A Spectral Radius Condition for a Graph to Have(a,b)-Parity Factors

Let a,b be two positive integers such that a≤b and a≡b(mod 2).We say that a graph G has an(a,b)-parity factor if G has a spanning subgraph F such that dF(v)≡b(mod 2)and a≤dF(v)≤b for all v∈V(G).In this paper,we provide a tight spectral radius condition for a graph to have(a,b)-parity factors.

Method for Analog Circuit Soft-Fault Diagnosis and Parameter Identification Based on Indictor of Phase Deviation and Spectral Radius

The soft fault induced by parameter variation is one of the most challenging problems in the domain of fault diagnosis for analog circuits.A new fault location and parameter prediction approach for soft-faults diagnosis in analog circuits is presented in this paper.The proposed method extracts the original signals from the output terminals of the circuits under test（CUT） by a data acquisition board.Firstly,the phase deviation value between fault-free and faulty conditions is obtained by fitting the sampling sequence with a sine curve.Secondly,the sampling sequence is organized into a square matrix and the spectral radius of this matrix is obtained.Thirdly,the smallest error of the spectral radius and the corresponding component value are obtained through comparing the spectral radius and phase deviation value with the trend curves of them,respectively,which are calculated from the simulation data.Finally,the fault location is completed by using the smallest error,and the corresponding component value is the parameter identification result.Both simulated and experimental results show the effectiveness of the proposed approach.It is particularly suitable for the fault location and parameter identification for analog integrated circuits.

On the Spectral Radius of Trees with the Given Diameter d

Let T denote a tree with the diameter d(d≥2) and order n. Let Pd,r,n-d-1 denote the tree obtained by identifying the rth vertex of path Pd+1 and the center of star K1,n-d-1, where r = r(d) is the integer part about d+2/2. Then p(T) ≤p(Pd,r,n-d-1),and equality holds if and only if T≌ Pd,r,n-d-1

On the Laplacian Spectral Radius of Trees

Some sharp upper bounds of Laplacian spectral radius of trees in terms of order,diameter,pendant vertex number,covering number,edge covering number or total independence number are given.And the ninth to thirteenth largest values of Laplacian spectral radius over the class of trees on a given order are also given.

On the Maximum Spectral Radius of (m,n)-trees with Given Diameter

Let （V, U） be the vertex-partition of tree T as a bipartite graph. T is called an （m, n）-tree if ｜V｜ = m and ｜U｜ = n. For given positive integers m, n and d, the maximum spectral radius of all （m, n）-trees on diameter d are obtained, and all extreme graphs are determined.

Sharp upper bounds for the adjacency and the signless Laplacian spectral radius of graphs

Let G be a simple graph with n vertices and m edges. In this paper, we present some new upper bounds for the adjacency and the signless Laplacian spectral radius of graphs in which every pair of adjacent vertices has at least one common adjacent vertex. Our results improve some known upper bounds. The main tool we use here is the Lagrange identity.

Bipartite Graphs with the First and Second Largest Laplacian Spectral Radius

Let Bn^k be the class of bipartite graphs with n vertices and k cut edges. The extremal graphs with the first and the second largest Laplacian spectral radius among all graphs in Bn^K are presented. The bounds of the Laplacian spectral radius of these extremal graphs are also obtained.

On the p-norm joint spectral radius

The p-norm joint spectral radius is defined by a bounded collection of square matrices with complex entries and of the same size. In the present paper the author investigates the p-norm joint spectral radius for integers. The method introduced in this paper yields some basic formulas for these spectral radii. The approach used in this paper provides a simple proof of Berger-Wang' s relation concerning the ∞-norm joint spectral radius.

SPECTRAL RADIUSES OF THE GALTON-WATSON BRANCHING PROCESSES

The spectral radiuses of Galton-Watson branching processes which describes the speed of the process escaping from any state are calculated. Under the condition of irreducibility,it is show that this is equal to the spectral radius of Jacobi matrix of its generating function.

On the Signless Laplacian Spectral Radius of C4-free k-cyclic Graphs

A k-cyclic graph is a connected graph of order n and size n + k-1. In this paper, we determine the maximal signless Laplacian spectral radius and the corresponding extremal graph among all C_4-free k-cyclic graphs of order n. Furthermore, we determine the first three unicycles and bicyclic, C_4-free graphs whose spectral radius of the signless Laplacian is maximal. Similar results are obtained for the(combinatorial)

The Signless Laplacian Spectral Radius of Some Special Bipartite Graphs

This paper mainly researches on the signless laplacian spectral radius of bipartite graphs Dr(m1,m2;n1,n2). We consider how the signless laplacian spectral radius of Dr(m1,m2;n1,n2)?changes under some special cases. As application, we give two upper bounds on the signless laplacian spectral radius of Dr(m1,m2;n1,n2), and determine the graphs that obtain the upper bounds.

A Note on the Spectral Radius of Weighted Signless Laplacian Matrix

A weighted graph is a graph that has a numeric label associated with each edge, called the weight of edge. In many applications, the edge weights are usually represented by nonnegative integers or square matrices. The weighted signless Laplacian matrix of a weighted graph is defined as the sum of adjacency matrix and degree matrix of same weighted graph. In this paper, a brief overview of the notation and concepts of weighted graphs that will be used throughout this study is given. In Section 2, the weighted signless Laplacian matrix of simple connected weighted graphs is considered, some upper bounds for the spectral radius of the weighted signless Laplacian matrix are obtained and some results on weighted and unweighted graphs are found.

Preoperative prediction of lymphovascular and perineural invasion in gastric cancer using spectral computed tomography imaging and machine learning

BACKGROUND Lymphovascular invasion(LVI)and perineural invasion(PNI)are important prognostic factors for gastric cancer(GC)that indicate an increased risk of metastasis and poor outcomes.Accurate preoperative prediction of LVI/PNI status could help clinicians identify high-risk patients and guide treatment deci-sions.However,prior models using conventional computed tomography(CT)images to predict LVI or PNI separately have had limited accuracy.Spectral CT provides quantitative enhancement parameters that may better capture tumor invasion.We hypothesized that a predictive model combining clinical and spectral CT parameters would accurately preoperatively predict LVI/PNI status in GC patients.AIM To develop and test a machine learning model that fuses spectral CT parameters and clinical indicators to predict LVI/PNI status accurately.METHODS This study used a retrospective dataset involving 257 GC patients(training cohort,n=172;validation cohort,n=85).First,several clinical indicators,including serum tumor markers,CT-TN stages and CT-detected extramural vein invasion(CT-EMVI),were extracted,as were quantitative spectral CT parameters from the delineated tumor regions.Next,a two-step feature selection approach using correlation-based methods and information gain ranking inside a 10-fold cross-validation loop was utilized to select informative clinical and spectral CT parameters.A logistic regression(LR)-based nomogram model was subsequently constructed to predict LVI/PNI status,and its performance was evaluated using the area under the receiver operating characteristic curve(AUC).RESULTS In both the training and validation cohorts,CT T3-4 stage,CT-N positive status,and CT-EMVI positive status are more prevalent in the LVI/PNI-positive group and these differences are statistically significant(P<0.05).LR analysis of the training group showed preoperative CT-T stage,CT-EMVI,single-energy CT values of 70 keV of venous phase(VP-70 keV),and the ratio of standardized iodine concentration of equilibrium phase(EP-NIC)were independent influencing factors.The AUCs of VP-70 keV and EP-NIC were 0.888 and 0.824,respectively,which were slightly greater than those of CT-T and CT-EMVI(AUC=0.793,0.762).The nomogram combining CT-T stage,CT-EMVI,VP-70 keV and EP-NIC yielded AUCs of 0.918(0.866-0.954)and 0.874(0.784-0.936)in the training and validation cohorts,which are significantly higher than using each of single independent factors(P<0.05).CONCLUSION The study found that using portal venous and EP spectral CT parameters allows effective preoperative detection of LVI/PNI in GC,with accuracy boosted by integrating clinical markers.

Noninvasive Detection of Salt Stress in Cotton Seedlings by Combining Multicolor Fluorescence-Multispectral Reflectance Imaging with EfficientNet-OB2

Salt stress is considered one of the primary threats to cotton production.Although cotton is found to have reasonable salt tolerance,it is sensitive to salt stress during the seedling stage.This research aimed to propose an effective method for rapidly detecting salt stress of cotton seedlings using multicolor fluorescence-multispectral reflectance imaging coupled with deep learning.A prototyping platform that can obtain multicolor fluorescence and multispectral reflectance images synchronously was developed to get different characteristics of each cotton seedling.The experiments revealed that salt stress harmed cotton seedlings with an increase in malondialdehyde and a decrease in chlorophyll content,superoxide dismutase,and catalase after 17 days of salt stress.The Relief algorithm and principal component analysis were introduced to reduce data dimension with the first 9 principal component images(PC1 to PC9)accounting for 95.2%of the original variations.An optimized EfficientNet-B2(EfficientNet-OB2),purposely used for a fixed resource budget,was established to detect salt stress by optimizing a proportional number of convolution kernels assigned to the first convolution according to the corresponding contributions of PC1 to PC9 images.EfficientNet-OB2 achieved an accuracy of 84.80%,91.18%,and 95.10%for 5,10,and 17 days of salt stress,respectively,which outperformed EfficientNet-B2 and EfficientNet-OB4 with higher training speed and fewer parameters.The results demonstrate the potential of combining multicolor fluorescence-multispectral reflectance imaging with the deep learning model EfficientNet-OB2 for salt stress detection of cotton at the seedling stage,which can be further deployed in mobile platforms for high-throughput screening in the field.

Rare Bilateral Radius and Ulna Fractures: A Case Report

Introduction: Forearm fractures involving both the radius and ulna, present distinctive challenges in orthopedic trauma management. This case report explores the complexities of a rare case of bilateral fractures, emphasizing the importance of a comprehensive approach for optimal outcomes. Case Presentation: This report presents the case of a 40-year-old motorcyclist who was involved in a road accident and arrived at the emergency department shortly after the incident. Clinical examination revealed closed fractures in both forearms with mild swelling and severe tenderness. Fortunately, no neurovascular issues or compartment syndrome were detected. The patient was administered intravenous fluids and effective pain relief. Forearm splints were applied and the arms were elevated using pillows. Radiographs showed fractures in the right distal radius and ulna, as well as the left mid-shaft radius and ulna. Under general anesthesia, open reduction and internal fixation were per-formed using plates and screws for all four fractures. Postoperatively, the patient’s arms were immobilized and elevated, with gradual recovery during follow-up appointments over six months, eventually achieving full function without complaints. Conclusion: This article highlights the possibility, although infrequent, of bilateral shaft fractures of the ulna and radius. With thorough clinical assessment and radiological investigation, such fractures can be well-defined. The required definitive treatment, which usually involves open reduction and internal fixation, can be performed.

Enhancing silicon spectral emission in LIBS using Tesla coil discharge

Laser-induced breakdown spectroscopy(LIBS)is a powerful technique for elemental analysis,offering rapid analysis,minimal sample preparation,wide elemental coverage,and portability.To enhance the detection sensitivity of LIBS,increasing the spectral emission intensity is crucial.This paper explores the use of Tesla coil(TC)discharge as an alternative to spark discharge in silicon LIBS.The study examines the influence of TC discharge on both time-integrated and timeresolved spectra,with and without TC discharge;the corresponding electron temperature and density are obtained.The results show that TC discharge significantly amplifies the spectral intensity,improving signal sensitivity in LIBS analysis.Specifically,in the laser energy range from 7.4 to 24.0 mJ,TC discharge increased the average spectral line intensities of Si(II)385.60 nm and Si(I)390.55 nm by factors of 8.4 and 5.1,respectively.Additionally,the average electron temperature and density were enhanced by approximately 3.2%and 4.2%,respectively,under TC discharge.The advantages of TC discharge include higher energy deposition,extended discharge duration,reduced electrode erosion,and enhanced safety.This research contributes to advancing LIBS technology and expanding its applications in various fields.

RE-SMOTE:A Novel Imbalanced Sampling Method Based on SMOTE with Radius Estimation

Imbalance is a distinctive feature of many datasets,and how to make the dataset balanced become a hot topic in the machine learning field.The Synthetic Minority Oversampling Technique(SMOTE)is the classical method to solve this problem.Although much research has been conducted on SMOTE,there is still the problem of synthetic sample singularity.To solve the issues of class imbalance and diversity of generated samples,this paper proposes a hybrid resampling method for binary imbalanced data sets,RE-SMOTE,which is designed based on the improvements of two oversampling methods parameter-free SMOTE(PF-SMOTE)and SMOTE-Weighted Ensemble Nearest Neighbor(SMOTE-WENN).Initially,minority class samples are divided into safe and boundary minority categories.Boundary minority samples are regenerated through linear interpolation with the nearest majority class samples.In contrast,safe minority samples are randomly generated within a circular range centered on the initial safe minority samples with a radius determined by the distance to the nearest majority class samples.Furthermore,we use Weighted Edited Nearest Neighbor(WENN)and relative density methods to clean the generated samples and remove the low-quality samples.Relative density is calculated based on the ratio of majority to minority samples among the reverse k-nearest neighbor samples.To verify the effectiveness and robustness of the proposed model,we conducted a comprehensive experimental study on 40 datasets selected from real applications.The experimental results show the superiority of radius estimation-SMOTE(RE-SMOTE)over other state-of-the-art methods.Code is available at:https://github.com/blue9792/RE-SMOTE(accessed on 30 September 2024).

Wind-sand flow simulation and radius optimization of highway embankment under different vertical curve radius

It is of great practical value to explore the correlation between the vertical curve radius of desert highway and the increase of sand accumulation in local lines,and to select the appropriate vertical curve radius for reducing the risk of sand accumulation.In this study,three-dimensional models of desert highway embankments with different vertical curve radii were constructed,and Fluent software was used to simulate the wind-sand flow field and sand accumulation distribution of vertical curve embankments.The results show that:(1)Along the direction of the road,the concave and the convex vertical curve embankments have the effect of collecting and diverging the wind-sand flow,respectively.When the radius of the concave vertical curve is 3000 m,5000 m,8000 m,10000 m and 20000 m,the wind velocity in the middle of the vertical curve is 31.76%,22.58%,10.78%,10.53%and 10.44%,higher than that at both ends.When the radius of the convex vertical curve is 6500 m,8000 m,10000 m,20000 m and 30000 m,the wind velocity at both ends of the vertical curve is 14.06%,9.99%,6.14%,3.22%and 2.41%,higher than that in the middle.The diversion effect also decreases with the increase of the radius.(2)The conductivity of the concave and convex vertical curve embankments with different radii is greater than 1,which is the sediment transport roadbed.The conductivity increases with the increase of radius and gradually tends to be stable.When the radius of the concave and convex vertical curves reaches 8000 m and 20000 m respectively,the phenomenon of sand accumulation is no longer serious.Under the same radius condition,the concave vertical curve embankment is more prone to sand accumulation than the convex one.(3)Considering the strength of the collection and diversion of the vertical curve embankment with different radii,and the sand accumulation of the vertical curve embankment in the desert section of Wuma Expressway,the radius of the concave vertical curve is not less than 8000 m,and the radius of the convex vertical curve is not less than 20000 m,which can effectively reduce the sand accumulation of the vertical curve embankment.In the desert highway area,the research results of this paper can provide reference for the design of vertical curve to ensure the safe operation of desert highway.

Experimental investigation of spectral evolution in flash radiation by hypervelocity impact on aluminum plates

In this study,a series of hypervelocity impact tests were carried out based on a two-stage light gas gun,and the sequence spectrum and radiation evolution data of the impact products under different impact conditions were obtained.The diameter of the projectile is 3-5 mm,the impact velocity is 3.13-6.58 km/s,and the chamber pressure is 0.56-990 Pa.The spectrum of ejected debris cloud in the 250-310 nm band were obtained using a transient spectral measurement system and a multi-channel radiometer measurement system.The test results reveal that the flash radiation intensity increases as a power function with the kinetic energy of the impact.Furthermore,the peak value of the line spectrum decreases as the chamber vacuum degree increases,while the radiation width gradually expands.The line spectrum in the spectral characterization curve corresponds to the ejected debris clouds splitting phase,which does not produce significant line spectrum during material fragmentation and is dominated by the continuum spectrum produced by blackbody radiation.There will appear one or three characteristic peaks in the flash radiation time curve,the first and second peaks correspond to the penetration phase and the third peak corresponds to the expansion phase of the ejected debris clouds on the time scale,the first and second peaks are more sensitive to the chamber vacuum degree,and when the pressure is higher than 99 Pa,the first and second characteristic peaks will disappear.The radiant heat attenuation of the flash under different impact conditions is significantly different,the attenuation exponent has a power function relationship with the impact velocity and the chamber vacuum degree,while the attenuation exponent has a linear relationship with the diameter of the projectile,the specific expression of the attenuation exponent is obtained by fitting.The findings from this research can serve as a valuable reference for remote diagnostic technologies based on flash radiation characteristics.