Influence of renal function on the ability of TyG Index to predict all-cause mortality.

BACKGROUND: The association between triglyceride-glucose (TyG) index and poor prognosis remains controversial. Whether renal function status affects the ability of the TyG index to predict poor prognosis has not yet been elucidated and merits further studies. METHODS: This retrospective cohort study included 22,031 participants from communities in the U.S. By juxtaposing the TyG categories with the estimated glomerular filtration rate (eGFR, either < 60 mL/min/1.73m2 or ≥ 60 mL/min/1.73m2), participants were categorized into four distinct groups: (1) TyG_L/eGFR_H; (2) TyG_H/eGFR_H; (3) TyG_L/eGFR_L; and (4) TyG_H/eGFR_L. The endpoint was the all-cause mortality rate. Standard Kaplan-Meier plots were constructed and multifactor Cox regression analyses were carried out and restricted cubic spline regression analysis was utilized to assess the association between death and the TyG index for different renal function statuses. RESULTS: No statistical differences were found in the TyG groups in participants with normal renal function after adjustment for all covariates (P = 0.070). However, in the high TyG index group with renal insufficiency, the risk of all-cause mortality rates was reduced by 18%. (HR, 0.82; CI, 0.69-0.98). The TyG index (high vs. low) and renal function (eGFR < 60 vs. eGFR ≥ 60) had statistically significant interactions with death (P < 0.001). When all covariates were adjusted, the risk of mortality for the TyG_L combined with eGFR_L group was 56% higher than that for the TyG_L combined with eGFR_H group (HR, 1.56; CI, 1.33-1.82). In the renal insufficiency population, a nonlinear relationship was observed between mortality and the TyG index, albeit with a differing pattern (P for nonlinearity < 0.001). CONCLUSIONS: While it has been known that TyG index was a prognosis marker of CVD, this research highlights that higher TyG index was associated with higher all-cause mortality rates for all participants. Furthermore, renal function status significantly moderates the effect of the TyG index on all-cause mortality in community-dwelling adults.

Association of the dietary inflammation index (DII) with the prevalence of chronic kidney disease in patients with type-2 diabetes mellitus.

Chronic kidney disease (CKD) is a major complication of diabetes mellitus (DM). Inflammation is an essential component in the process of CKD progression in patients with DM. Diet is a significant determinant of systemic inflammation levels. However, the association between the dietary inflammatory index (DII) and CKD in individuals with DM remains largely unknown; therefore, the aim of this study was to explore whether the DII is linked to the prevalence of CKD in patients with DM. The research method was as follows: first, data from the National Health and Nutrition Examination Survey (NHANES) between 1999 and 2018 were obtained. There were 7,974 participants in our study. These individuals were then classified into three groups according to DII tertiles (T1-T3), with each group consisting of 2,658 participants. Logistic regression analysis was employed to examine whether there was a connection between the DII and CKD. We observed a significant association between the DII and the prevalence of CKD in individuals with DM. After full adjustment for age, sex, ethnicity, smoking, drinking, body mass index (BMI), triglyceride (TG), total cholesterol (TC), metabolic equivalents (METs), energy intake, hypoglycemic medications, hypertension, and cardiovascular disease (CVD), the group with a higher DII had a greater frequency of CKD (T2 group: OR: 1.40; 95% CI: 1.10-1.76; p = 0.006; T3 group: OR: 1.67; 95% CI: 1.29-2.17; p < 0.001). The implementation of an anti-inflammatory diet could serve as an intervention strategy for patients with DM to prevent the onset of CKD.

Epidemiological Investigation of Pediatric Fractures-A Retrospective Cohort Study of 1129 Patients.

Background and Objectives: Fractures are common in pediatric trauma, and they are caused by a broad spectrum of factors. Only a few studies have discussed the mechanisms of injury and their relationships to different types of fractures. The most frequent type of fractures in different age groups remains unclear. Therefore, we aim to summarize the epidemiological characteristics of pediatric fractures in a medical center in Zhuhai, China from 2006 to 2021 and analyze the causes of fractures with the highest frequency in different age groups. Materials and Methods: We extracted the information from the Zhuhai Center for Maternal and Child Health Care of those under 14 years old who had fractures from 2006 to 2021. Results: We reviewed the information of 1145 children. The number of patients increased during the 15 years (p < 0.0001). The number of patients was significantly different between genders after Y2 (p = 0.014). In addition, more than two-thirds of patients (71.3%) had upper limb fractures, and all types of falls were the most common cause of fractures (83.6%). The incidence demonstrated an insignificant difference in age groups except for the fractures of humerus and radius. Moreover, we discovered that the prevalence of fall-related injuries decreased with age, while that of sports-related injuries increased with age. Conclusions: Our study demonstrates that the prevalence of fall-related injuries decreases with age, and that of sports-related injuries increases with age. Most patients have upper limb fractures, and all types of falls are the most common cause of fractures. Fracture types with the highest frequency differ in each age group. These findings might supplement current epidemiological knowledge of childhood fracture and provide references for decision-making in children's health policies.

Robust wide-range chirp rate measurement based on a flexible photonic fractional Fourier transformer.

We propose a photonic-assisted approach to measure the chirp rate of a linear frequency modulation waveform (LFMW) with a long duration, based on tunable photonic fractional Fourier transform (FrFT). Since the FrFT order can be continuously tuned by varying the frequency shift in an optical frequency-shifting loop (FSL), a specific FrFT order leads the fundamental frequency component arising in the output electrical spectrum to reach its maximum value, after the photonic-to-electrical conversion. Based on the designated FrFT order and the corresponding fundamental frequency in the output electrical spectrum, the chirp rate measurement over a wide range can be accessed, even the signal-to-noise ratio (SNR) of the input LFMW is substantially low. Simulation results indicate that the chirp rate of a 0.16-ms LFMW over a frequency range from 20 GHz to 26 GHz can be precisely characterized, with a relative measurement error of less than 0.13%, under the SNR condition of 0 dB. Moreover, an unambiguous chirp-rate measurement within the range of -5200 MHz/µs to 550 MHz/µs can be achieved. Hence, the proposed chirp rate measurement is featured with broadband operation, robust noise tolerance, low-frequency detection, and long-duration LFMW characterization.

Revealing potential diagnostic gene biomarkers of septic shock based on machine learning analysis.

BACKGROUND: Sepsis is an inflammatory response caused by infection with pathogenic microorganisms. The body shock caused by it is called septic shock. In view of this, we aimed to identify potential diagnostic gene biomarkers of the disease. MATERIAL AND METHODS: Firstly, mRNAs expression data sets of septic shock were retrieved and downloaded from the GEO (Gene Expression Omnibus) database for differential expression analysis. Functional enrichment analysis was then used to identify the biological function of DEmRNAs (differentially expressed mRNAs). Machine learning analysis was used to determine the diagnostic gene biomarkers for septic shock. Thirdly, RT-PCR (real-time polymerase chain reaction) verification was performed. Lastly, GSE65682 data set was utilized to further perform diagnostic and prognostic analysis of identified superlative diagnostic gene biomarkers. RESULTS: A total of 843 DEmRNAs, including 458 up-regulated and 385 down-regulated DEmRNAs were obtained in septic shock. 15 superlative diagnostic gene biomarkers (such as RAB13, KIF1B, CLEC5A, FCER1A, CACNA2D3, DUSP3, HMGN3, MGST1 and ARHGEF18) for septic shock were identified by machine learning analysis. RF (random forests), SVM (support vector machine) and DT (decision tree) models were used to construct classification models. The accuracy of the DT, SVM and RF models were very high. Interestingly, the RF model had the highest accuracy. It is worth mentioning that ARHGEF18 and FCER1A were related to survival. CACNA2D3 and DUSP3 participated in MAPK signaling pathway to regulate septic shock. CONCLUSION: Identified diagnostic gene biomarkers may be helpful in the diagnosis and therapy of patients with septic shock.

MicroRNA-342-3p loaded by human umbilical cord mesenchymal stem cells-derived exosomes attenuates deep vein thrombosis by downregulating EDNRA.

Exosomes (exos) exert biological functions to maintain the dynamic balance of cells and tissues by transferring biological cargo to recipient cells. Thus, this study explored human umbilical cord mesenchymal stem cells (hucMSCs)-derived exo transfer of microRNA (miR)-342-3p in deep vein thrombosis (DVT). DVT rat models were established via inferior vena cava (IVC) ligation. HucMSCs-exos were extracted and injected into rats with DVT to observe whether they could influences thrombus formation in vivo. HucMSCs-exos were co-cultured with human umbilical vein endothelial cells (HUVECs) in vitro to observe angiogenesis. miR-342-3p and endothelin A receptor (EDNRA) expression in rats with DVT, as well as their interaction was analyzed. miR-342-3p was downregulated and EDNRA was upregulated in rats with DVT. HucMSCs-exos inhibited the formation of thrombus in rats with DVT, as well as promoted angiogenesis of HUVECs. Upregulated miR-342-3p delivery by hucMSCs-exos alleviated DVT in rats and improved angiogenesis of HUVECs. miR-342-3p targeted EDNRA, and the effect of hucMSCs-exos transfer of upregulated miR-342-3p was rescued by overexpressing EDNRA. Briefly, miR-342-3p loaded by hucMSCs-exos attenuates DVT by downregulating EDNRA, offering a novel direction to treat DVT.

Decentralized Primal-Dual Proximal Operator Algorithm for Constrained Nonsmooth Composite Optimization Problems over Networks.

In this paper, we focus on the nonsmooth composite optimization problems over networks, which consist of a smooth term and a nonsmooth term. Both equality constraints and box constraints for the decision variables are also considered. Based on the multi-agent networks, the objective problems are split into a series of agents on which the problems can be solved in a decentralized manner. By establishing the Lagrange function of the problems, the first-order optimal condition is obtained in the primal-dual domain. Then, we propose a decentralized algorithm with the proximal operators. The proposed algorithm has uncoordinated stepsizes with respect to agents or edges, where no global parameters are involved. By constructing the compact form of the algorithm with operators, we complete the convergence analysis with the fixed-point theory. With the constrained quadratic programming problem, simulations verify the effectiveness of the proposed algorithm.

LncRNA FLVCR1-AS1 promotes proliferation, migration and activates Wnt/ß-catenin pathway through miR-381-3p/CTNNB1 axis in breast cancer.

BACKGROUND: Understanding the molecular mechanism of long non-coding RNAs (lncRNAs) in carcinogenesis is conducive for providing potential target for cancers. The role of FLVCR1-AS1 in breast cancer (BC) has not been probed yet. MATERIALS AND METHODS: qRT-PCR and western blot assays were used to estimate relevant expressions of mRNAs and proteins. CCK8, MTT and EdU were implemented to assess cell proliferation ability. TUNEL was performed to investigate cell apoptosis, whereas transwell assay was performed to test cell migration and invasion capacities. TOP/FOP Flash assay was conducted to determine the activity of Wnt/ß-catenin pathway. Luciferase reporter, RNA pull down and RIP assays were performed to verify interaction between genes. RESULTS: FLVCR1-AS1 was abnormally up-regulated in BC cells. Silencing FLVCR1-AS1 inhibited cell proliferation, migration, invasion, yet accelerating apoptosis. Inhibition of miR-381-3p reversed the tumor restraining impacts of FLVCR1-AS1 depletion on BC progression. Additionally, CTNNB1 was recognized to be targeted by miR-381-3p. FLVCR1-AS1 aggravated BC malignant progression via up-regulation CTNNB1 through sponging miR-381-3p. CONCLUSION: FLVCR1-AS1 regulates BC malignant behavior via sequestering miR-381-3p and then freeing CTNNB1, implying a promising target for BC therapy.

Furosemide reduces BK-αß4-mediated K+ secretion in mice on an alkaline high-K+ diet.

Special high-K diets have cardioprotective effects and are often warranted in conjunction with diuretics such as furosemide for treating hypertension. However, it is not understood how a high-K diet (HK) influences the actions of diuretics on renal K+ handling. Furosemide acidifies the urine by increasing acid secretion via the Na+-H+ exchanger 3 (NHE3) in TAL and vacuolar H+-ATPase (V-ATPase) in the distal nephron. We previously found that an alkaline urine is required for large conductance Ca2+-activated K+ (BK)-αß4-mediated K+ secretion in mice on HK. We therefore hypothesized that furosemide could reduce BK-αß4-mediated K+ secretion by acidifying the urine. Treating with furosemide (drinking water) for 11 days led to decreased urine pH in both wild-type (WT) and BK-ß4-knockout mice (BK-ß4-KO) with increased V-ATPase expression and elevated plasma aldosterone levels. However, furosemide decreased renal K+ clearance and elevated plasma [K+] in WT but not BK-ß4-KO. Western blotting and immunofluorescence staining showed that furosemide treatment decreased cortical expression of BK-ß4 and reduced apical localization of BK-α in connecting tubules. Addition of the carbonic anhydrase inhibitor, acetazolamide, to furosemide water restored urine pH along with renal K+ clearance and plasma [K+] to control levels. Acetazolamide plus furosemide also restored the cortical expression of BK-ß4 and BK-α in connecting tubules. These results indicate that in mice adapted to HK, furosemide reduces BK-αß4-mediated K+ secretion by acidifying the urine.

Net K+ secretion in the thick ascending limb of mice on a low-Na, high-K diet.

Because of its cardio-protective effects, a low-Na, high-K diet (LNaHK) is often warranted in conjunction with diuretics to treat hypertensive patients. However, it is necessary to understand the renal handling of such diets in order to choose the best diuretic. Wild-type (WT) or Renal Outer Medullary K channel (ROMK) knockout mice (KO) were given a regular (CTRL), LNaHK, or high-K diet (HK) for 4-7 days. On LNaHK, mice treated with either IP furosemide for 12 hrs, or given furosemide in drinking water for 7 days, exhibited decreased K clearance. We used free-flow micropuncture to measure the [K+] in the early distal tubule (EDT [K+]) before and after furosemide treatment. Furosemide increased the EDT [K+] in WT on CTRL but decreased that in WT on LNaHK. Furosemide did not affect the EDT [K+] of KO on LNaHK or WT on HK. Furosemide-sensitive Na+ excretion was significantly greater in mice on LNaHK than those on CTRL or HK. Patch clamp analysis of split-open TALs revealed that 70-pS ROMK exhibited a higher open probability (Po) but similar density in mice on LNaHK, compared with CTRL. No difference was found in the density or Po of the 30 pS K channels between the two groups. These results indicate mice on LNaHK exhibited furosemide-sensitive net K+ secretion in the TAL that is dependent on increased NKCC2 activity and mediated by ROMK. We conclude that furosemide is a K-sparing diuretic by decreasing the TAL net K+ secretion in subjects on LNaHK.

Deficient acid handling with distal RTA in the NBCe2 knockout mouse.

In many circumstances, the pathogenesis of distal renal tubular acidosis (dRTA) is not understood. In the present study, we report that a mouse model lacking the electrogenic Na(+)-HCO3 (-) cotransporter [NBCe2/Slc4a5; NBCe2 knockout (KO) mice] developed dRTA after an oral acid challenge. NBCe2 expression was identified in the connecting tubule (CNT) of wild-type mice, and its expression was significantly increased after acid loading. NBCe2 KO mice did not have dRTA when on a standard mouse diet. However, after acid loading, NBCe2 KO mice exhibited complete features of dRTA, characterized by insufficient urinary acidification, hyperchloremic hypokalemic metabolic acidosis, and hypercalciuria. Additional experiments showed that NBCe2 KO mice had decreased luminal transepithelial potential in the CNT, as revealed by micropuncture. Further immunofluorescence and Western blot experiments found that NBCe2 KO mice had increased expression of H(+)-ATPase B1 in the plasma membrane. These results showed that NBCe2 KO mice with acid loading developed increased urinary K(+) and Ca(2+) wasting due to decreased luminal transepithelial potential in the CNT. NBCe2 KO mice compensated to maintain systemic pH by increasing H(+)-ATPase in the plasma membrane. Therefore, defects in NBCe2 can cause dRTA, and NBCe2 has an important role to regulate urinary acidification and the transport of K(+) and Ca(2+) in the distal nephron.

Relation between BK-α/ß4-mediated potassium secretion and ENaC-mediated sodium reabsorption.

The large-conductance, calcium-activated BK-α/ß4 potassium channel, localized to the intercalated cells of the distal nephron, mediates potassium secretion during high-potassium, alkaline diets. Here we determine whether BK-α/ß4-mediated potassium transport is dependent on epithelial sodium channel (ENaC)-mediated sodium reabsorption. We maximized sodium-potassium exchange in the distal nephron by feeding mice a low-sodium, high-potassium diet. Wild-type and BK-ß4 knockout mice were maintained on a low-sodium, high-potassium, alkaline diet or a low-sodium, high-potassium, acidic diet for 7-10 days. Wild-type mice maintained potassium homeostasis on the alkaline, but not acid, diet. BK-ß4 knockout mice could not maintain potassium homeostasis on either diet. During the last 12 h of diet, wild-type mice on either a regular, alkaline, or an acid diet, or knockout mice on an alkaline diet, were administered amiloride (an ENaC inhibitor). Amiloride enhanced sodium excretion in all wild-type and knockout groups to similar values; however, amiloride diminished potassium excretion by 59% in wild-type but only by 33% in knockout mice on an alkaline diet. Similarly, amiloride decreased the trans-tubular potassium gradient by 68% in wild-type but only by 42% in knockout mice on an alkaline diet. Amiloride treatment equally enhanced sodium excretion and diminished potassium secretion in knockout mice on an alkaline diet and wild-type mice on an acid diet. Thus, the enhanced effect of amiloride on potassium secretion in wild-type compared to knockout mice on the alkaline diet clarify a BK- α/ß4-mediated potassium secretory pathway in intercalated cells driven by ENaC-mediated sodium reabsorption linked to bicarbonate secretion.

Explanatory subgraph attacks against Graph Neural Networks.

Graph Neural Networks (GNNs) are often viewed as black boxes due to their lack of transparency, which hinders their application in critical fields. Many explanation methods have been proposed to address the interpretability issue of GNNs. These explanation methods reveal explanatory information about graphs from different perspectives. However, the explanatory information may also pose an attack risk to GNN models. In this work, we will explore this problem from the explanatory subgraph perspective. To this end, we utilize a powerful GNN explanation method called SubgraphX and deploy it locally to obtain explanatory subgraphs from given graphs. Then we propose methods for conducting evasion attacks and backdoor attacks based on the local explainer. In evasion attacks, the attacker gets explanatory subgraphs of test graphs from the local explainer and replace their explanatory subgraphs with an explanatory subgraph of other labels, making the target model misclassify test graphs as wrong labels. In backdoor attacks, the attacker employs the local explainer to select an explanatory trigger and locate suitable injection locations. We validate the effectiveness of our proposed attacks on state-of-art GNN models and different datasets. The results also demonstrate that our proposed backdoor attack is more efficient, adaptable, and concealed than previous backdoor attacks.

Prescribed-time containment control of multi-agent systems subject to collision avoidance and connectivity maintenance.

In this paper, the problem of prescribed-time containment control for a second-order multiple leader-follower systems (MLFSs) is studied, in where both collision avoidance and connectivity maintenance of the agents are considered. Firstly, an effective exponential potential field function (EAPF) with constraints based on the estimated distance is designed to achieve collision resistance and connectivity preservation of the agents at a prescribed-time. Secondly, an estimator-based distributed control protocol is proposed, which drives the agents to achieve containment control in a cooperative manner at a prescribed-time. Furthermore, a novel distributed control protocol containing a collision avoidance term and a containment control term is addressed as well, which enables all followers to complete collision avoidance and connectivity maintenance in any prescribed-time and enter the leaders' convex packet. Finally, the stability of the system is technically analyzed by using Lyapunov theory, and the effectiveness of the presented strategies is verified by several simulations.

Leader-Following Synchronization Control of Multiagent Systems Under Hybrid Cyber Attacks via Impulsive Control Based on Topology Switching.

This article investigates the leader-following synchronization problem of multiagent systems (MASs) under hybrid cyber attacks, which refers to deception attacks and multichannel independent denial-of-service (DoS) attacks in communication channels. In order to achieve the secure control of MASs under hybrid cyber attacks, a novel impulsive control method based on topology switching is proposed, and a new algorithm for determining impulsive instants is designed. In addition, the cooperative-competitive relationship between agents is also considered, which is more in line with reality. Sufficient conditions for ensuring secure control of MASs and a parametric upper bound on the error vector norm between the agents and the leader are obtained. Finally, the numerical simulation verified the effectiveness of the proposed algorithm.

Eosin Y Post-Decorated Metal-Organic Framework as a Selectivity Regulator for the Alcohols Oxidation.

The selective oxidation of alcohols into aldehydes is a basic and significant procedure, with great potential for scientific research and industrial applications. However, as an important factor in the C(sp3)-H activation process, high selectivity is generally difficult to achieve due to the fact that the more easily activated properties of aldehydes are compared to alcohols. Herein, by the ingenious decoration of eosin Y into a Zr-based metal-organic framework (MOF-808), EY@MOF-808 was prepared as a selectivity regulator for the aerobic oxidation of the benzyl alcohols into corresponding aldehydes, possessing applicability for the benzylic alcohols with various substituents. By anchoring eosin Y on Zr6O4(OH)4 clusters of MOF-808 and maintaining open metal nodes with selective binding effects, the benzyl alcohol substrates were selectively coordinated to the unsaturated metal clusters adjacent to eosin Y, which ensured that the excited eosin Y rapidly activated substrates to generate carbon radicals by the hydrogen atom transfer (HAT) process. The rapid electron transfer (ET) simultaneously produced reactive oxygen species (O2•-) and then a combination of both to further promote the generation of benzaldehydes. The weak interaction of benzaldehydes with the skeleton allowed it to dissociate rapidly, thus preventing overoxidation. Under the catalysis of EY@MOF-808, the selectivity of various benzaldehydes was more than 99%. In contrast, eosin Y gave only benzoic acid products under the same conditions, which demonstrated the superiority of regulatory selectivity of EY@MOF-808. Taking advantage of the heterogeneity of the MOF, EY@MOF-808 was recycled four times without a decrease in its selectivity and avoided the quenching effect of eosin Y. The organic functional units postdecorated MOF-based photocatalyst strategy exhibits a promising new perspective approach to sustainably regulating the selectivity of inert oxidation.

Primal-Dual Fixed Point Algorithms Based on Adapted Metric for Distributed Optimization.

This article considers distributed optimization by a group of agents over an undirected network. The objective is to minimize the sum of a twice differentiable convex function and two possibly nonsmooth convex functions, one of which is composed of a bounded linear operator. A novel distributed primal-dual fixed point algorithm is proposed based on an adapted metric method, which exploits the second-order information of the differentiable convex function. Furthermore, by incorporating a randomized coordinate activation mechanism, we propose a randomized asynchronous iterative distributed algorithm that allows each agent to randomly and independently decide whether to perform an update or remain unchanged at each iteration, and thus alleviates the communication cost. Moreover, the proposed algorithms adopt nonidentical stepsizes to endow each agent with more independence. Numerical simulation results substantiate the feasibility of the proposed algorithms and the correctness of the theoretical results.

Exhaustive drainage versus fixed-time drainage for chronic subdural hematoma after one-burr hole craniostomy (ECHO): study protocol for a multicenter randomized controlled trial.

BACKGROUND: Chronic subdural hematomas (CSDHs) are one of the most common neurosurgical conditions. The standard surgical technique includes burr-hole craniostomy, followed by intraoperative irrigation and placement of subdural closed-system drainage. The drainage is generally removed after 48 h, which can be described as fixed-time drainage strategy. According to literature, the recurrence rate is 5-33% with this strategy. In our retrospective study, postoperative hematoma volume was found to significantly increase the risk of recurrence. Based on these results, an exhaustive drainage strategy is conducted to minimize postoperative hematoma volume and achieve a low recurrence rate and good outcomes. METHODS: This is a prospective, multicenter, open-label, blinded endpoint randomized controlled trial designed to include 304 participants over the age of 18-90 years presenting with a symptomatic CSDH verified on cranial computed tomography or magnetic resonance imaging. Participants will be randomly allocated to perform exhaustive drainage (treatment group) or fixed-time drainage (control group) after a one-burr hole craniostomy. The primary endpoint will be recurrence indicating a reoperation within 6 months. DISCUSSION: This study will validate the effect and safety of exhaustive drainage after one-burr hole craniostomy in reducing recurrence rates and provide critical information to improve CSDH surgical management. TRIAL REGISTRATION: Clinicaltrials.gov, NCT04573387. Registered on October 5, 2020.

Pattern Formation in a Reaction-Diffusion BAM Neural Network With Time Delay: (k1, k2) Mode Hopf-Zero Bifurcation Case.

This article investigates the joint effects of connection weight and time delay on pattern formation for a delayed reaction-diffusion BAM neural network (RDBAMNN) with Neumann boundary conditions by using the (k1,k2) mode Hopf-zero bifurcation. First, the conditions for k1 mode zero bifurcation are obtained by choosing connection weight as the bifurcation parameter. It is found that the connection weight has a great impact on the properties of steady state. With connection weight increasing, the homogeneous steady state becomes inhomogeneous, which means that the connection weight can affect the spatial stability of steady state. Then, the specified conditions for the k2 mode Hopf bifurcation and the (k1,k2) mode Hopf-zero bifurcation are established. By using the center manifold, the third-order normal form of the Hopf-zero bifurcation is obtained. Through the analysis of the normal form, the bifurcation diagrams on two parameters' planes (connection weight and time delay) are obtained, which contains six areas. Some interesting spatial patterns are found in these areas: a homogeneous periodic solution, a homogeneous steady state, two inhomogeneous steady state, and two inhomogeneous periodic solutions.

Event-Triggering Interaction Scheme for Discrete-Time Decentralized Optimization With Nonuniform Step Sizes.

In this article, we study the discrete-time decentralized optimization problems of multiagent systems by an event-triggering interaction scheme, in which each agent privately knows its local convex cost function, and collectively minimizes the total cost functions. The underlying interaction and the corresponding weight matrix are required to be undirected connected and doubly stochastic, respectively. To resolve this optimization problem collaboratively, we propose a decentralized event-triggering algorithm (DETA) that is based on the consensus theory and inexact gradient tracking technique. DETA involves each agent interacting with its neighboring agents only at some independent event-triggering sampling time instants. Under the assumptions that the global convex cost function is coercive and has Lipschitz continuous gradient, we prove that DETA steers all agents' states to an optimal solution even with nonuniform constant step sizes. Moreover, our analysis also shows that DETA converges at a rate of O(1/√t) if the step sizes are uniform and do not exceed some upper bounds. We illustrate the effectiveness of DETA on a canonical simple decentralized parameter estimation problem.