OPTIMAL CONVERGENCE RATES OF LANDAU EQUATION WITH EXTERNAL FORCING IN THE WHOLE SPACE

In this paper, we combine the method of constructing the compensating function introduced by Kawashima and the standard energy method for the study on the Landau equation with external forcing. Both the global existence of solutions near the time asymptotic states which are local Maxwellians and the optimal convergence rates are obtained. The method used here has its own advantage for this kind of studies because it does not involve the spectrum analysis of the corresponding linearized operator.

Axonal remodeling in the corticospinal tract after stroke： how does rehabilitative training modulate it？

Stroke causes long-term disability, and rehabilitative training is commonly used to improve the consecutive functional recovery. Following brain damage, surviving neurons undergo morphological alterations to reconstruct the remaining neural network. In the motor system, such neural network remodeling is observed as a motor map reorganization. Because of its significant correlation with functional recovery, motor map reorganization has been regarded as a key phenomenon for functional recovery after stroke. Although the mechanism underlying motor map reorganization remains unclear, increasing evidence has shown a critical role for axonal remodeling in the corticospinal tract. In this study, we review previous studies investigating axonal remodeling in the corticospinal tract after stroke and discuss which mechanisms may underlie the stimulatory effect of rehabilitative training. Axonal remodeling in the corticospinal tract can be classified into three types based on the location and the original targets of corticospinal neurons, and it seems that all the surviving corticospinal neurons in both ipsilesional and contralesional hemisphere can participate in axonal remodeling and motor map reorganization. Through axonal remodeling, corticospinal neurons alter their output selectivity from a single to multiple areas to compensate for the lost function. The remodeling of the corticospinal axon is influenced by the extent of tissue destruction and promoted by various therapeutic interventions, including rehabilitative training. Although the precise molecular mechanism underlying rehabilitation-promoted axonal remodeling remains elusive, previous data suggest that rehabilitative training promotes axonal remodeling by upregulating growth-promoting and downregulating growth-inhibiting signals.

THE VLASOV-MAXWELL-FOKKER-PLANCK SYSTEM WITH RELATIVISTIC TRANSPORT IN THE WHOLE SPACE

In this paper, we consider the Vlasov-Maxwell-Fokker-Planck system with relativistic transport in the whole space. The global solutions to this system near the relativistic Maxwellian are constructed and the optimal time decay rate of global solutions are also obtained by an approach by combining the compensating function and energy method.

Effects of Nectar Property on Compensated Dipping Behavior of Honey Bees with Damaged Tongues

In nature,bees with damaged tongues are adapted to have a feat in collecting nectariferous sources in a large spectrum of concentrations(19%-69%)or viscosities(10^(-3)Pa·s to 10^(-1)Pa·s);however,eff ects of nectar property on compensated dipping behavior remain elusive.Combining the bee tongue anatomy,high-speed videography,and mathematical models,we investigate responses of honey bees with damaged tongues to fluidic sources in various properties.We find that,bees with 80%damaged tongues are deprived of feeding capability and remarkably,the dipping frequency increases from 4.24 Hz to 5.08 Hz while ingesting 25%sugar water when the tongue loses 0-30%in length,while declines from 5.08 to 3.86 Hz in case of 30%damaged tongue when sucrose concentration increases from 25%to 45%.We employ the energetic compensation rate and energetic utilization rate to evaluate eff ectiveness of the compensation from the perspective of energetic regulation.The mathematical model indicates that the energetic compensation rate turns higher in bees with less damaged tongues for ingesting dilute sugar water,demonstrating its capability of functional compensation for combined factors.Also,the tongue-damaged bees achieve the highest energetic utilization rate when ingesting~30%sugar water.Beyond biology,the findings may shed lights on biomimetic materials and technologies that aim to compensate for geometrical degradations without regeneration.