CHAOS IN PERTURBED PLANAR NON-HAMILTONIAN INTEGRABLE SYSTEMS WITH SLOWLY-VARYINGANGLE PARAMETERS

The Melnikov method was extended to perturbed planar non-Hamiltonian integrable systems with slowly-varying angle parameters. Based on the analysis of the geometric structure of unperturbed systems, the condition of transversely homoclinic intersection was established. The generalized Melnikov function of the perturbed system was presented by applying the theorem on the differentiability of ordinary differential equation solutions with respect to parameters. Chaos may occur in the system if the generalized Melnikov function has simple zeros.

Nonlinear interaction of head-on solitary waves in integrable and nonintegrable systems

This study numerically investigates the nonlinear interaction of head-on solitary waves in a granular chain(a nonintegrable system)and compares the simulation results with the theoretical results in fluid(an integrable system).Three stages(the pre-in-phase traveling stage,the central-collision stage,and the post-in-phase traveling stage)are identified to describe the nonlinear interaction processes in the granular chain.The nonlinear scattering effect occurs in the central-collision stage,which decreases the amplitude of the incident solitary waves.Compared with the leading-time phase in the incident and separation collision processes,the lagging-time phase in the separation collision process is smaller.This asymmetrical nonlinear collision results in an occurrence of leading phase shifts of time and space in the post-in-phase traveling stage.We next find that the solitary wave amplitude does not influence the immediate space-phase shift in the granular chain.The space-phase shift of the post-in-phase traveling stage is only determined by the measurement position rather than the wave amplitude.The results are reversed in the fluid.An increase in solitary wave amplitude leads to decreased attachment,detachment,and residence times for granular chains and fluid.For the immediate time-phase shift,leading and lagging phenomena appear in the granular chain and the fluid,respectively.These results offer new knowledge for designing mechanical metamaterials and energy-mitigating systems.

NOVEL INTEGRABLE HAMILTONIAN HIERARCHIES WITH SIX POTENTIALS

This paper aims to construct six-component integrable hierarchies from a kind of matrix spectral problems within the zero curvature formulation.Their Hamiltonian formulations are furnished by the trace identity,which guarantee the commuting property of infinitely many symmetries and conserved Hamiltonian functionals.Illustrative examples of the resulting integrable equations of second and third orders are explicitly computed.

Astrocytes integrate time and space

Astrocytes read and react to synaptic transmission through tripartite synapses,where the binding of neurotransmitters onto astrocytic receptors triggers an increase in intracellular calcium.Recent investigations have revealed that astrocytes exhibit two distinct states of intracellular calcium activity:(1)graded subcellular localized clusters with independently active microdomains,likely influenced by nearby synaptic events,and(2)whole-cell astrocyte calcium surges,believed to result from the coordinated activation of multiple synapses.Notably,astrocyte calcium responses are not solely graded;instead,a spatial threshold of intracellular calcium activity can be overcome to elicit an astrocyte calcium surge.Together these calcium responses,in turn,initiate downstream signaling pathways capable of modifying synaptic communication and overall network activity.In summary,astrocytes can function as integrators of local synaptic events,actively contributing to information processing within the brain.

An Eight Component Integrable Hamiltonian Hierarchy from a Reduced Seventh-Order Matrix Spectral Problem

We present an eight component integrable Hamiltonian hierarchy, based on a reduced seventh order matrix spectral problem, with the aim of aiding the study and classification of multicomponent integrable models and their underlying mathematical structures. The zero-curvature formulation is the tool to construct a recursion operator from the spatial matrix problem. The second and third set of integrable equations present integrable nonlinear Schrödinger and modified Korteweg-de Vries type equations, respectively. The trace identity is used to construct Hamiltonian structures, and the first three Hamiltonian functionals so generated are computed.

Multisensory mechanisms of gait and balance in Parkinson’s disease:an integrative review

Understanding the neural underpinning of human gait and balance is one of the most pertinent challenges for 21st-century translational neuroscience due to the profound impact that falls and mobility disturbances have on our aging population.Posture and gait control does not happen automatically,as previously believed,but rather requires continuous involvement of central nervous mechanisms.To effectively exert control over the body,the brain must integrate multiple streams of sensory information,including visual,vestibular,and somatosensory signals.The mechanisms which underpin the integration of these multisensory signals are the principal topic of the present work.Existing multisensory integration theories focus on how failure of cognitive processes thought to be involved in multisensory integration leads to falls in older adults.Insufficient emphasis,however,has been placed on specific contributions of individual sensory modalities to multisensory integration processes and cross-modal interactions that occur between the sensory modalities in relation to gait and balance.In the present work,we review the contributions of somatosensory,visual,and vestibular modalities,along with their multisensory intersections to gait and balance in older adults and patients with Parkinson’s disease.We also review evidence of vestibular contributions to multisensory temporal binding windows,previously shown to be highly pertinent to fall risk in older adults.Lastly,we relate multisensory vestibular mechanisms to potential neural substrates,both at the level of neurobiology(concerning positron emission tomography imaging)and at the level of electrophysiology(concerning electroencephalography).We hope that this integrative review,drawing influence across multiple subdisciplines of neuroscience,paves the way for novel research directions and therapeutic neuromodulatory approaches,to improve the lives of older adults and patients with neurodegenerative diseases.

Cohort study on the treatment of BRAF V600E mutant metastatic colorectal cancer with integrated Chinese and western medicine

BACKGROUND Patients with BRAF V600E mutant metastatic colorectal cancer(mCRC)have a low incidence rate,poor biological activity,suboptimal response to conventional treatments,and a poor prognosis.In the previous cohort study on mCRC conducted by our team,it was observed that integrated Chinese and Western medicine treatment could significantly prolong the overall survival(OS)of patients with colorectal cancer.Therefore,we further explored the survival benefits in the population with BRAF V600E mutant mCRC.AIM To evaluate the efficacy of integrated Chinese and Western medicine in the treatment of BRAF V600E mutant metastatic colorectal cancer.METHODS A cohort study was conducted on patients with BRAF V600E mutant metastatic colorectal cancer admitted to Xiyuan Hospital of China Academy of Chinese Medical Sciences and Traditional Chinese Medicine Hospital of Xinjiang Uygur Autonomous Region from January 2016 to December 2022.The patients were divided into two cohorts.RESULTS A total of 34 cases were included,with 23 in Chinese-Western medicine cohort(cohort A)and 11 in Western medicine cohort(cohort B).The median overall survival was 19.9 months in cohort A and 14.2 months in cohort B,with a statistically significant difference(P=0.038,hazard ratio=0.46).The 1-3-year survival rates were 95.65%(22/23),39.13%(9/23),and 26.09%(6/23)in cohort A,and 63.64%(7/11),18.18%(2/11),and 9.09%(1/11)in cohort B,respectively.Subgroup analysis showed statistically significant differences in median OS between the two cohorts in the right colon,liver metastasis,chemotherapy,and first-line treatment subgroups(P<0.05).CONCLUSION Integrated Chinese and Western medicine can prolong the survival and reduce the risk of death in patients with BRAF V600E mutant metastatic colorectal cancer,with more pronounced benefits observed in patients with right colon involvement,liver metastasis,combined chemotherapy,and first-line treatment.

Mechanistic insights into the amelioration effects of diabetic cardiomyopathy by berberine:an integrated systems pharmacology study and experimental validation

Background:Diabetic cardiomyopathy(DCM)is a type of cardiomyopathy caused by long-term diabetes,characterized by abnormal myocardial structure and function,which can lead to heart failure.Berberine(BBR),a quaternary ammonium alkaloid isolated from Coptidis Rhizoma,a traditional Chinese medicine,has superior anti-diabetic and heart-protective properties.The purpose of this study is to assess the impact of BBR on DCM.Methods:This study used a systems pharmacology approach to evaluate the related proteins and signalling pathways between BBR and DCM targets,combined with experimental validation using diabetic mouse heart sections.Microstructural and pathological changes were observed using Hematoxylin-eosin,Masson’s trichrome stain and wheat germ agglutinin staining.Immunofluorescence and western blot were used to determine protein expression.Results:The results indicate that BBR and DCM share 21 core relevant targets,with cross-targets predominantly located in mitochondrial,endoplasmic reticulum,and plasma membrane components.BBR exerts its main effects in improving DCM by maintaining mitochondrial integrity,particularly involving the PI3K-AKT-GSK3βand apoptosis signalling pathways.In addition,post-treatment changes in the key targets of BBR,including cysteine aspartate specific protease(Caspase)-3,phosphoinositide 3-kinase(PI3K)and mitochondria-related proteins,are suggestive of its efficacy.Conclusion:BBR crucially improves DCM by maintaining mitochondrial integrity,inhibiting apoptosis,and modulating PI3K-AKT-GSK3βsignaling.Further studies must address animal model limitations and validate clinical efficacy to understand BBR’s mechanisms fully and its potential clinical use.

Integrated Sensing and Communication Enabled Sensing Base Station:System Design,Beamforming,Interference Cancellation and Performance Analysis

This paper studies the sensing base station(SBS)that has great potential to improve the safety of vehicles and pedestrians on roads.SBS can detect the targets on the road with communication signals using the integrated sensing and communication(ISAC)technique.Compared with vehicle-mounted radar,SBS has a better sensing field due to its higher deployment position,which can help solve the problem of sensing blind areas.In this paper,key technologies of SBS are studied,including the beamforming algorithm,beam scanning scheme,and interference cancellation algorithm.To transmit and receive ISAC signals simultaneously,a double-coupling antenna array is applied.The free detection beam and directional communication beam are proposed for joint communication and sensing to meet the requirements of beamwidth and pointing directions.The joint timespace-frequency domain division multiple access algorithm is proposed to cancel the interference of SBS,including multiuser interference and duplex interference between sensing and communication.Finally,the sensing and communication performance of SBS under the industrial scientific medical power limitation is analyzed and simulated.Simulation results show that the communication rate of SBS can reach over 100 Mbps and the range of sensing and communication can reach about 500 m.

Two new integrable couplings of the soliton hierarchies with self-consistent sources

A kind of integrable coupling of soliton equations hierarchy with self-consistent sources associated with s/（4） has been presented （Yu F J and Li L 2009 Appl. Math. Comput. 207 171; Yu F J 2008 Phys. Lett. A 372 6613）. Based on this method, we construct two integrable couplings of the soliton hierarchy with self-consistent sources by using the loop algebra sl（4）. In this paper, we also point out that there are some errors in these references and we have corrected these errors and set up new formula. The method can be generalized to other soliton hierarchy with self-consistent sources.

Multi-component Dirac equation hierarchy and its multi-component integrable couplings system

A general scheme for generating a multi-component integrable equation hierarchy is proposed. A simple 3M- dimensional loop algebra ~X is produced. By taking advantage of ~X a new isospectral problem is established and then by making use of the Tu scheme the multi-component Dirac equation hierarchy is obtained. Finally, an expanding loop algebra ~FM of the loop algebra ~X is presented. Based on the ~FM, the multi-component integrable coupling system of the multi-component Dirac equation hierarchy is investigated. The method in this paper can be applied to other nonlinear evolution equation hierarchies.

A New Nonlinear Integrable Couplings of Yang Equations Hierarchy and Its Hamiltonian Structure

Based on a kind of non-semisimple Lie algebras, we establish a way to construct nonlinear continuous integrable couplings. Variational identities over the associated loop algebras are used to furnish Hamiltonian structures of the resulting continuous couplings.As an illustrative example of the scheme is given nonlinear continuous integrable couplings of the Yang hierarchy.

An integrable Hamiltonian hierarchy and associated integrable couplings system

This paper establishes a new isospectral problem. By making use of the Tu scheme, a new intcgrablc system is obtained. It gives integrable couplings of the system obtained. Finally, the Hamiltonian form of a binary symmetric constrained flow of the system obtained is presented.

Lie Algebras for Constructing Nonlinear Integrable Couplings

Two new explicit Lie algebras are introduced for which the nonlinear integrable couplings of the Giachetti- Johnson （G J） hierarchy and the Yang hierarchy are obtained, respectively. By employing the variational identity their ttamiltonian structures are also generated. The approach presented in the paper can also provide nonlinear integrable couplings of other soliton hierarchies of evolution equations.

The Exact Solutions of Some (2 + 1)-Dimensional Integrable Systems

The equivalence of three (2 + 1)-dimensional soliton equations is proved, and the quite generalsolutionswitha some arbitrary functions of x, t and y respectively are obtained. By selecting the arbitrary functions, many specialtypes of the localized excitations like the solitoff solitons, multi-dromion solutions, lump, and multi-ring soliton solutionsare obtained.

THE BASIC THEORY OF SOLUTIONS OF FUNCTIONAL DIFFERENTIAL EQUATIONS WITH BOUNDED DELAY IN THE SPACE OF INTEGRABLE FUNCTIONS

在可积函数空间中讨论有界滞量泛函微分方程，建立其解的基本理论，包括解的存在性，唯一性及延展性。

Matrix Lie Algebras and Integrable Couplings

Three kinds of higher-dimensional Lie algebras are given which can be used to directly construct integrable couplings of the soliton integrable systems. The relations between the Lie algebras are discussed. Finally, the integrable couplings and the Hamiltonian structure of Giachetti-Johnson hierarchy and a new integrable system are obtained, respectively.

GENERALIZED FRACTIONAL TRACE VARIATIONAL IDENTITY AND A NEW FRACTIONAL INTEGRABLE COUPLINGS OF SOLITON HIERARCHY

Based on fractional isospectral problems and general bilinear forms, the gener-alized fractional trace identity is presented. Then, a new explicit Lie algebra is introduced for which the new fractional integrable couplings of a fractional soliton hierarchy are derived from a fractional zero-curvature equation. Finally, we obtain the fractional Hamiltonian structures of the fractional integrable couplings of the soliton hierarchy.

INTEGRABLE SYSTEM AND SPACELIKE SURFACES WITH PRESCRIBED MEAN CURVATURE IN MINKOWSKI 3-SPACE

Authors discover that a spacelike surface in Minkowski 3-space is related to a integrable system. They obtain a representation formula for spacelike surfaces with prescribed mean curvature. This representation formula is equivalent to that obtained ly Akutagawa and Nishikawa.

An Integrating Algorithm and Theoretical Analysis for Fully Rheonomous Affine Constraints: Completely Integrable Case

This paper develops an integrating algorithm for fully rheonomous affine constraints and gives theoretical analysis of the algorithm for the completely integrable case. First, some preliminaries on the fully rheonomous affine constraints are shown. Next, an integrating algorithm that calculates independent first integrals is derived. In addition, the existence of an inverse function utilized in the algorithm is investigated. Then, an example is shown in order to evaluate the effectiveness of the proposed method. By using the proposed integrating algorithm, we can easily calculate independent first integrals for given constraints, and hence it can be utilized for various research fields.