Matrix Riccati Equations in Optimal Control

In this paper, the matrix Riccati equation is considered. There is no general way for solving the matrix Riccati equation despite the many fields to which it applies. While scalar Riccati equation has been studied thoroughly, matrix Riccati equation of which scalar Riccati equations is a particular case, is much less investigated. This article proposes a change of variable that allows to find explicit solution of the Matrix Riccati equation. We then apply this solution to Optimal Control.

Factors influencing Frey syndrome after parotidectomy with acellular dermal matrix

BACKGROUND Frey syndrome,also known as ototemporal nerve syndrome or gustatory sweating syndrome,is one of the most common complications of parotid gland surgery.This condition is characterized by abnormal sensations in the facial skin accompanied by episodes of flushing and sweating triggered by cognitive processes,visual stimuli,or eating.AIM To investigate the preventive effect of acellular dermal matrix(ADM)on Frey syndrome after parotid tumor resection and analyzed the effects of Frey syndrome across various surgical methods and other factors involved in parotid tumor resection.METHODS Retrospective data from 82 patients were analyzed to assess the correlation between sex,age,resection sample size,operation time,operation mode,ADM usage,and occurrence of postoperative Frey syndrome.RESULTS Among the 82 patients,the incidence of Frey syndrome was 56.1%.There were no significant differences in sex,age,or operation time between the two groups(P>0.05).However,there was a significant difference between ADM implantation and occurrence of Frey syndrome(P<0.05).ADM application could reduce the variation in the incidence of Frey syndrome across different operation modes.CONCLUSION ADM can effectively prevent Frey syndrome and delay its onset.

Biofabrication of nanocomposite-based scaffolds containing human bone extracellularmatrix for the differentiation of skeletal stem and progenitor cells

Autograft or metal implants are routinely used in skeletal repair.However,they fail to provide long-term clinical resolution,necessitating a functional biomimetic tissue engineering alternative.The use of native human bone tissue for synthesizing a biomimeticmaterial inkfor three-dimensional(3D)bioprintingof skeletal tissueis anattractivestrategyfor tissueregeneration.Thus,human bone extracellular matrix(bone-ECM)offers an exciting potential for the development of an appropriate microenvironment for human bone marrow stromal cells(HBMSCs)to proliferate and differentiate along the osteogenic lineage.In this study,we engineered a novel material ink(LAB)by blending human bone-ECM(B)with nanoclay(L,Laponite®)and alginate(A)polymers using extrusion-based deposition.The inclusion of the nanofiller and polymeric material increased the rheology,printability,and drug retention properties and,critically,the preservation of HBMSCs viability upon printing.The composite of human bone-ECM-based 3D constructs containing vascular endothelial growth factor(VEGF)enhanced vascularization after implantation in an ex vivo chick chorioallantoic membrane(CAM)model.The inclusion of bone morphogenetic protein-2(BMP-2)with the HBMSCs further enhanced vascularization and mineralization after only seven days.This study demonstrates the synergistic combination of nanoclay with biomimetic materials(alginate and bone-ECM)to support the formation of osteogenic tissue both in vitro and ex vivo and offers a promising novel 3D bioprinting approach to personalized skeletal tissue repair.

An approximate analytical model for unconventional reservoir considering variable matrix blocks and simultaneous matrix depletion

In regard to unconventional oil reservoirs,the transient dual-porosity and triple-porosity models have been adopted to describe the fluid flow in the complex fracture network.It has been proven to cause inaccurate production evaluations because of the absence of matrix-macrofracture communication.In addition,most of the existing models are solved analytically based on Laplace transform and numerical inversion.Hence,an approximate analytical solution is derived directly in real-time space considering variable matrix blocks and simultaneous matrix depletion.To simplify the derivation,the simultaneous matrix depletion is divided into two parts:one part feeding the macrofractures and the other part feeding the microfractures.Then,a series of partial differential equations(PDEs)describing the transient flow and boundary conditions are constructed and solved analytically by integration.Finally,a relationship between oil rate and production time in real-time space is obtained.The new model is verified against classical analytical models.When the microfracture system and matrix-macrofracture communication is neglected,the result of the new model agrees with those obtained with the dual-porosity and triple-porosity model,respectively.Certainly,the new model also has an excellent agreement with the numerical model.The model is then applied to two actual tight oil wells completed in western Canada sedimentary basin.After identifying the flow regime,the solution suitably matches the field production data,and the model parameters are determined.Through these output parameters,we can accurately forecast the production and even estimate the petrophysical properties.

Reinforced tissue matrix to strengthen the abdominal wall following reversal of temporary ostomies or to treat incisional hernias

BACKGROUND Abdominal wall deficiencies or weakness are a common complication of tem-porary ostomies,and incisional hernias frequently develop after colostomy or ileostomy takedown.The use of synthetic meshes to reinforce the abdominal wall has reduced hernia occurrence.Biologic meshes have also been used to enhance healing,particularly in contaminated conditions.Reinforced tissue matrices(R-TMs),which include a biologic scaffold of native extracellular matrix and a syn-thetic component for added strength/durability,are designed to take advantage of aspects of both synthetic and biologic materials.To date,RTMs have not been reported to reinforce the abdominal wall following stoma reversal.METHODS Twenty-eight patients were selected with a parastomal and/or incisional hernia who had received a temporary ileostomy or colostomy for fecal diversion after rectal cancer treatment or trauma.Following hernia repair and proximal stoma closure,RTM(OviTex®1S permanent or OviTex®LPR)was placed to reinforce the abdominal wall using a laparoscopic,robotic,or open surgical approach.Post-operative follow-up was performed at 1 month and 1 year.Hernia recurrence was determined by physical examination and,when necessary,via computed tomo-graphy scan.Secondary endpoints included length of hospital stay,time to return to work,and hospital readmissions.Evaluated complications of the wound/repair site included presence of surgical site infection,seroma,hematoma,wound dehiscence,or fistula formation.RESULTS The observational study cohort included 16 male and 12 female patients with average age of 58.5 years±16.3 years and average body mass index of 26.2 kg/m^(2)±4.1 kg/m^(2).Patients presented with a parastomal hernia(75.0%),in-cisional hernia(14.3%),or combined parastomal/incisional hernia(10.7%).Using a laparoscopic(53.6%),robotic(35.7%),or open(10.7%)technique,RTMs(OviTex®LPR:82.1%,OviTex®1S:17.9%)were placed using sublay(82.1%)or intraperitoneal onlay(IPOM;17.9%)mesh positioning.At 1-month and 1-year follow-ups,there were no hernia recurrences(0%).Average hospital stays were 2.1 d±1.2 d and return to work occurred at 8.3 post-operative days±3.0 post-operative days.Three patients(10.7%)were readmitted before the 1-month follow up due to mesh infection and/or gastrointestinal issues.Fistula and mesh infection were observed in two patients each(7.1%),leading to partial mesh removal in one patient(3.6%).There were no complications between 1 month and 1 year(0%).CONCLUSION RTMs were used successfully to treat parastomal and incisional hernias at ileostomy reversal,with no hernia recurrences and favorable outcomes after 1-month and 1-year.

Amino-functionalized UiO-66-doped mixed matrix membranes with high permeation performance and fouling resistance

For the reduction of bovine serum proteins from wastewater,a novel mixed matrix membrane was prepared by functionalizing the substrate material polyaryletherketone(PAEK),followed by carboxyl groups(C-SPAEKS),and then adding amino-functionalized UiO-66-NH_(2)(Am-UiO-66-NH_(2)).Aminofunctionalization of UiO-66 was accomplished by melamine,followed by an amidation reaction to immobilize Am-UiO-66-NH_(2),which was immobilized on the surface of the membrane as well as in the pore channels,which enhanced the hydrophilicity of the membrane surface while increasing the negative potential of the membrane surface.This nanoparticle-loaded ultrafiltration membrane has good permeation performance,with a pure water flux of up to 482.3 L·m^(-2)·h^(-1) for C-SPAEKS/AmUiO-66-NH_(2) and a retention rate of up to 98.7%for bovine serum albumin(BSA)-contaminated solutions.Meanwhile,after several hydrophilic modifications,the flux recovery of BSA contaminants by this series of membranes increased from 56.2%to 80.55%of pure membranes.The results of ultra-filtration flux time tests performed at room temperature showed that the series of ultrafiltration membranes remained relatively stable over a test time of 300 min.Thus,the newly developed mixed matrix membrane showed potential for high efficiency and stability in wastewater treatment containing bovine serum proteins.

Low-Complexity Reconstruction of Covariance Matrix in Hybrid Uniform Circular Array

Spatial covariance matrix(SCM) is essential in many multi-antenna systems such as massive multiple-input multiple-output(MIMO). For multi-antenna systems operating at millimeter-wave bands, hybrid analog-digital structure has been widely adopted to reduce the cost of radio frequency chains.In this situation, signals received at the antennas are unavailable to the digital receiver, and as a consequence, traditional sample average approach cannot be used for SCM reconstruction in hybrid multi-antenna systems. To address this issue, beam sweeping algorithm(BSA) which can reconstruct the SCM effectively for a hybrid uniform linear array, has been proposed in our previous works. However, direct extension of BSA to a hybrid uniform circular array(UCA)will result in a huge computational burden. To this end, a low-complexity approach is proposed in this paper. By exploiting the symmetry features of SCM for the UCA, the number of unknowns can be reduced significantly and thus the complexity of reconstruction can be saved accordingly. Furthermore, an insightful analysis is also presented in this paper, showing that the reduction of the number of unknowns can also improve the accuracy of the reconstructed SCM. Simulation results are also shown to demonstrate the proposed approach.

Association between Gene Polymorphisms and SNP-SNP Interactions of the Matrix Metalloproteinase 2 Signaling Pathway and the Risk of Vascular Senescence

Objective This study aimed to explore the association of single nucleotide polymorphisms(SNP)in the matrix metalloproteinase 2(MMP-2)signaling pathway and the risk of vascular senescence(VS).Methods In this cross-sectional study,between May and November 2022,peripheral venous blood of151 VS patients(case group)and 233 volunteers(control group)were collected.Fourteen SNPs were identified in five genes encoding the components of the MMP-2 signaling pathway,assessed through carotid-femoral pulse wave velocity(cf PWV),and analyzed using multivariate logistic regression.The multigene influence on the risk of VS was assessed using multifactor dimensionality reduction(MDR)and generalized multifactor dimensionality regression(GMDR)modeling.Results Within the multivariate logistic regression models,four SNPs were screened to have significant associations with VS:chemokine(C-C motif)ligand 2(CCL2)rs4586,MMP2 rs14070,MMP2rs7201,and MMP2 rs1053605.Carriers of the T/C genotype of MMP2 rs14070 had a 2.17-fold increased risk of developing VS compared with those of the C/C genotype,and those of the T/T genotype had a19.375-fold increased risk.CCL2 rs4586 and MMP-2 rs14070 exhibited the most significant interactions.Conclusion CCL2 rs4586,MMP-2 rs14070,MMP-2 rs7201,and MMP-2 rs1053605 polymorphisms were significantly associated with the risk of VS.

Analysis of the Tragedy of Vila Socóin Cubatão (São Paulo, Brazil) Using the Haddon Matrix: A Comprehensive Examination of Socio-Environmental Factors and Risk Mitigation Strategies

The tragedy of Vila Socó epitomizes the socio-environmental repercussions of rapid industrialization in Cubatão. Beginning in the 1940s with the construction of the Anchieta highway, the city experienced an influx of migrants drawn by burgeoning industries, leading to unplanned urban growth and the emergence of vulnerable communities like Vila Socó. This article examines the interconnected factors—such as demographic shifts, inadequate planning, and regulatory oversight—that culminated in the devastating fire of 1984, claiming numerous lives and highlighting systemic failures. Utilizing the Haddon Matrix, this study dissects the Vila Socó incident, emphasizing the roles of human error, infrastructure integrity, and socio-economic disparities in disaster causation. By contextualizing the tragedy within Cubatão’s industrial trajectory, it underscores the urgent need for comprehensive risk assessment and proactive mitigation strategies in rapidly developing regions globally. Beyond its immediate focus, this work offers broader insights into the dynamics of industrial disasters and their socio-economic implications. As pipelines continue to play a vital role in global energy infrastructure, the lessons drawn from Vila Socó’s tragedy resonate deeply, emphasizing the imperative of robust safety protocols and accountable governance to prevent similar catastrophes in the future.

Recent progress in ternary mixed matrix membranes for CO_(2) separation

Mixed matrix membranes(MMMs)could combine the advantages of both polymeric membranes and porousfillers,making them an effective alternative to conventional polymer membranes.However,interfacial incompatibility issues,such as the presence of interfacial voids,hardening of polymer chains,and blockage of micropores by polymers between common MMMsfillers and the polymer matrix,currently limit the gas sep-aration performance of MMMs.Ternary phase MMMs(consisting of afiller,an additive,and a matrix)made by adding a third compound,usually functionalized additives,can overcome the structural problems of binary phase MMMs and positively impact membrane separation performance.This review introduces the structure and fabrication processes for ternary MMMs,categorizes various nanofillers and the third component,and summarizes and analyzes in detail the CO_(2) separation performance of newly developed ternary MMMs based on both rubbery and glassy polymers.Based on this separation data,the challenges of ternary MMMs are also discussed.Finally,future directions for ternary MMMs are proposed.

Placenta-derived mesenchymal stem cells attenuate secondary brain injury after controlled cortical impact in rats by inhibiting matrix metalloproteinases

Background:As a form of biological therapy,placenta-derived mesenchymal stem cells(PDMSCs)exhibit considerable promise in addressing the complex pathological processes of traumaticbrain injury(TBI)due to their multi-target and multi-pathway mode of action.Material&Methods:This study investigates the protective mechanisms and benefits of PDMSCs in mitigating the effects of controlled cortical impact(CCI)in rats and glutamate-induced oxidative stress injury in HT22 cells in vitro.Our primary objective is to provide evidence supporting the clinical application of PDMSCs.Results:In the in vivo arm of our investigation,we observed a swift elevation of matrix metalloproteinase-9(MMP-9)in the proximal cortex of injured brain tissues after CCI.PDMSCs,distinguished by their heightened expression of metalloproteinase tissue inhibitors-1 and-2(TIMP-1 and TIMP-2):were intravenously administered via the caudal vein.This intervention yielded significant reductions in the permeability of the blood-brain barrier(BBB):the extent of brain edema,the levels of inflammatory cytokines IL-1βand TNF-αin damaged brain tissue,and the activation status of microglia in CCI-afflicted rats.In the realm of in vitro experiments,PDMSC-conditioned media demonstrated substantial reductions in mortality rates and cleaved caspase-3 levels in glutamate-induced HT22 cells compared with conventional media.Notably,this advantage was negated upon the introduction of neutralizing antibodies targeting TIMP-1 and TIMP-2.Conclusion:Collectively,our findings underscore the potential of PDMSCs in alleviating oxidative stress injury and secondary brain injury in the pathological process of TBI.

Effect of Heat Treatment on Microstructure and Mechanical Properties of Multiscale SiC_p Hybrid Reinforced 6061 Aluminum Matrix Composites

The performance of solid solution aging treatment on aluminum matrix composites prepared by powder metallurgy and reinforced with 6061 aluminum alloy powder as matrix;meanwhile, nano silicon carbide particles(nm Si Cp), submicron silicon carbide particles(1 μm Si Cp) and Ti particles were studied. The Al/Si Cp composite powder was prepared by high-energy ball milling, and then cold-pressed, sintered, hotextruded, and then heat-treated with different solution temperatures and aging times for the extruded composites. Optical microscopy, scanning electron microscopy, energy dispersive X-ray spectroscopy(EDS), X-ray diffractometer(XRD) and extrusion testing were used to analyze and test the microstructure and mechanical properties of aluminum matrix composites. The results show that after the multi-stage solid solution at 530 ℃×2 h+535 ℃×2 h+540 ℃×2 h, the particles are mainly equiaxed grains and uniformly distributed. There is no reinforcement agglomeration, and the surface is dense and the insoluble phase is basically dissolved. In the matrix, the strengthening effect is good, and the hardness and compressive strength are 179.43 HV and 680.42 MPa, respectively. Under this solution process, when the aluminum matrix composites are aged at 170 ℃ for 10 h, the hardness and compressive strength can reach their peaks and increase to 195.82 HV and 721.48 MPa, respectively.

Working condition recognition of sucker rod pumping system based on 4-segment time-frequency signature matrix and deep learning

High-precision and real-time diagnosis of sucker rod pumping system(SRPS)is important for quickly mastering oil well operations.Deep learning-based method for classifying the dynamometer card(DC)of oil wells is an efficient diagnosis method.However,the input of the DC as a two-dimensional image into the deep learning framework suffers from low feature utilization and high computational effort.Additionally,different SRPSs in an oil field have various system parameters,and the same SRPS generates different DCs at different moments.Thus,there is heterogeneity in field data,which can dramatically impair the diagnostic accuracy.To solve the above problems,a working condition recognition method based on 4-segment time-frequency signature matrix(4S-TFSM)and deep learning is presented in this paper.First,the 4-segment time-frequency signature(4S-TFS)method that can reduce the computing power requirements is proposed for feature extraction of DC data.Subsequently,the 4S-TFSM is constructed by relative normalization and matrix calculation to synthesize the features of multiple data and solve the problem of data heterogeneity.Finally,a convolutional neural network(CNN),one of the deep learning frameworks,is used to determine the functioning conditions based on the 4S-TFSM.Experiments on field data verify that the proposed diagnostic method based on 4S-TFSM and CNN(4S-TFSM-CNN)can significantly improve the accuracy of working condition recognition with lower computational cost.To the best of our knowledge,this is the first work to discuss the effect of data heterogeneity on the working condition recognition performance of SRPS.

Automatic modulation recognition of radiation source signals based on two-dimensional data matrix and improved residual neural network

Automatic modulation recognition(AMR)of radiation source signals is a research focus in the field of cognitive radio.However,the AMR of radiation source signals at low SNRs still faces a great challenge.Therefore,the AMR method of radiation source signals based on two-dimensional data matrix and improved residual neural network is proposed in this paper.First,the time series of the radiation source signals are reconstructed into two-dimensional data matrix,which greatly simplifies the signal preprocessing process.Second,the depthwise convolution and large-size convolutional kernels based residual neural network(DLRNet)is proposed to improve the feature extraction capability of the AMR model.Finally,the model performs feature extraction and classification on the two-dimensional data matrix to obtain the recognition vector that represents the signal modulation type.Theoretical analysis and simulation results show that the AMR method based on two-dimensional data matrix and improved residual network can significantly improve the accuracy of the AMR method.The recognition accuracy of the proposed method maintains a high level greater than 90% even at -14 dB SNR.

先锋女性主义者的建筑实验--英国Matrix的女性主义建筑观念与实践研究

英国的Matrix是西方第一个明确以女性主义为主张的女性建筑事务所。在特定的时代背景下,她们试图挑战父权制下的建筑体系并发展一种女性主义的设计方法,是西方将女性主义理论运用到建筑空间实践中的先锋者。本文回溯了Matrix组建时的政治与社会背景,分析她们以建筑师的身份采取集体合作工作模式、以女性为主体的参与式机制、以技能培训为辅助的女性建筑教育介入的方法来促进女性解放并重构建筑的空间生产。基于女性主义社会建构论的观念,解读Matrix是如何以性别批判的视角来看待和认知城市空间与女性主义建筑,并结合具体建筑案例分析女性视角下的包容性建筑设计。最后本文探讨了以Matrix为代表的女性建筑师及其女性主义建筑观念与实践对于当下建筑学科研究的价值与意义。

High quality repair of osteochondral defects in rats using the extracellular matrix of antler stem cells

BACKGROUND Cartilage defects are some of the most common causes of arthritis.Cartilage lesions caused by inflammation,trauma or degenerative disease normally result in osteochondral defects.Previous studies have shown that decellularized extracellular matrix(ECM)derived from autologous,allogenic,or xenogeneic mesenchymal stromal cells(MSCs)can effectively restore osteochondral integrity.AIM To determine whether the decellularized ECM of antler reserve mesenchymal cells(RMCs),a xenogeneic material from antler stem cells,is superior to the currently available treatments for osteochondral defects.METHODS We isolated the RMCs from a 60-d-old sika deer antler and cultured them in vitro to 70%confluence;50 mg/mL L-ascorbic acid was then added to the medium to stimulate ECM deposition.Decellularized sheets of adipocyte-derived MSCs(aMSCs)and antlerogenic periosteal cells(another type of antler stem cells)were used as the controls.Three weeks after ascorbic acid stimulation,the ECM sheets were harvested and applied to the osteochondral defects in rat knee joints.RESULTS The defects were successfully repaired by applying the ECM-sheets.The highest quality of repair was achieved in the RMC-ECM group both in vitro(including cell attachment and proliferation),and in vivo(including the simultaneous regeneration of well-vascularized subchondral bone and avascular articular hyaline cartilage integrated with surrounding native tissues).Notably,the antler-stem-cell-derived ECM(xenogeneic)performed better than the aMSC-ECM(allogenic),while the ECM of the active antler stem cells was superior to that of the quiescent antler stem cells.CONCLUSION Decellularized xenogeneic ECM derived from the antler stem cell,particularly the active form(RMC-ECM),can achieve high quality repair/reconstruction of osteochondral defects,suggesting that selection of decellularized ECM for such repair should be focused more on bioactivity rather than kinship.

Health risk assessment of trace metal(loid)s in agricultural soils based on Monte Carlo simulation coupled with positive matrix factorization model in Chongqing, southwest China

This study aimed to investigate the pollution characteristics, source apportionment, and health risks associated with trace metal(loid)s(TMs) in the major agricultural producing areas in Chongqing, China. We analyzed the source apportionment and assessed the health risk of TMs in agricultural soils by using positive matrix factorization(PMF) model and health risk assessment(HRA) model based on Monte Carlo simulation. Meanwhile, we combined PMF and HRA models to explore the health risks of TMs in agricultural soils by different pollution sources to determine the priority control factors. Results showed that the average contents of cadmium(Cd), arsenic (As), lead(Pb), chromium(Cr), copper(Cu), nickel(Ni), and zinc(Zn) in the soil were found to be 0.26, 5.93, 27.14, 61.32, 23.81, 32.45, and 78.65 mg/kg, respectively. Spatial analysis and source apportionment analysis revealed that urban and industrial sources, agricultural sources, and natural sources accounted for 33.0%, 27.7%, and 39.3% of TM accumulation in the soil, respectively. In the HRA model based on Monte Carlo simulation, noncarcinogenic risks were deemed negligible(hazard index <1), the carcinogenic risks were at acceptable level(10^(-6)<total carcinogenic risk ≤ 10^(-4)), with higher risks observed for children compared to adults. The relationship between TMs, their sources, and health risks indicated that urban and industrial sources were primarily associated with As, contributing to 75.1% of carcinogenic risks and 55.7% of non-carcinogenic risks, making them the primary control factors. Meanwhile, agricultural sources were primarily linked to Cd and Pb, contributing to 13.1% of carcinogenic risks and 21.8% of non-carcinogenic risks, designating them as secondary control factors.

Non-Linear Matrix Completion

Current methods for predicting missing values in datasets often rely on simplistic approaches such as taking median value of attributes, limiting their applicability. Real-world observations can be diverse, taking stock price as example, ranging from prices post-IPO to values before a company’s collapse, or instances where certain data points are missing due to stock suspension. In this paper, we propose a novel approach using Nonlinear Matrix Completion (NIMC) and Deep Matrix Completion (DIMC) to predict associations, and conduct experiment on financial data between dates and stocks. Our method leverages various types of stock observations to capture latent factors explaining the observed date-stock associations. Notably, our approach is nonlinear, making it suitable for datasets with nonlinear structures, such as the Russell 3000. Unlike traditional methods that may suffer from information loss, NIMC and DIMC maintain nearly complete information, especially in high-dimensional parameters. We compared our approach with state-of-the-art linear methods, including Inductive Matrix Completion, Nonlinear Inductive Matrix Completion, and Deep Inductive Matrix Completion. Our findings show that the nonlinear matrix completion method is particularly effective for handling nonlinear structured data, as exemplified by the Russell 3000. Additionally, we validate the information loss of the three methods across different dimensionalities.

A matrix metalloproteinase-responsive hydrogel system controls angiogenic peptide release for repair of cerebral ischemia/reperfusion injury

Vascular endothelial growth factor and its mimic peptide KLTWQELYQLKYKGI(QK)are widely used as the most potent angiogenic factors for the treatment of multiple ischemic diseases.However,conventional topical drug delivery often results in a burst release of the drug,leading to transient retention(inefficacy)and undesirable diffusion(toxicity)in vivo.Therefore,a drug delivery system that responds to changes in the microenvironment of tissue regeneration and controls vascular endothelial growth factor release is crucial to improve the treatment of ischemic stroke.Matrix metalloproteinase-2(MMP-2)is gradually upregulated after cerebral ischemia.Herein,vascular endothelial growth factor mimic peptide QK was self-assembled with MMP-2-cleaved peptide PLGLAG(TIMP)and customizable peptide amphiphilic(PA)molecules to construct nanofiber hydrogel PA-TIMP-QK.PA-TIMP-QK was found to control the delivery of QK by MMP-2 upregulation after cerebral ischemia/reperfusion and had a similar biological activity with vascular endothelial growth factor in vitro.The results indicated that PA-TIMP-QK promoted neuronal survival,restored local blood circulation,reduced blood-brain barrier permeability,and restored motor function.These findings suggest that the self-assembling nanofiber hydrogel PA-TIMP-QK may provide an intelligent drug delivery system that responds to the microenvironment and promotes regeneration and repair after cerebral ischemia/reperfusion injury.

A Perturbation Analysis of Low-Rank Matrix Recovery by Schatten p-Minimization

A number of previous papers have studied the problem of recovering low-rank matrices with noise, further combining the noisy and perturbed cases, we propose a nonconvex Schatten p-norm minimization method to deal with the recovery of fully perturbed low-rank matrices. By utilizing the p-null space property (p-NSP) and the p-restricted isometry property (p-RIP) of the matrix, sufficient conditions to ensure that the stable and accurate reconstruction for low-rank matrix in the case of full perturbation are derived, and two upper bound recovery error estimation ns are given. These estimations are characterized by two vital aspects, one involving the best r-approximation error and the other concerning the overall noise. Specifically, this paper obtains two new error upper bounds based on the fact that p-RIP and p-NSP are able to recover accurately and stably low-rank matrix, and to some extent improve the conditions corresponding to RIP.