: Forced waves for a three-species predator-prey system with nonlocal dispersal in a shifting environment abstract: We consider a three-species predator-prey system involving two competing predators and one prey. The species diffuse with nonlocal dispersal kernels with possibly non-compact support, and they interact in a heterogeneous environment moving with a positive forced speed such that the environment is favorable to the prey in the absence of predators far ahead of the shifting boundary and it is unfavorable far behind. Such systems arise in the modeling of population dynamics under the effect of a shifting environment, such as climate change. We show on the one hand the existence of waves connecting the trivial state to the unique constant positive co-existence state for any value of the forced speed. On the other hand, we show the existence of critical positive speeds for the existence of waves connecting the trivial state to the states corresponding to the absence of one or two predators.
<br>Regression analysis of randomized response event time data
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/124010
title: Regression analysis of randomized response event time data abstract: The randomized response techniques (RRTs), including the related-question RRT of
Warner (1965) and the unrelated-question RRT of Greenberg et al. (1969), have been
utilized to reduce under-reporting of sensitive characteristics in survey studies by enhancing privacy protection. Currently, the RRT is mainly applied for prevalence estimation
of some sensitive event. This work extends the application of the RRT to the analysis of
time-to-event outcome. We apply the proposed method to the Taiwan extramarital sex
data surveyed by the RRT to make statistical inferences on the time to the incidence of
extramarital sex since marriage. In final, we discuss the authenticity of “the seven year
itch” based on the Taiwan survey data.
<br>Knowledge of Chinese Pediatric Professionals Regarding Pediatric Pain Management
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/122897
title: Knowledge of Chinese Pediatric Professionals Regarding Pediatric Pain Management abstract: Many healthcare professionals base their perceptions of pediatric pain on their knowledge of the subject. Therefore, knowledge deficits in this area may yield negative attitudes toward pain management and add to the complexity of pain management in hospitalized children. This study evaluated the knowledge of pediatric clinicians in China regarding pediatric pain management. Adopting a cross-sectional descriptive comparative design, we surveyed pediatric clinicians using a structured questionnaire. Inclusive criteria were pediatric clinicians, both pediatricians and nurses, with professional pediatric experience of over one year. A total of 507 pediatric clinicians participated. Most were aware of the importance of pain management in sick children but misunderstood pediatric pain, lacked knowledge for performing pediatric pain assessments and lacked knowledge for providing pain relief interventions. Background factors including differing professions (pediatricians and nurses; p = 0.012), age (p < 0.05) and hospital setting of employment (p = 0.003) were significantly related to clinicians’ knowledge regarding pain management. Participating pediatricians had higher levels of knowledge of pediatric pain management than nurses. Research revealed four barriers affecting clinicians’ knowledge, including misconception of pain in children, lack of professional knowledge and confidence in the practice of pediatric pain assessment, lack of professional knowledge to provide pain relief interventions, and a significant knowledge gap between pediatricians and nurses. The results point out a crucial need for multidisciplinary education to remedy these deficiencies. Further study is needed to explore strategies to strengthen clinicians’ knowledge of this vital area of practice.
<br>Comparing the Therapeutic Efficacies of Lung Cancer: Network Meta-analysis Approaches
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/122896
title: Comparing the Therapeutic Efficacies of Lung Cancer: Network Meta-analysis Approaches abstract: Background: In recent years, reduction of nuclear power generation and the use of coal-fired power for filling the power supply gap might have increased the risk of lung cancer. This study aims to explore the most effective treatment for different stages of lung cancer patients. Methods: We searched databases to investigate the treatment efficacy of lung cancer. The network me-ta-analysis was used to explore the top three effective therapeutic strategies among all collected treatment methodologies. Results: A total of 124 studies were collected from 115 articles with 171,757 participants in total. The results of network meta-analyses showed that the best top three treatments: (1) in response rate, for advanced lung cancer were Targeted + Targeted, Chemo + Immuno, and Targeted + Other Therapy with cumulative probabilities 82.9, 80.8, and 69.3%, re-spectively; for non-advanced lung cancer were Chemoradio + Targeted, Chemoradi + Immuno, and Chemoradio + Other Therapy with cumulative probabilities 69.0, 67.8, and 60.7%, respectively; (2) in disease-free control rate, for advanced lung cancer were Targeted + Others, Chemo + Im-muno, and Targeted + Targeted Therapy with cumulative probabilities 93.4, 91.5, and 59.4%, re-spectively; for non-advanced lung cancer were Chemo + Surgery, Chemoradio + Targeted, and Surgery Therapy with cumulative probabilities 80.1, 71.5, and 43.1%, respectively. Conclusion: The therapeutic strategies with the best effectiveness will be different depending on the stage of lung cancer patients.
<br>Statistics of partial permutations via Catalan matrices
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/122895
title: Statistics of partial permutations via Catalan matrices abstract: A generalized Catalan matrix (an,k)n,k≥0 is generated by two seed sequences s=(s0,s1,…) and t=(t1,t2,…) together with a recurrence relation. By taking sℓ=2ℓ+1 and tℓ=ℓ2 we can interpret an,k as the number of partial permutations, which are n×n 0,1-matrices of k zero rows with at most one 1 in each row or column. In this paper we prove that most of fundamental statistics and some set-valued statistics on permutations can also be defined on partial permutations and be encoded in the seed sequences. Results on two interesting permutation families, namely the connected permutations and cycle-up-down permutations, are also given.
<br>Rankin-Selberg integrals for SO(2n+1)xGL(r) attached to newforms and oldforms.
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/122894
title: Rankin-Selberg integrals for SO(2n+1)xGL(r) attached to newforms and oldforms. abstract: The conjectural newform theory for generic representations of p-adic SO2n+1 was formulated by P.-Y. Tsai in her thesis in which Tsai also verified the conjecture when the representations are supercuspidal. The main purpose of this work is to compute the Rankin–Selberg integrals for SO2n+1×GLr with 1≤r≤n attached to newforms and also oldforms under the validity of the conjecture.
<br>Comparison of Fragmentation and Dusting Modality Using Holmium YAG Laser during Ureteroscopy for the Treatment of Ureteral Stone: A Single-Enter’s Experience
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/122893
title: Comparison of Fragmentation and Dusting Modality Using Holmium YAG Laser during Ureteroscopy for the Treatment of Ureteral Stone: A Single-Enter’s Experience abstract: Laser ureteroscopic lithotripsy (URSL) is an efficacious treatment for ureteral stones. There have been few previous studies comparing the different energy and frequency settings for URSL in a single center. We compared these two laser modalities, which were simultaneously used in our medical center for the treatment of ureteral stones. Patients who underwent fragmentation or dusting laser URSL between September 2018 and June 2020 were retrospectively reviewed. We compared patients who underwent fragmentation and dusting laser and assessed the enhancing factors for stone free rate. There were a total of 421 patients with ureteral stones who met the study criteria. There was no significant difference between the characteristics of both groups. The fragmentation group had a better stone free rate and a lower retropulsion rate compared with the dusting group. Multivariate analysis revealed that stone basket use, no upper ureteral stone or pyuria significantly improved the stone free rate. Both laser modes were effective and safe for ureteral lithotripsy although the fragmentation system showed slightly higher effectiveness and lower complication rate. View Full-Text
<br>On connected graphs of order n with girth g and nullity n-g
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/122892
title: On connected graphs of order n with girth g and nullity n-g abstract: Let G be a simple graph of order n. The nullity of a graph G, denoted by , is the multiplicity of 0 as an eigenvalue of its adjacency matrix. If G has at least one cycle, then the girth of G, denoted by , is the length of the shortest cycle in G. It is known that is bounded above by if and by if . In this paper it is proved that when G is connected, if and only if G is a complete bipartite graph, different from a star, or a cycle of length a multiple of 4; that if G is not a complete bipartite graph or a cycle of length a multiple of 4, then . Connected graphs of order n with girth g and nullity are characterized. This work also settles the problem of characterizing connected graphs with rank equal to girth and the problem of identifying all connected graphs G that contains a given nonsingular cycle as a shortest cycle and with the same rank as G.
<br>Correlation Analysis of Physical Fitness and Its Impact on Falls in 2130 Community-Dwelling Older Adults: a Retrospective Cross-Sectional Study
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/122891
title: Correlation Analysis of Physical Fitness and Its Impact on Falls in 2130 Community-Dwelling Older Adults: a Retrospective Cross-Sectional Study abstract: Background
As the community-dwelling population ages in Taiwan, concerns regarding long-term care have grown more urgent. Physical fitness plays a key role in enabling community-dwelling older adults to independently complete daily tasks and avoid falling accidents. However, the effect of physical fitness on falls and other fitness-related factors remains poorly understood.
Methods
In this retrospective cross-sectional study, 2130 community-dwelling older adults were recruited from a rural region of Taiwan. Each of these participants completed a demographics interview and frailty questionnaire and reported their history of falls. We evaluated each participant’s height and body weight measurements, calf circumference, bone mass density, and results on the grip strength, single-leg standing, chair sit-and-reach, 8-ft up-and-go, 30-second chair stand, 2-minute step, 30-second arm curl, 6-m walk, and back scratch tests to determine their overall physical fitness, which consisted of their body composition, muscular strength and endurance, flexibility, and cardiopulmonary fitness.
Results
The prevalence of falls in the preceding year among the older adults surveyed was 20.8%, and the resultant hospitalization rate was 10.9%. The older adults who were more physically active in the past week, had regular exercise habits, lived with family, and had no history of hospitalization due to falls, exhibited greater performance on the physical fitness tests. Three time fallers exhibited lower levels of overall physical fitness than did those who had not fallen. The nonfallers outperformed the fallers in grip strength (participants who had not fallen and those who had fallen once, twice, or three times in the preceding year: 24.66 ± 0.19 vs. 23.66 ± 0.35 vs. 20.62 ± 0.71 vs. 22.20 ± 0.90 kg) and single-leg standing duration (19.38 ± 0.39 vs. 16.33 ± 0.78 vs. 13.95 ± 1.67 vs. 12.34 ± 1.82 seconds).
Conclusions
Exercise habits, living status, hospitalization due to falls, and amount of exercise were all associated with physical fitness in community-dwelling older adults. The results of all of the assessments indicated that the participants who had fallen three times exhibited lower levels of physical fitness than did those who had not fallen in the previous year. Physical measurements, including grip strength and single-leg standing duration, are associated with an individual’s risk of falling, which indicates that they should be considered in the development of geriatric physical fitness and fall-prevention programs.
<br>Transferable domination number of graphs
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/122890
title: Transferable domination number of graphsAnalyzing recurrent and nonrecurrent terminal events data in discrete time
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/122889
title: Analyzing recurrent and nonrecurrent terminal events data in discrete time abstract: Joint analysis of recurrent and nonrecurrent terminal events has attracted substantial attention in literature. However, there lacks formal methodology for such analysis when the event time data are on discrete scales, even though some modeling and inference strategies have been developed for discrete-time survival analysis. We propose a discrete-time joint modeling approach for the analysis of recurrent and terminal events where the two types of events may be correlated with each other. The proposed joint modeling assumes a shared frailty to account for the dependence among recurrent events and between the recurrent and the terminal terminal events. Also, the joint modeling allows for time-dependent covariates and rich families of transformation models for the recurrent and terminal events. A major advantage of our approach is that it does not assume a distribution for the frailty, nor does it assume a Poisson process for the analysis of the recurrent event. The utility of the proposed analysis is illustrated by simulation studies and two real applications, where the application to the biochemists' rank promotion data jointly analyzes the biochemists' citation numbers and times to rank promotion, and the application to the scleroderma lung study data jointly analyzes the adverse events and off-drug time among patients with the symptomatic scleroderma-related interstitial lung disease.
<br>Bifurcation diagram of a Robin boundary value problem arising in MEMS
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/122888
title: Bifurcation diagram of a Robin boundary value problem arising in MEMS abstract: We consider a parabolic problem with Robin boundary condition which arises when the edge of a micro-electro-mechanical-system (MEMS) device is connected with a flexible nonideal support. Then via a rigorous analysis we investigate the structure of the solution set of the corresponding steady-state problem. We show that a critical value (the pull-in voltage) exists so that the system has exactly two stationary solutions when the applied voltage is lower than this critical value, one stationary solution for applying this critical voltage, and no stationary solution above the critical voltage.
<br>Sturm-Liouville-type operators with frozen argument and Chebyshev polynomials.
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/122887
title: Sturm-Liouville-type operators with frozen argument and Chebyshev polynomials. abstract: In recent years, there appeared a growing interest in the inverse spectral theory for functional-differential operators with frozen argument. Such operators are nonlocal and belong to the so-called loaded differential operators, which frequently appear in mathematics as well as natural sciences and engineering. However, to various classes of nonlocal operators, classical methods of the inverse spectral theory are not applicable. For this reason, it is relevant to develop new methods and approaches for solving inverse problems for operators of this type. We establish a deep connection between the inverse problem for operators with frozen argument and Chebyshev polynomials of the first and the second kinds. Appearing to be of an interest from the point of view of the Chebyshev polynomials theory itself, this connection gives a new perspective method for studying inverse problems for operators with frozen argument. In particular, it allows one to completely describe all non-degenerate and degenerate cases, that is, when the corresponding inverse problem is uniquely solvable or not, respectively. Moreover, it gives a convenient description of all isospectral potentials in the degenerate case, which is demonstrated by some illustrative examples.
<br>Inverse resonance problem with partial information on the interval
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/122886
title: Inverse resonance problem with partial information on the interval abstract: We consider the inverse resonance problem in scattering theory. In one-dimensional setting, the scattering matrix consists of 2×2
entries of meromorphic functions. The resonances are defined as the poles of the meromorphic determinant. For the compactly supported perturbation, we are able to quantitatively estimate the zeros and poles of each meromorphic entry. The size of potential support is connected to the zero density of scattered wave field due to the form of Fourier transform. We will investigate certain properties of Fourier transforms in scattering theory and derive the inverse uniqueness on scattering source given certain knowledge on the perturbation and all the given resonances.
<br>Identification of Early Response to Hypertonic Dextrose Prolotherapy Markers in Knee Osteoarthritis Patients by an Inflammation-related Cytokine Array,
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/122885
title: Identification of Early Response to Hypertonic Dextrose Prolotherapy Markers in Knee Osteoarthritis Patients by an Inflammation-related Cytokine Array, abstract: Background: Osteoarthritis (OA) is one of the most common forms of arthritis, and hypertonic dextrose prolotherapy has long been used clinically to treat knee OA. The aim of this study was to investigate the inflammation-related protein-expression profile characterizing the efficacy of the hypertonic dextrose prolotherapy in knee OA as prognostic markers.
Methods: OA patients over the age of 65 were recruited for Western Ontario McMaster University Osteoarthritis (WOMAC) index, knee X-ray evaluation and knee joint synovial fluid analysis before and after hypertonic dextrose prolotherapy. The expressions of inflammation-related factors were measured using a novel cytokine antibody array methodology. The cytokine levels were quantified by quantitative protein expression and analyzed by ELISA using the patients' knee-joint synovial fluid.
Results: The WOMAC Index and minimum joint space width before receiving the intra-articular injection and at 2-week intervals were compared. Twelve patients who received OA intervention were enrolled and finally a clinical evaluation of 12 knee joints and knee synovial fluid samples were analyzed. In this study, after receiving hypertonic dextrose prolotherapy, the OA patients clearly demonstrated a significant improvement in WOMAC index and increasing tendency in the medial minimum joint space width after intervention. Meanwhile, we observed a significantly associated tendency between hypertonic dextrose treatment of knee OA and the upregulation of MMP2, TIMP-1, EGF, CXCL9 and IL-22.
Conclusion: The findings provide knee OA patients receiving hypertonic dextrose prolotherapy, which is accompained by the improvemeny of knee symptoms and associated tendency of upregulation of MMP2, EGF, CXCL 9 and IL-22.
<br>Statistical Inference and Optimum Life-Testing Plans with Joint Progressively Type-II Censoring Scheme
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/122884
title: Statistical Inference and Optimum Life-Testing Plans with Joint Progressively Type-II Censoring Scheme abstract: This article discusses the estimation of model parameters and the determination of optimal life-testing plans for Weibull-distributed lifetimes under a joint progressive Type-II censoring scheme. We obtain the maximum likelihood estimates numerically and propose a modified variable-neighborhood-search-based approach for determining the optimum joint progressive Type-II censoring scheme. Different optimal criteria, including a cost minimization criterion, the A-optimality criterion, and the D-optimality criterion, are considered. A sensitivity analysis is used to study the effect of misspecification of parameter values on the optimal schemes.
<br>Low Hepatitis B Core-Related Antigen Levels Correlate Higher Spontaneous Seroclearance of HBsAg in Chronic Hepatitis B Patients with High HBsAg Levels
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/122883
title: Low Hepatitis B Core-Related Antigen Levels Correlate Higher Spontaneous Seroclearance of HBsAg in Chronic Hepatitis B Patients with High HBsAg Levels abstract: Background & aims: Seroclearance of hepatitis B surface antigen (HBsAg) indicates functional cure for hepatitis B virus (HBV) infection. Low HBsAg levels can predict HBsAg seroclearance over time. However, little is known about the association between hepatitis B core-related antigen (HBcrAg) levels and spontaneous seroclearance of HBsAg.
Methods: We conducted a retrospective cohort study including 2614 treatment-naïve patients with chronic HBV infection who received long-term follow-up at the National Taiwan University Hospital. The primary end point was spontaneous HBsAg seroclearance. We aimed to explore whether HBcrAg levels could predict HBsAg seroclearance, especially for patients with HBsAg levels >1000 IU/mL.
Results: There were 465 patients who cleared HBsAg with 32,414.72 person-years of follow-up, with a mean clearance rate of 1.43% per year. We found that lower HBcrAg levels at baseline were associated with an increased likelihood of HBsAg seroclearance (log rank P < .001). When restricting the study population to 1539 patients with HBsAg levels >1000 IU/mL, only HBcrAg <10,000 U/mL (vs ≥100,000 U/mL) served as an independent viral predictor for HBsAg seroclearance, with adjusted hazard ratio of 1.95 (95% CI, 1.16-3.27). In contrast to the late decline of HBsAg levels (5-9 years before HBsAg seroclearance), HBcrAg levels became undetectable 10-14 years before HBsAg seroclearance. This finding was confirmed by the different annual HBsAg seroclearance rates in the first and second decades of follow-up (0.97% vs 3.75%; P < .001) in patients achieving undetectable HBcrAg levels.
Conclusions: Lower serum HBcrAg levels were associated with increased probability of HBsAg seroclearance over time. In patients with HBsAg levels >1000 IU/mL, clearing HBcrAg may serve as an early biomarker for HBsAg seroclearance.
<br>Results related to the transverse Yamabe problem
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/122881
title: Results related to the transverse Yamabe problem abstract: Let (M,F,g0)
be a Riemannian minimal foliation. The transverse Yamabe problem is to find a metric g
in the basic conformal class of g0
such that the transverse scalar curvature of g
is constant. We first study the uniqueness of the solutions of the transverse Yamabe problem. As a generalization of the transverse Yamabe problem, we study the problem of prescribing transverse scalar curvature by using geometric flow. We then prove a version of conformal Schwarz lemma on (M,F,g0)
. Finally, we consider the transverse Yamabe soliton, which is the self-similar solution of the transverse Yamabe flow.
<br>Ancient caloric functions on pseudohermitian manifolds
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/122882
title: Ancient caloric functions on pseudohermitian manifolds abstract: For any Riemannian manifold with polynomial volume growth, Colding and Minicozzi obtained a sharp bound on the dimension of the space of ancient caloric functions with polynomial growth. For any pseudohermitian manifold satisfies doubling volume property and parabolic mean value property, we obtain in this paper a sharp bound on the dimension of the space of ancient pseudohermitian caloric functions with polynomial growth.
<br>Physical Fitness and Its Correlation with Handgrip Strength in Active Community-dwelling Older Adults
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/122880
title: Physical Fitness and Its Correlation with Handgrip Strength in Active Community-dwelling Older Adults abstract: In this cross-sectional study, we assessed the physical fitness levels of active community-dwelling older adults. Moreover, we investigated the correlation of their (stratified by age and sex) fitness levels with handgrip strength (HGS). Comprehensive physical fitness tests, including sarcopenia screening, were conducted with a total of 2,130 older adults residing in a rural area of Taiwan. The 5th, 10th, 25th, 50th, 75th, 90th, and 95th percentiles of age- and sex-specific physical fitness levels were determined. Furthermore, we identified the key parameters for assessing the physical fitness of older adults and performed stepwise multiple linear regression analysis. Both men and women exhibited age-related decreases in all aspects of functional fitness, a trend indicating that older adults in Taiwan may lose their independence in the future. Furthermore, the regression analysis revealed that HGS was positively correlated with sex, body mass index, and the results of 30-s arm curl and back scratch tests but negatively correlated with age and the result of 8-foot up-and-go test. Our reference values for physical fitness may help assess the fitness levels of active community-dwelling older adults and design community-based health programs to prevent the early loss of independence in community-dwelling older adults in Taiwan.
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