Higher-dimensional Chen-Lee-Liu equation and asymmetric peakon soliton

Integrable systems play a crucial role in physics and mathematics.In particular,the traditional(1+1)-dimensional and(2+1)-dimensional integrable systems have received significant attention due to the rarity of integrable systems in higher dimensions.Recent studies have shown that abundant higher-dimensional integrable systems can be constructed from(1+1)-dimensional integrable systems by using a deformation algorithm.Here we establish a new(2+1)-dimensional Chen-Lee-Liu(C-L-L)equation using the deformation algorithm from the(1+1)-dimensional C-L-L equation.The new system is integrable with its Lax pair obtained by applying the deformation algorithm to that of the(1+1)-dimension.It is challenging to obtain the exact solutions for the new integrable system because the new system combines both the original C-L-L equation and its reciprocal transformation.The traveling wave solutions are derived in implicit function expression,and some asymmetry peakon solutions are found.

Preparation of lactic acid bacteria compound starter cultures based on pasting properties and its improvement of glutinous rice flour and dough

The effects of 5 lactic acid bacteria(LAB)fermentation on the pasting properties of glutinous rice flour were compared,and suitable fermentation strains were selected based on the changes of viscosity,setback value,and breakdown value to prepare LAB compound starter cultures.The results revealed that Latilactobacillus sakei HSD004 and Lacticaseibacillus rhamnosus HSD005 had apparent advantages in increasing the viscosity and reducing the setback and breakdown values of glutinous rice flour.In particular,the compound starter created using the two abovementioned LAB in the ratio of 3:1 had better performance than that using a single LAB in improving the pasting properties and increasing the water and oil absorption capacity of glutinous rice flour.Moreover,the gelatinization enthalpy of the fermented samples increased significantly.For frozen glutinous rice dough stored for 28 days,the viscoelasticity of frozen dough prepared by compound starter was better than that of control dough,and the freezable water content was lower than that of control dough.These results indicate that compound LAB fermentation is a promising technology in the glutinous rice-based food processing industry,which has significance for its application.

3-Dimensional Kinematic Comparison of Arm Movements between an Individual with NGLY1 Deficiency and a Neurotypical Individual

NGLY1 Deficiency is an ultra-rare autosomal recessively inherited disorder. Characteristic symptoms include among others, developmental delays, movement disorders, liver function abnormalities, seizures, and problems with tear formation. Movements are hyperkinetic and may include dysmetric, choreo-athetoid, myoclonic and dystonic movement elements. To date, there have been no quantitative reports describing arm movements of individuals with NGLY1 Deficiency. This report provides quantitative information about a series of arm movements performed by an individual with NGLY1 Deficiency and an aged-matched neurotypical participant. Three categories of arm movements were tested: 1) open ended reaches without specific end point targets;2) goal-directed reaches that included grasping an object;3) picking up small objects from a table placed in front of the participants. Arm movement kinematics were obtained with a camera-based motion analysis system and “initiation” and “maintenance” phases were identified for each movement. The combination of the two phases was labeled as a “complete” movement. Three-dimensional analysis techniques were used to quantify the movements and included hand trajectory pathlength, joint motion area, as well as hand trajectory and joint jerk cost. These techniques were required to fully characterize the movements because the NGLY1 individual was unable to perform movements only in the primary plane of progression instead producing motion across all three planes of movement. The individual with NGLY1 Deficiency was unable to pick up objects from a table or effectively complete movements requiring crossing the midline. The successfully completed movements were analyzed using the above techniques and the results of the two participants were compared statistically. Almost all comparisons revealed significant differences between the two participants, with a notable exception of the 3D initiation area as a percentage of the complete movement. The statistical tests of these measures revealed no significant differences between the two participants, possibly suggesting a common underlying motor control strategy. The 3D techniques used in this report effectively characterized arm movements of an individual with NGLY1 deficiency and can be used to provide information to evaluate the effectiveness of genetic, pharmacological, or physical rehabilitation therapies.

Further Analysis of Machine Tool Dimensional Accuracy and Thermal Stability under Varying Floor Temperature

Machining is as old as humanity, and changes in temperature in both the machine’s internal and external environments can be of great concern as they affect the machine’s thermal stability and, thus, the machine’s dimensional accuracy. This paper is a continuation of our earlier work, which aimed to analyze the effect of the internal temperature of a machine tool as the machine is put into operation and vary the external temperature, the machine floor temperature. Some experiments are carried out under controlled conditions to study how machine tool components get heated up and how this heating up affects the machine’s accuracy due to thermally induced deviations. Additionally, another angle is added by varying the machine floor temperature. The parameters mentioned above are explored in line with the overall thermal stability of the machine tool and its dimensional accuracy. A Robodrill CNC machine tool is used. The CNC was first soaked with thermal energy by gradually raising the machine floor temperature to a certain level before putting the machine in operation. The machine was monitored, and analytical methods were deplored to evaluate thermal stability. Secondly, the machine was run idle for some time under raised floor temperature before it was put into operation. Data was also collected and analyzed. It is observed that machine thermal stability can be achieved in several ways depending on how the above parameters are joggled. This paper, in conclusion, reinforces the idea of machine tool warm-up process in conjunction with a carefully analyzed and established machine floor temperature variation for the approximation of the machine tool’s thermally stability to map the long-time behavior of the machine tool.

Study on creep deformation and energy development of underground surrounding rock under four‐dimensional support

There is an urgent need to develop optimal solutions for deformation control of deep high‐stress roadways,one of the critical problems in underground engineering.The previously proposed four‐dimensional support(hereinafter 4D support),as a new support technology,can set the roadway surrounding rock under three‐dimensional pressure in the new balanced structure,and prevent instability of surrounding rock in underground engineering.However,the influence of roadway depth and creep deformation on the surrounding rock supported by 4D support is still unknown.This study investigated the influence of roadway depth and creep deformation time on the instability of surrounding rock by analyzing the energy development.The elastic strain energy was analyzed using the program redeveloped in FLAC3D.The numerical simulation results indicate that the combined support mode of 4D roof supports and conventional side supports is highly applicable to the stability control of surrounding rock with a roadway depth exceeding 520 m.With the increase of roadway depth,4D support can effectively restrain the area and depth of plastic deformation in the surrounding rock.Further,4D support limits the accumulation range and rate of elastic strain energy as the creep deformation time increases.4D support can effectively reduce the plastic deformation of roadway surrounding rock and maintain the stability for a long deformation period of 6 months.As confirmed by in situ monitoring results,4D support is more effective for the long‐term stability control of surrounding rock than conventional support.

Four Dimensions of Integrating Chinese Culture Into College English Teaching From the Perspective of Tyler’s Basic Principles

Integrating Chinese culture into college English can not only enhance students’humanities literacy and cultivate their cultural confidence,but also facilitate the inheritance and international dissemination of Chinese culture.Taking Tyler’s curriculum framework as the starting point,this paper analyzes some factors that affect the integration of Chinese culture into the college English teaching and proposes some strategies for the integration of Chinese culture into college English teaching by innovating teaching objectives,enriching teaching contents,transforming modes of course delivery,and reconstructing the assessment system.

A Dimensional Reduction Approach Based on Essential Constraints in Linear Programming

This paper presents a new dimension reduction strategy for medium and large-scale linear programming problems. The proposed method uses a subset of the original constraints and combines two algorithms: the weighted average and the cosine simplex algorithm. The first approach identifies binding constraints by using the weighted average of each constraint, whereas the second algorithm is based on the cosine similarity between the vector of the objective function and the constraints. These two approaches are complementary, and when used together, they locate the essential subset of initial constraints required for solving medium and large-scale linear programming problems. After reducing the dimension of the linear programming problem using the subset of the essential constraints, the solution method can be chosen from any suitable method for linear programming. The proposed approach was applied to a set of well-known benchmarks as well as more than 2000 random medium and large-scale linear programming problems. The results are promising, indicating that the new approach contributes to the reduction of both the size of the problems and the total number of iterations required. A tree-based classification model also confirmed the need for combining the two approaches. A detailed numerical example, the general numerical results, and the statistical analysis for the decision tree procedure are presented.

Hyper Catastrophe on 4-Dimensional Canards

When discovering the potential of canards flying in 4-dimensional slow-fast system with a bifurcation parameter, the key notion “symmetry” plays an important role. It is of one parameter on slow vector field. Then, it should be determined to introduce parameters to all slow/fast vectors. It is, however, there might be no way to explore for another potential in this system, because the geometrical structure is quite different from the system with one parameter. Even in this system, the “symmetry” is also useful to obtain the potentials classified by R. Thom. In this paper, via the coordinates changing, the possible way to explore for the potential will be shown. As it is analyzed on “hyper finite time line”, or done by using “non-standard analysis”, it is called “Hyper Catastrophe”. In the slow-fast system which includes a very small parameter , it is difficult to do precise analysis. Thus, it is useful to get the orbits as a singular limit. When trying to do simulations, it is also faced with difficulty due to singularity. Using very small time intervals corresponding small , we shall overcome the difficulty, because the difference equation on the small time interval adopts the standard differential equation. These small intervals are defined on hyper finite number N, which is nonstandard. As and the intervals are linked to use 1/N, the simulation should be done exactly.

Hepatospheres:Three dimensional cell cultures resemble physiological conditions of the liver

Studying physiological and pathophysiological mechanisms in the liver on a molecular basis is a challenging task.During two dimensional(2D) culture conditions hepatocytes dedifferentiate rapidly by losing metabolic functions and structural integrity.Hence,inappropriate 2D hepatocellular models hamper studies on the xenobiotic metabolism of the liver which strongly influences drug potency.Also,the lack of effective therapies against hepatocellular carcinoma shows the urgent need for robust models to investigate liver functions in a defined hepatic microenvironment.Here,we summarize and discuss three-dimensional cultures of hepatocytes,herein referred to as hepatospheres,which provide versatile tools to investigate hepatic metabolism,stemness and cancer development.

Optimal Estimation of High-Dimensional Covariance Matrices with Missing and Noisy Data

The estimation of covariance matrices is very important in many fields, such as statistics. In real applications, data are frequently influenced by high dimensions and noise. However, most relevant studies are based on complete data. This paper studies the optimal estimation of high-dimensional covariance matrices based on missing and noisy sample under the norm. First, the model with sub-Gaussian additive noise is presented. The generalized sample covariance is then modified to define a hard thresholding estimator , and the minimax upper bound is derived. After that, the minimax lower bound is derived, and it is concluded that the estimator presented in this article is rate-optimal. Finally, numerical simulation analysis is performed. The result shows that for missing samples with sub-Gaussian noise, if the true covariance matrix is sparse, the hard thresholding estimator outperforms the traditional estimate method.

Inhibition of mammalian target of rapamycin induces phenotypic reversion in three-dimensional cultures of malignant breast epithelial cells

Inhibition of mammalian target of rapamycin (m- TOR) is a potential method for cancer treatment. Effects of rapamycin (RAP) on the reversion of malignant breast epithelial cells were investigated on three-dimensional (3D) basement membrane extract (BME) cultures. Through continuous exposure to 20 nM of RAP, cell colony size was significantly reduced in 3D BME cultures of malignant breast epithelial cells, while normal cell colony size appeared unaffected. In unfixed 3D BME cultures of normal and RAP-treated malignant breast epithelial cells, the presence of luminal cell death was confirmed by ethidium bromide and propidium iodide labeling. Increased structural organization was observed by im- munofluorescence staining of F-actin and β-catenin in RAP-treated malignant breast epithelial cells. In monolayer cultures of normal and malignant breast epithelial cells, continuous exposure to 20 nM of RAP increased caspase 3/7 activity and decreased proliferation. Reverse transcriptase polymerase ch- ain reaction (RT-PCR) array analysis indicated a fold increase in the expression of a number of proteins related to polarity, cell-cell adhesion, and cell-matrix adhesion in the presence of RAP. Our data showed that phenotypic reversion of malignancy can be ach- ieved through RAP exposure on 3D BME cultures. This 3D BME culture system will provide correct microenvironments for observing the effects of other mTOR inhibitors on phenotypic reversion of malignant breast epithelial cells.

Earth Pressure of the Trapdoor Problem Using Three-Dimensional Discrete Element Method

Load transformation from the yielding part of the soil to the adjacent part is known as the soil arching effect,which plays an important role in the design of various geotechnical infrastructures.Terzaghi’s trapdoor test was an importantmilestone in the development of theories on soil arching.The research on earth pressure of the trapdoor problem is presented in this paper using the three-dimensional(3D)discrete element method(DEM).Five 3D trapdoor models with different heights are established by 3DDEMsoftware PFC 3D.The variation of earth pressure on the trapdoor with the downward movement of the trapdoor,the distribution of vertical earth pressure along the horizontal direction,the distribution of vertical earth pressure along the vertical direction,the distribution of lateral earth pressure coefficient along the depth direction,the magnitude and direction of contact force chain are studied,respectively.Related research results show that the earth pressure on the trapdoor decreases rapidly after the downward movement of the trapdoor,and then reaches the minimum earth pressure.After that,the earth’s pressure will rise slightly,and whether this phenomenon occurs depends on the depth ratio.For the bottom soil,due to the stress transfer caused by the soil arching effect,the ratio of earth pressure in the loose area decreases,while the ratio of earth pressure in the stable area increases.With the trapdoor moving down,the vertical earth pressure along the depth in the stable zone is basically consistent with the initial state,which shows an approximate linear distribution.After the trapdoor moves down,the distribution of earth pressure along with the depth in the loose area changes,which is far less than the theoretical value of vertical earth pressure of its self-weight.Because of the compression of the soil on both sides,the lateral earth pressure coefficient of most areas on the central axis of the loose zone is close to the passive earth pressure coefficient Kp.The existence of a‘soil arch’can be observed intuitively from the distribution diagram of the contact force chain in the loose zone.

Isolation and Identification of Cancer Stem Cells from Human Osteosarcom by Serum-free Three-dimensional Culture Combined with Anticancer Drugs

The cancer stem cells(CSCs)from human osteosarcoma by serum-free three-dimensional culture combined with anticancer drugs were isolated and identified.The primary cells derived from human osteosarcoma were digested by trypsin to prepare a single-cell suspension,and mixed homogeneously into 1.2% alginate gel.Single-cell alginate gel was cultured with serum-free DMEM/F12 medium.Epirubicin(0.8μg/mL)was added to the medium to enrich CSCs.After cultured conventionally for 7 to 10 days,most of cells suspended in ...

Three-dimensional cell culture systems as an in vitro platform for cancer and stem cell modeling

Three-dimensional(3D)culture systems are becoming increasingly popular due to their ability to mimic tissue-like structures more effectively than the monolayer cultures.In cancer and stem cell research,the natural cell characteristics and architectures are closely mimicked by the 3D cell models.Thus,the 3D cell cultures are promising and suitable systems for various proposes,ranging from disease modeling to drug target identification as well as potential therapeutic substances that may transform our lives.This review provides a comprehensive compendium of recent advancements in culturing cells,in particular cancer and stem cells,using 3D culture techniques.The major approaches highlighted here include cell spheroids,hydrogel embedding,bioreactors,scaffolds,and bioprinting.In addition,the progress of employing 3D cell culture systems as a platform for cancer and stem cell research was addressed,and the prominent studies of 3D cell culture systems were discussed.

Simplified three-dimensional culture system for long-term expansion of embryonic stem cells

AIM: To devise a simplified and efficient method for long-term culture and maintenance of embryonic stem cells requiring less frequent passaging. METHODS: Mouse embryonic stem cells(ESCs) labeled with enhanced yellow fluorescent protein were cultured in three-dimensional(3-D) self-assembling scaffolds and compared with traditional two-dimentional(2-D) culture techniques requiring mouse embryonic fibroblast feeder layers or leukemia inhibitory factor. 3-D scaffolds encapsulating ESCs were prepared by mixing ESCs with polyethylene glycol tetra-acrylate(PEG-4-Acr) and thiolfunctionalized dextran(Dex-SH). Distribution of ESCs in 3-D was monitored by confocal microscopy. Viability and proliferation of encapsulated cells during long-term culture were determined by propidium iodide as well as direct cell counts and PrestoB lue(PB) assays. Genetic expression of pluripotency markers(Oct4, Nanog, Klf4, and Sox2) in ESCs grown under 2-D and 3-D cultureconditions was examined by quantitative real-time polymerase chain reaction. Protein expression of selected stemness markers was determined by two different methods, immunofluorescence staining(Oct4 and Nanog) and western blot analysis(Oct4, Nanog, and Klf4). Pluripotency of 3-D scaffold grown ESCs was analyzed by in vivo teratoma assay and in vitro differentiation via embryoid bodies into cells of all three germ layers. RESULTS: Self-assembling scaffolds encapsulating ESCs for 3-D culture without the loss of cell viability were prepared by mixing PEG-4-Acr and Dex-SH(1:1 v/v) to a final concentration of 5%(w/v). Scaffold integrity was dependent on the degree of thiol substitution of Dex-SH and cell concentration. Scaffolds prepared using Dex-SH with 7.5% and 33% thiol substitution and incubated in culture medium maintained their integrity for 11 and 13 d without cells and 22 ± 5 d and 37 ± 5 d with cells, respectively. ESCs formed compact colonies, which progressively increased in size over time due to cell proliferation as determined by confocal microscopy and PB staining. 3-D scaffold cultured ESCs expressed significantly higher levels(P < 0.01) of Oct4, Nanog, and Kl4, showing a 2.8, 3.0 and 1.8 fold increase, respectively, in comparison to 2-D grown cells. A similar increase in the protein expression levels of Oct4, Nanog, and Klf4 was observed in 3-D grown ESCs. However, when 3-D cultured ESCs were subsequently passaged in 2-D culture conditions, the level of these pluripotent markers was reduced to normal levels. 3-D grown ESCs produced teratomas and yielded cells of all three germ layers, expressing brachyury(mesoderm), NCAM(ectoderm), and GATA4(endoderm) markers. Furthermore, these cells differentiated into osteogenic, chondrogenic, myogenic, and neural lineages expressing Col1, Col2, Myog, and Nestin, respectively. CONCLUSION: This novel 3-D culture system demonstrated long-term maintenance of mouse ESCs without the routine passaging and manipulation necessary for traditional 2-D cell propagation.

Microfluidic three-dimensional cell culture of stem cells for high-throughput analysis

Although the recent advances in stem cell engineering have gained a great deal of attention due to their high potential in clinical research,the applicability of stem cells for preclinical screening in the drug discovery process is still challenging due to difficulties in controlling the stem cell microenvironment and the limited availability of high-throughput systems.Recently,researchers have been actively developing and evaluating three-dimensional(3D)cell culture-based platforms using microfluidic technologies,such as organ-on-a-chip and organoid-on-a-chip platforms,and they have achieved promising breakthroughs in stem cell engineering.In this review,we start with a comprehensive discussion on the importance of microfluidic 3D cell culture techniques in stem cell research and their technical strategies in the field of drug discovery.In a subsequent section,we discuss microfluidic 3D cell culture techniques for high-throughput analysis for use in stem cell research.In addition,some potential and practical applications of organ-on-a-chip or organoid-on-a-chip platforms using stem cells as drug screening and disease models are highlighted.

In Vitro Invasive Pattern of Hepatocellular Carcinoma Cell Line HCCLM9 Based on Three-dimensional Cell Culture and Quantum Dots Molecular Imaging

Summary： This study aimed to establish a new in vitro three-dimensional （3D） cell culture and use quantum dots （QDs） molecular imaging to examine the invasive behaviors of hepatocellular carcinoma （HCC） cells. Each well of the 24-well cell culture plate was cover-slipped. Matrigel diluted with se- rum-free DMEM was added and HCCLM9 cells were cultured on the Matrigel. The cell morphological and cell growth characteristics were observed by inverted microscopy and laser confocal microscopy at different culture time. Cell invasive features were monitored by QDs-based real-time molecular imaging techniques. The results showed that on this 3D cell culture platform, HCCLM9 cells exhibited typical multi-step invasive behaviors, including reversion of cell senescence, active focal proliferation and dominant clones invasion. During the process, cells under 3D cell culture showed biological behaviors of spatio-temporal characteristics. Cells first merged on the surface of matrix, then gradually infiltrated and migrated into deep part of matrix, presenting polygonal morphology with stretched protrusions, forming tubular, annular and even network structure, which suggested that HCC cells have the morpho- logical basis for vasculogenic mimicry. In addition, small cell clones with their edges well-circumscribed in early stage, progressed into a large irregular clone with ill-defined edge, while the other cells developed invadopodia. And QDs probing showed MT1-MMP was strongly expressed in the invadopodia. These findings indicate that a novel 3D cell culture platform has been successfully estab- lished, which can mimic the in vivo tumor microenvironment, and when combined with QDs-based mo- lecular imaging, it can help to better investigate the invasive behaviors of HCC cells.

A Dimension-Splitting Variational Multiscale Element-Free Galerkin Method for Three-Dimensional Singularly Perturbed Convection-Diffusion Problems

By introducing the dimensional splitting(DS)method into the multiscale interpolating element-free Galerkin(VMIEFG)method,a dimension-splitting multiscale interpolating element-free Galerkin(DS-VMIEFG)method is proposed for three-dimensional(3D)singular perturbed convection-diffusion(SPCD)problems.In the DSVMIEFG method,the 3D problem is decomposed into a series of 2D problems by the DS method,and the discrete equations on the 2D splitting surface are obtained by the VMIEFG method.The improved interpolation-type moving least squares(IIMLS)method is used to construct shape functions in the weak form and to combine 2D discrete equations into a global system of discrete equations for the three-dimensional SPCD problems.The solved numerical example verifies the effectiveness of the method in this paper for the 3D SPCD problems.The numerical solution will gradually converge to the analytical solution with the increase in the number of nodes.For extremely small singular diffusion coefficients,the numerical solution will avoid numerical oscillation and has high computational stability.

Three-dimensional Culture of Human Airway Epithelium in Matrigel for Evaluation of Human Rhinovirus C and Bocavirus Infections

Objective Newly identified human rhinovirus C （HRV-C） and human bocavirus （HBoV） cannot propagate in vitro in traditional cell culture models; thus obtaining knowledge about these viruses and developing related vaccines are difficult. Therefore, it is necessary to develop a novel platform for the propagation of these types of viruses.Methods A platform for culturing human airway epithelia in a three-dimensional （3D） pattern using Matrigel as scaffold was developed. The features of 3D culture were identified by immunochemical staining and transmission electron microscopy. Nucleic acid levels of HRV-C and HBoV in 3D cells at designated time points were quantitated by real-time polymerase chain reaction {PCR）. Levels of cytokines, whose secretion was induced by the viruses, were measured by ELISA.Results Properties of bronchial-like tissues, such as the expression of biomarkers CK5, ZO-2, and PCK, and the development of cilium-like protuberances indicative of the human respiration tract, were observed in 3D-cultured human airway epithelial （HAE） cultures, but not in monolayer-cultured cells. Nucleic acid levels of HRV-C and HBoV and levels of virus-induced cytokines were also measured using the 3D culture system.Conclusion Our data provide a preliminary indication that the 3D culture model of primary epithelia using a Matrigel scaffold in vitro can be used to propagate HRV-C and HBoV.

Theoretical model of radiation heat wave in two-dimensional cylinder with sleeve

A semi-analytical model is constructed to investigate two-dimensional radiation heat waves(Marshak waves)in a low-Z foam cylinder with a sleeve made of high-Z material.In this model,the energy loss to the high-Z wall is regarded as the primary two-dimensional effect and is taken into account via an indirect approach in which the energy loss is subtracted from the drive source and the wall loss is ignored.The interdependent Marshak waves in the low-Z foam and high-Z wall are used to estimate the energy loss.The energies and the heat front position calculated using the model under typical inertial confinement fusion conditions are verified by simulations.The validated model provides a theoretical tool for studying two-dimensional Marshak waves and should be helpful in providing further understanding of radiation transport.