On the Complexity of Computing Galois Groups of Differential Equations

The differential Galois group is an analogue for a linear differential equation of the classical Galois group for a polynomial equation. An important application of the differential Galois group is that a linear differential equation can be solved by integrals, exponentials and algebraic functions if and only if the connected component of its differential Galois group is solvable. Computing the differential Galois groups would help us determine the existence of the solutions expressed in terms of elementary functions (integrals, exponentials and algebraic functions) and understand the algebraic relations among the solutions. Hrushovski first proposed an algorithm for computing the differential Galois group of a general linear differential equation. Recently, Feng approached finding a complexity bound of the algorithm, which is the degree bound of the polynomials used in the first step of the algorithm for finding a proto-Galois group. The bound given by Feng is quintuply exponential in the order n of the differential equation. The complexity, in the worst case, of computing a Gröbner basis is doubly exponential in the number of variables. Feng chose to represent the radical of the ideal generated by the defining equations of a proto-Galois group by its Gröbner basis. Hence, a double-exponential degree bound for computing Gröbner bases was involved when Feng derived the complexity bound of computing a proto-Galois group. Triangular decomposition provides an alternative method for representing the radical of an ideal. It represents the radical of an ideal by the triangular sets instead of its generators. The first step of Hrushovski\u27s algorithm is to find a proto-Galois group which can be used further to find the differential Galois group. So it is important to analyze the complexity for finding a proto-Galois group. We represent the radical of the ideal generated by the defining equations of a proto-Galois group using the triangular sets instead of the generating sets. We apply Szántó\u27s modified Wu-Ritt type decomposition algorithm and make use of the numerical bound for Szántó\u27s algorithm to adapt to the complexity analysis of Hrushovski\u27s algorithm. We present a triple exponential degree upper bound for finding a proto-Galois group in the first step of Hrushovski\u27s algorithm

ShuffleNet: An Extremely Efficient Convolutional Neural Network for Mobile Devices

We introduce an extremely computation-efficient CNN architecture named ShuffleNet, which is designed specially for mobile devices with very limited computing power (e.g., 10-150 MFLOPs). The new architecture utilizes two new operations, pointwise group convolution and channel shuffle, to greatly reduce computation cost while maintaining accuracy. Experiments on ImageNet classification and MS COCO object detection demonstrate the superior performance of ShuffleNet over other structures, e.g. lower top-1 error (absolute 7.8%) than recent MobileNet on ImageNet classification task, under the computation budget of 40 MFLOPs. On an ARM-based mobile device, ShuffleNet achieves ~13x actual speedup over AlexNet while maintaining comparable accuracy

Flashlight-Net : A Modular Convolutional Neural Network for Motor Imagery EEG Classification

Peer reviewe

Calcium channel blocker and risk of postoperation lymphatic-related complications among gynecologic malignances

PurposeThis study was performed to assess the association of calcium channel blockers (CCB) and other potential factors with postoperative lymphatic-related morbidity in patients with cervical cancer and endometrial carcinoma.MethodsPatients diagnosed with cervical cancer or endometrial carcinoma with pelvic lymphadenectomy between January 2017 and January 2022 were enrolled. Postoperative lymphatic-related morbidity was evaluated by calculating the lymph cyst occurrence within 3 months after surgery and the duration of pelvic drainage. Univariate analyses evaluating the risk factors for lymphatic-related morbidity were performed.ResultsOf a total of 251 patients, 52 patients were diagnosed with lymphatic cysts by B-ultrasound or computed tomography, and the duration of drainage from 110 patients exceeded the average number of days. Univariable analysis revealed that hypertension, CCB, and lymph node metastasis were independent predictors of postoperative complications.ConclusionsThis study demonstrated that CCB may be a factor associated with the incidence of postoperation lymph cysts, and CCB usage prolongs the duration of pelvic drainage

Quality of Life in Patients with a Permanent Stoma after Rectal Cancer Surgery : A descriptive review

Abstract Background: Currently, colorectal cancer (CRC) is the third most common cancer in the world. After enterostomy, some people have difficulty dealing with physical,psychological, and social problems. Therefore, the quality of life of patients after enterostomy has been paid more and more attention by society.Aim: The aim of the review was to explore the quality of life in patients with a permanent stoma after rectal cancer surgery.Methods: We used two databases, Cinahl and PubMed, to search for articles. Quality of life after permanent enterostomy was assessed using the European Organization for Research and Treatment of Cancer (EORTC) QLQ-C30, CR38 and COH-QOL, SF12V2 and SF36 scales.Results: A total of nine studies met the inclusion criteria. The result showed that enterostomy reduces the quality of life of patients undergoing the procedure. Stomarelated problems include sexual function, depression, unsatisfactory appearance, fatigue and many social problems such as role function, role physical, social function, cognitive function, future perspective and financial difficulties.Conclusions: The studies included in the review showed that the presence of permanent stoma has a negative effect on a person's quality of life. Some patients who undergo permanent ostomy surgery have physical, psychological and social problems. This resultenables nurses to understand the impact of a stoma on patients' lives and provides nurses with better nursing guidance from various aspects

Fireside Corrosion on Heat Exchanger Surfaces and Its Effect on the Performance of Gas-Fired Instantaneous Water Heaters

The heat exchanger in a gas instantaneous water heater is a thermal device used for heat transfer from the high-temperature flue gas to the low-temperature water. The fireside corrosion, due to the reaction of acidic condensate formed on the heat exchanger surfaces and its metallic material, is one of the major hazards for gas instantaneous water heaters. This paper focuses on identifying and quantifying the fireside corrosion on the surface of heat exchangers in gas-fired instantaneous water heaters. Durability tests lasting for 2000 cycles were undertaken for five gas-fired instantaneous water heaters, which were different in terms of the heat input and coating of heat exchangers. The corrosion deposits on the surface of the heat exchangers were surveyed by several methods. The results show that the corrosion deposit grew as the test duration increased. The fins of the heat exchanger with a lead coating had been corroded and copper was exposed. Cu4(OH)6SO4 was the main corrosion product of heat exchangers without a lead coating, whereas PbSO4 was the main corrosion product of heat exchangers with a lead coating. The experiments demonstrate that the corrosion rate decreased with the increase of the heat input. The experiments also show that the thermal efficiency of gas instantaneous water heaters decreased by 2.4% to 6% at the end of the test duration

Dielectric loss behavior and microwaves absorption properties of TiB2 ceramic

Searching for microwaves absorption (MA) with outstanding resistance to harsh condition shows great potential in various special applications. As a typical high-temperature and conducting ceramic, TiB _2 can meet this requirement, but its high electrical conductivity will lead to high reflection of electromagnetic waves. In this paper, we find that TiB _2 ceramic can exhibit excellent MA performance after doping by C/N elements. The chemical structures, dielectric properties and MA performance of ZrB _2 ceramic are systematically measured and analyzed. The MA performance of TiB _2 ceramic reaches −21 dB at 8.00 GHz under a thickness of 2 mm. The results indicate that the MA performance of ZrB _2 can be ascribed to the multiple nonlinear dielectric resonance and polarization relaxation mechanism. This research significantly expands the application scope of TiB _2 ceramic to MA area

Three-dimensional (3D) α-Fe2O3/polypyrrole (PPy) nanocomposite for effective electromagnetic absorption

The lightweight and 3-dimensional reticulated α-Fe2O3/PPy hybrids were successfully fabricated via a facile one-pot polyreaction. The measured complex permittivity and microwave attenuation performance suggest that the dielectric properties of PPy can be regulated by the mass ratio of added α-Fe2O3. The two dielectric resonance peaks of complex permittivity can be ascribed to the interface capacitor-like structure. An equivalent circuit model was established to explain the nonlinear resonance behavior of the α-Fe2O3/PPy wax composites. The addition of α-Fe2O3 properly tuned the dielectric constant to endow the composites with highly efficient microwave absorption. The minimum reflection loss of α-Fe2O3/PPy wax composites were enhanced to nearly −29dB with an effective bandwidth (RL≤ − 10dB) up to 5.0GHz. The numerical method was proposed to calculate the optimum thickness for minimum RL at expected frequency by detailed investigation on the transmission formula. Moreover, the required thickness for optimum absorption efficiency at expected frequency can be obtained directly