Inverse Fourier Transform in the Gamma Coordinate System

This paper provides auxiliary results for our general scheme of computed tomography. In 3D parallel-beam geometry, we first demonstrate that the inverse Fourier transform in different coordinate systems leads to different reconstruction formulas and explain why the Radon formula cannot directly work with truncated projection data. Also, we introduce a gamma coordinate system, analyze its properties, compute the Jacobian of the coordinate transform, and define weight functions for the inverse Fourier transform assuming a simple scanning model. Then, we generate Orlov's theorem and a weighted Radon formula from the inverse Fourier transform in the new system. Furthermore, we present the motion equation of the frequency plane and the conditions for sharp points of the instantaneous rotation axis. Our analysis on the motion of the frequency plane is related to the Frenet-Serret theorem in the differential geometry

Constructive Analysis of Partial Differential Equations

This thesis presents the results produced in the study of weak solutions of the Dirichlet Problem within Errett Bishop's constructive mathematics. It roughly falls into three major parts: a critical analysis of the classical approaches from a constructive point of view (Chapter 2); constructive results on the existence, stability, and maximality of weak solutions (Chapter 5); and related results on the domains discovered during the course of study on the Dirichlet Problem (Chapters 3 and 6). Chapter 1 introduces constructive mathematics, and Chapter 4 is an auxiliary one in which I give two different constructions of a cut-off function

A General Local Reconstruction Approach Based on a Truncated Hilbert Transform

Exact image reconstruction from limited projection data has been a central topic in the computed tomography (CT) field. In this paper, we present a general region-of-interest/volume-of-interest (ROI/VOI) reconstruction approach using a truly truncated Hilbert transform on a line-segment inside a compactly supported object aided by partial knowledge on one or both neighboring intervals of that segment. Our approach and associated new data sufficient condition allows the most flexible ROI/VOI image reconstruction from the minimum account of data in both the fan-beam and cone-beam geometry. We also report primary numerical simulation results to demonstrate the correctness and merits of our finding. Our work has major theoretical potentials and innovative practical applications

Experimental and numerical investigation on the influence of the clocking position on hydraulic performance of a centrifugal pump with guide vane

The investigation of the clocking effect mainly concentrates on turbines and compressors, but seldom in centrifugal pumps. In this paper, using numerical simulation and experiment, the influence of the clocking effect on the hydraulic performance of centrifugal pump with guide vane is studied. Numerical simulations with SST k-w turbulence model were applied to obtain the inner flow field of the test pump. The numerical simulations coincide with the test result, which indicates the accurate of the utilized numerical approach. The results show the clocking positions have an important effect on hydraulic performance of the centrifugal pump with guide vane. The pump demonstrates the higher efficiency and head as the tongue locate between two guide vanes. The hydraulic performance of the volute is a major factor impacting the performance of the centrifugal pump with different clocking positions. However, the clocking position has almost no effect on the performances of the impeller and diffuser. When the guide vane is close to the volute tongue, flow field of volute is more non-uniform, and the energy loss in volute appears to be larger. The results and the method of this paper can provide theoretical reference for the design and installation of guide vane in centrifugal pump

Nonexistence of solutions to fractional parabolic problem with general nonlinearities

In this content, we investigate a class of fractional parabolic equation with general nonlinearities ∂z(x, t) ∂t − ( + λ) β 2 z(x, t) = a(x1) f (z), where a and f are nondecreasing functions. We first prove that the monotone increasing property of the positive solutions in x1 direction. Based on this, nonexistence of the solutions are obtained by using a contradiction argument. We believe these new ideas we introduced will be applied to solve more fractional parabolic problemsThe research of Zhang has been partially supported by National Natural Science Foun dation of China(No. 12001344) and the Graduate Education and Teaching Innovation Project of Shanxi, China (No. 2022YJJG124), the research of Nieto has been partially supported by the Agencia Estatal de Investigación (AEI) of Spain under Grant PID2020-113275GB-I00, cofinanced by the European Community fund FEDER, as well as Xunta de Galicia grant ED431C 2019/02 for Competitive Reference Research Groups (2019–22) and the research of Wang has been partially supported by Natural Science Foundation of Shanxi Province, China(No. 20210302123339)S

Towards Higher Ranks via Adversarial Weight Pruning

Convolutional Neural Networks (CNNs) are hard to deploy on edge devices due to its high computation and storage complexities. As a common practice for model compression, network pruning consists of two major categories: unstructured and structured pruning, where unstructured pruning constantly performs better. However, unstructured pruning presents a structured pattern at high pruning rates, which limits its performance. To this end, we propose a Rank-based PruninG (RPG) method to maintain the ranks of sparse weights in an adversarial manner. In each step, we minimize the low-rank approximation error for the weight matrices using singular value decomposition, and maximize their distance by pushing the weight matrices away from its low rank approximation. This rank-based optimization objective guides sparse weights towards a high-rank topology. The proposed method is conducted in a gradual pruning fashion to stabilize the change of rank during training. Experimental results on various datasets and different tasks demonstrate the effectiveness of our algorithm in high sparsity. The proposed RPG outperforms the state-of-the-art performance by 1.13% top-1 accuracy on ImageNet in ResNet-50 with 98% sparsity. The codes are available at https://github.com/huawei-noah/Efficient-Computing/tree/master/Pruning/RPG and https://gitee.com/mindspore/models/tree/master/research/cv/RPG.Comment: NeurIPS 2023 Accepte

Primary clear cell adenocarcinoma of the bladder with recurrence: a case report and literature review

Clear cell carcinoma of the bladder is a rare tumor of the bladder. There are few reports available on this rare disease, and no cases with recurrence were reported. Here we present a case of 68-year-old woman with primary clear cell carcinoma of the bladder, who underwent repeat TUR-BT and tumor recurrence. We also reviewed the previous treatments and prognoses in previous case reports and evaluate the proper treatment for this disease. Once the diagnosis is determined, the radical surgery should be recommended. The recurrence is not prevented based on post-TUR intravesical therapy

Quantized squeezing and even-odd asymmetry of trapped bosons

We investigate the exact nature of the superfluid-to-Mott-insulator crossover for interacting bosons on an optical lattice in a one-dimensional, harmonic trap by high-precision density-matrix renormalization-group calculations. The results reveal an intermediate regime characterized by a cascade of microscopic steps. These arise as a consequence of individual boson "squeezing" events and display an even-odd alternation dependent on the trap symmetry. We discuss the experimental observation of this behavior, which is generic in an external trapping potential.Comment: 4.05 pages, 4 figures. Presents significantly more, and more systematic, calculations and explanations than cond-mat/070169

Semantically-Shifted Incremental Adapter-Tuning is A Continual ViTransformer

Class-incremental learning (CIL) aims to enable models to continuously learn new classes while overcoming catastrophic forgetting. The introduction of pre-trained models has brought new tuning paradigms to CIL. In this paper, we revisit different parameter-efficient tuning (PET) methods within the context of continual learning. We observe that adapter tuning demonstrates superiority over prompt-based methods, even without parameter expansion in each learning session. Motivated by this, we propose incrementally tuning the shared adapter without imposing parameter update constraints, enhancing the learning capacity of the backbone. Additionally, we employ feature sampling from stored prototypes to retrain a unified classifier, further improving its performance. We estimate the semantic shift of old prototypes without access to past samples and update stored prototypes session by session. Our proposed method eliminates model expansion and avoids retaining any image samples. It surpasses previous pre-trained model-based CIL methods and demonstrates remarkable continual learning capabilities. Experimental results on five CIL benchmarks validate the effectiveness of our approach, achieving state-of-the-art (SOTA) performance.Comment: To appear at CVPR 202