Octahedral developing of knot complement II: Ptolemy coordinates and applications

It is known that a knot complement (minus two points) decomposes into ideal octahedra with respect to a given knot diagram. In this paper, we study the Ptolemy variety for such an octahedral decomposition in perspective of Thurston's gluing equation variety. More precisely, we compute explicit Ptolemy coordinates in terms of segment and region variables, the coordinates of the gluing equation variety motivated from the volume conjecture. As a consequence, we present an explicit formula for computing the obstruction to lifting a $(\mathrm{PSL}(2,\mathbb{C}),P)$-representation of the knot group to a $(\mathrm{SL}(2,\mathbb{C}),P)$-representation. We also present a diagrammatic algorithm to compute a holonomy representation of the knot group.Comment: 32 pages, 21 figue

Volume of Hypercubes Clipped by Hyperplanes and Combinatorial Identities

There was an elegant expression for the volume of hypercube $[0,1]^n$ clipped by a hyperplane. We generalize the formula to the case of more than one hyperplane. Furthermore we derive several combinatorial identities from the volume expressions of clipped hypercubes

Legendrian singular links and singular connected sums

We study Legendrian singular links up to contact isotopy. Using a special property of the singular points, we define the singular connected sum of Legendrian singular links. This concept is a generalization of the connected sum and can be interpreted as a tangle replacement, which provides a way to classify Legendrian singular links. Moreover, we investigate several phenomena only occur in the Legendrian setup

Adjoint Reidemeister torsions from wrapped M5-branes

We introduce a vanishing property of adjoint Reidemeister torsions of a cusped hyperbolic 3-manifold derived from the physics of wrapped M5-branes on the manifold. To support our physical observation, we present a rigorous proof for the figure-eight knot complement with respect to all slopes. We also present numerical verification for several knots

The ReInforcement of adherence via self-monitoring app orchestrating biosignals and medication of RivaroXaban in patients with atrial fibrillation and co-morbidities: a study protocol for a randomized controlled trial (RIVOX-AF)

BackgroundBecause of the short half-life of non-vitamin K antagonist oral anticoagulants (NOACs), consistent drug adherence is crucial to maintain the effect of anticoagulants for stroke prevention in atrial fibrillation (AF). Considering the low adherence to NOACs in practice, we developed a mobile health platform that provides an alert for drug intake, visual confirmation of drug administration, and a list of medication intake history. This study aims to evaluate whether this smartphone app-based intervention will increase drug adherence compared with usual care in patients with AF requiring NOACs in a large population.MethodsThis prospective, randomized, open-label, multicenter trial (RIVOX-AF study) will include a total of 1,042 patients (521 patients in the intervention group and 521 patients in the control group) from 13 tertiary hospitals in South Korea. Patients with AF aged ≥19 years with one or more comorbidities, including heart failure, myocardial infarction, stable angina, hypertension, or diabetes mellitus, will be included in this study. Participants will be randomly assigned to either the intervention group (MEDI-app) or the conventional treatment group in a 1:1 ratio using a web-based randomization service. The intervention group will use a smartphone app that includes an alarm for drug intake, visual confirmation of drug administration through a camera check, and presentation of a list of medication intake history. The primary endpoint is adherence to rivaroxaban by pill count measurements at 12 and 24 weeks. The key secondary endpoints are clinical composite endpoints, including systemic embolic events, stroke, major bleeding requiring transfusion or hospitalization, or death during the 24 weeks of follow-up.DiscussionThis randomized controlled trial will investigate the feasibility and efficacy of smartphone apps and mobile health platforms in improving adherence to NOACs.Trial registrationThe study design has been registered in ClinicalTrial.gov (NCT05557123)

생성모델을 이용한 비지도 학습 기반 연속사진 디노이징과 디모자이킹

Burst raw image, Joint demosaicing and denoising, unsupervised learning, Implicit neural representations, denoising diffusion probabilistic models본 논문은 이미지 신호 처리 파이프라인에서 이미지의 품질을 결정하는 중요한 역문제 중 하나인 디노이징과 디모자이킹에 대해 다룬다. 이 문제를 해결하기 위해 기존에 가장 일반적으로 사용하던 컨볼루션 기반 신경망과 지도학습 기반의 모델들은 이미지 복원에 좋은 성능을 보였지만, 과도한 메모리 사용량, 학습 데이터에의 과 적합 등의 문제가 발생하였다. 우리는 이를 해결하고자 디노이징과 디모자이킹을 복합적으로 해내는 비지도 학습 기반 생성모델에 관해 연구하였다. 우리는 저품질 이미지로부터 정보를 더 얻기 위해 연속사진과 raw 사진을 이용하였다. 첫 번째 방법은 Implicit neural representation 기반 모델로, 해당 모델은 픽셀의 좌표와 프레임의 정보를 입력 받아 해당 픽셀의 색을 출력한다. 이때, 프레임의 정보를 전달하기 위해 t-distributed stochastic neighbor embedding (t-SNE)를 학습가능한 파라미터로 입력하여 모델이 학습을 거치는 과정에서 연속 영상의 정보를 전달하였다. 해당 방법은 기존의 컨볼루션 기반 신경망보다 훨씬 적은 메모리 사용량을 달성하였으나, 복구하고자 하는 이미지가 달라질 때마다 모델을 다시 학습해야 한다는 단점이 있었다. 또한 해당 모델은 노이즈를 제거하고 비어 있는 값을 잘 복원하였지만, 여전히 고주파 영역은 잘 복원하지 못하였다. 두 번째 방법은 denoising diffusion probabilistic models (DDPMs)를 이용한 조건부 샘플링 방법으로, 해당 방법은 특이값 분해 (SVD)를 기반으로 무조건 샘플 생성에 조건을 줌으로써 우리가 복원하고자 하는 이미지에 제한된 이미지를 생성한다. 해당 방법 역시 디노이징과 디모자이킹을 복합적으로 수행하였지만, 복원하고자 하는 이미지의 !를 고려해야 하고, 학습이 오래 걸리며, 메모리 소모량이 많다는 단점이 있다. 우리는 해당 모델이 INR 기반 모델로 대체된다면 연속적인 score 를 학습하는데 더 도움이 되고, 메모리 소모량을 줄일 수 있을 것이라고 예측한다.Denoising and demosaicing are one of the important inverse problems for deciding image quality in in-camera image signal processing (ISP) pipeline. To improve the performance of these tasks, deep convolutional neural networks (CNNs) have shown high performance, but it is hard to apply them in high-resolution images since they consume a lot of memory for computation. Also, supervised methods that are commonly used cause overfitting for the training domain and need paired datasets. Therefore, we propose two methods for joint denoising and demosaicing (JDD) based on unsupervised learning to reconstruct high-quality images without ground truth images. To get more information from the scenes, we use burst and raw images. First is the implicit neural representations (INRs) based method. It takes the coordinates of the pixels and frame information as an input and outputs the color of the pixels. We give the frame information of the burst by using t-distributed stochastic neighbor embedding (t-SNE). We set the t-SNE as a trainable parameter to estimate more accurate frame information. Since the network only consists of fully-connected layers, it requires much less memory for computation than CNNs. However, it needs re-train when the input burst changes and cannot restore the high frequency of the images. The second is the conditional sampling method using unconditional denoising diffusion probabilistic models (DDPMs). DDPMs learn the prior distributions during the diffusion process, and then they reconstruct images by subtracting noise from the initial noise iteratively. We construct a sampling method based on the singular value decomposition (SVD) method. We verify this method works well in JDD, but to reconstruct the original image, σ_y needs to be considered, training is too long, and memory consumption is large. We assume when the model of DDPMs is replaced by INR, it is helpful for learning the score of data distribution and reducing the memory consumption.Ⅰ. INTRODUCTION 1 1.1 Problem Setting 1 1.2 Proposed Methods 3 1.3 Contributions 4 ⅠI. BACKGROUND 4 2.1 Inverse Problem 4 2.2 Implicit Neural Representation 5 2.3 Denoising Diffusion Probabilistic Models 6 2.4 Denoising Diffusion Restoration Models 7 ⅠII. JOINT DENOISING AND DEMOSAICING USING GENERATIVE MODELS 8 3.1 Implicit Neural Representation based Method 8 3.2 Conditional Sampling using Unconditional DDPMs 10 ⅠV. EXPERIMENTAL RESULTS 10 4.1 Fidelity Check in Conditional Sampling using Unconditional DDPMs 10 4.2 Experimental Setup 12 4.3 Qualitative Experiments 13 4.4 Quantitative Experiments 16 4.5 Ablation Studies 16 V. DISCUSSIONS 18 5.1 INR based Model 18 5.2 Conditional Sampling using Unconditional DDPMs 19 VI. CONCLUSIONS 21 6.1 Conclusions 21 6.2 Future Works 22 VII. APPENDIX 22 7.1 Appendix A: Examples of the noise condition 22 7.2 Appendix B: Qualitative Results of Ablation Study of Method 3.2 26 7.3 Appendix C: Effect of σ_y on Noise Conditions 29 References 31 요약문 34MasterdCollectio

Octahedral developing of knot complement I: Pseudo-hyperbolic structure

It is known that a knot complement can be decomposed into ideal octahedra along a knot diagram. A solution to the gluing equations applied to this decomposition gives a pseudo-developing map of the knot complement, which will be called a pseudo-hyperbolic structure. In this paper, we study these in terms of segment and region variables which are motivated by the volume conjecture so that we can compute complex volumes of all the boundary parabolic representations explicitly. We investigate the octahedral developing and holonomy representation carefully, and obtain a concrete formula of Wirtinger generators for the representation and also of cusp shape. We demonstrate explicit solutions for T(2, N) torus knots, J(N, M) knots and also for other interesting knots as examples. Using these solutions we can observe the asymptotic behavior of complex volumes and cusp shapes of these knots. We note that this construction works for any knot or link, and reflects systematically both geometric properties of the knot complement and combinatorial aspects of the knot diagram. © 2018 Springer Science+Business Media B.V., part of Springer Natu