Combining stochastic density functional theory with deep potential molecular dynamics to study warm dense matter

In traditional finite-temperature Kohn–Sham density functional theory(KSDFT),the partial occupation of a large number of high-energy KS eigenstates restricts the use of first-principles molecular dynamics methods at extremely high temperatures.However,stochastic density functional theory(SDFT)can overcome this limitation.Recently,SDFT and the related mixed stochastic–deterministic density functional theory,based on a plane-wave basis set,have been implemented in the first-principles electronic structure software ABACUS[Q.Liu and M.Chen,Phys.Rev.B 106,125132(2022)].In this study,we combine SDFT with the Born–Oppenheimer molecular dynamics method to investigate systems with temperatures ranging from a few tens of eV to 1000 eV.Importantly,we train machine-learning-based interatomic models using the SDFT data and employ these deep potential models to simulate large-scale systems with long trajectories.Subsequently,we compute and analyze the structural properties,dynamic properties,and transport coefficients of warm dense matter.

Density functional theory study of B- and Si-doped carbons and their adsorption interactions with sulfur compounds

Understanding the adsorption interactions between carbon materials and sulfur compounds has far-reaching impacts,in addition to their well-known important role in energy storage and conversion,such as lithium-ion batteries.In this paper,properties of intrinsic B or Si single-atom doped,and B-Si codoped graphene(GR)and graphdiyne(GDY)were investigated by using density functional theory-based calculations,in which the optimal doping configurations were explored for potential applications in adsorbing sulfur compounds.Results showed that both B or Si single-atom doping and B-Si codoping could substantially enhance the electron transport properties of GR and GDY,improving their surface activity.Notably,B and Si atoms displayed synergistic effects for the codoped configurations,where B-Si codoped GR/GDY exhibited much better performance in the adsorption of sulfurcontaining chemicals than single-atom doped systems.In addition,results demonstrated that,after B-Si codoping,the adsorption energy and charge transfer amounts of GDY with sulfur compounds were much larger than those of GR,indicating that B-Si codoped GDY might be a favorable material for more effectively interacting with sulfur reagents.

Langmuir-Schaefer Film Investigation and Density Functional Theory Band Gap Calculations of Calix[n]arene-Para-Aminobenzoic Acid for Drug Nanosensor Application

Calix[n]arenes was utilized to detect PABA,the primary sunscreen component.This study investigates the interaction of calix[4]arene(C4),calix[6]arene(C6),and PABA using the Langmuir method and first-principle density functional theory(DFT).Using the Langmuir-Schaefer(LS)technique,an ultrathin film composed of calix[n]arenes and their complexes with PABA was deposited on various substrates.Based on the Langmuir study,the PABA molecule was bonded to the lower rims of both C4 and C6 with the host-guest ratio of 1:1.All of the LS films formed were then characterized by ultravioletvisible spectroscopy(UV-Vis),Fourier-transform infrared spectroscopy(FTIR)and carbon,hydrogen,nitrogen,sulfur elemental analyzer(CHNS).The band gap reduction obtained in the DFT study denotes the charge transfer interaction with promising reactivity between the calix[n]arenes and PABA.The sensing of PABA by C4 and C6 is successful based on the formation of bonding between them due to the hosts’effective trapping capacity.The outcomes of this study could be applied to drug delivery systems for future pharmaceutical and medical applications.

Sensitivity impacts owing to the variations in the type of zero-range pairing forces on the fission properties using the density functional theory

Using the Skyrme density functional theory,potential energy surfaces of^(240)Pu with constraints on the axial quadrupole and octupole deformations(q_(20)and q_(30))were calculated.The volume-like and surface-like pairing forces,as well as a combination of these two forces,were used for the Hartree–Fock–Bogoliubov approximation.Variations in the least-energy fission path,fission barrier,pairing energy,total kinetic energy,scission line,and mass distribution of the fission fragments based on the different forms of the pairing forces were analyzed and discussed.The fission dynamics were studied based on the timedependent generator coordinate method plus the Gaussian overlap approximation.The results demonstrated a sensitivity of the mass and charge distributions of the fission fragments on the form of the pairing force.Based on the investigation of the neutron-induced fission of^(239)Pu,among the volume,mixed,and surface pairing forces,the mixed pairing force presented a good reproduction of the experimental data.

Tetraethylenepentamine-functionalized magnetic mesoporous composites as a novel adsorbent for the removal Cr(Ⅲ)-ethylenediaminetetraacetic acid in complex solution

A novel tetraethylenepentamine(TEPA) functionalized magnetic mesoporous silica adsorbent(FNMs/TEPA) was prepared for the adsorption of Cr(Ⅲ)-ethylenediaminetetraacetic acid(EDTA)from wastewater. The characterization of the prepared adsorbent certified that TEPA was modified onto the magnetic mesoporous silicon(FNMs), while FNMs/TEPA maintained the ordered mesoporous and pristine magnetic properties. The batch adsorption experiments demonstrated that TEPA significantly enhanced the removal capacity of the adsorbent for Cr(Ⅲ)-EDTA. FNMs/TEPA exhibited an excellent adsorption property(13.84 mg·g-1) at p H 4.0. Even in the presence of high concentrations of coexisting ions and organic acids, the adsorption performance of FNMs/TEPA was stable. Experimental characterization and DFT demonstrated that the adsorption of Cr(Ⅲ)-EDTA was ascribed to the electrostatic interaction, hydrogen bonding, and complexation between Cr(Ⅲ)-EDTA and amino groups on the adsorbent surface. The analysis of the independent gradient model(IGM) shows that electrostatic interaction is the main mode of action in the adsorption process. Moreover, FNMs/TEPA demonstrated remarkable reusability in three regeneration cycles. These findings indicated that FNMs/TEPA possessed excellent application prospects in the disposal of wastewater containing Cr(Ⅲ)-EDTA.

Optimized numerical density functional theory calculation of rotationally symmetric jellium model systems

In real space density functional theory calculations,the effective potential depends on the electron density,requiring self-consistent iterations,and numerous integrals at each step,making the process time-consuming.In our research,we propose an optimization method to expedite density functional theory(DFT)calculations for systems with large aspect ratios,such as metallic nanorods,nanowires,or scanning tunneling microscope tips.This method focuses on employing basis set to expand the electron density,Coulomb potential,and exchange-correlation potential.By precomputing integrals and caching redundant results,this expansion streamlines the integration process,significantly accelerating DFT computations.As a case study,we have applied this optimization to metallic nanorod systems of various radii and lengths,obtaining corresponding ground-state electron densities and potentials.

Solvent effects on Diels-Alder reaction in ionic liquids:A reaction density functional study

Extensive experimental studies have been performed on the Diels-Alder(DA)reactions in ionic liquids(ILs),which demonstrate that the IL environment can significantly influence the reaction rates and selectivity.However,the underlying microscopic mechanism remains ambiguous.In this work,the multiscale reaction density functional theory is applied to explore the effect of 1-butyl-3-methylimidazolium hexafluorophosphate([BMIM][PF_(6)])solvent on the reaction of cyclopentadiene(CP)with acrolein,methyl acrylate,or acrylonitrile.By analyzing the free energy landscape during the reaction,it is found that the polarization effect has a relatively small influence,while the solvation effect makes both the activation free energy and reaction free energy decrease.In addition,the rearrangement of local solvent structure shows that the cation spatial distribution responds more evidently to the reaction than the anion,and this indicates that the cation plays a dominant role in the solvation effect and so as to affect the reaction rates and selectivity of the DA reactions.

Robustness of the octupole collectivity in 144Ba within the cranking covariant density functional theory in 3D lattice

The octupole deformation and collectivity in octupole double-magic nucleus 144Ba are investigated using the Cranking covariant density functional theory in a three-dimensional lattice space.The reduced B(E3)transition probability is implemented for the first time in semiclassical approximation based on the microscopically calculated electric octupole moments.The available data,including the I-ωrelation and electric transitional probabilities B(E2)and B(E3)are well reproduced.Furthermore,it is shown that the ground state of 144Ba exhibits axial octupole and quadrupole deformations that persist up to high spins(I≈24h).

Local thermal conductivity of inhomogeneous nano-fluidic films:A density functional theory perspective

Combining the mean field Pozhar-Gubbins(PG)theory and the weighted density approximation,a novel method for local thermal conductivity of inhomogeneous fluids is proposed.The correlation effect that is beyond the mean field treatment is taken into account by the simulation-based empirical correlations.The application of this method to confined argon in slit pore shows that its prediction agrees well with the simulation results,and that it performs better than the original PG theory as well as the local averaged density model(LADM).In its further application to the nano-fluidic films,the influences of fluid parameters and pore parameters on the thermal conductivity are calculated and investigated.It is found that both the local thermal conductivity and the overall thermal conductivity can be significantly modulated by these parameters.Specifically,in the supercritical states,the thermal conductivity of the confined fluid shows positive correlation to the bulk density as well as the temperature.However,when the bulk density is small,the thermal conductivity exhibits a decrease-increase transition as the temperature is increased.This is also the case in which the temperature is low.In fact,the decrease-increase transition in both the small-bulk-density and low-temperature cases arises from the capillary condensation in the pore.Furthermore,smaller pore width and/or stronger adsorption potential can raise the critical temperature for condensation,and then are beneficial to the enhancement of the thermal conductivity.These modulation behaviors of the local thermal conductivity lead immediately to the significant difference of the overall thermal conductivity in different phase regions.

Charge self-consistent dynamical mean field theory calculations incombination with linear combination of numerical atomic orbitalsframework based density functional theory

We present a formalism of charge self-consistent dynamical mean field theory(DMFT)in combination with densityfunctional theory(DFT)within the linear combination of numerical atomic orbitals(LCNAO)framework.We implementedthe charge self-consistent DFT+DMFT formalism by interfacing a full-potential all-electron DFT code with threehybridization expansion-based continuous-time quantum Monte Carlo impurity solvers.The benchmarks on several 3d,4fand 5f strongly correlated electron systems validated our formalism and implementation.Furthermore,within the LCANOframework,our formalism is general and the code architecture is extensible,so it can work as a bridge merging differentLCNAO DFT packages and impurity solvers to do charge self-consistent DFT+DMFT calculations.

Tailoring MXene Thickness and Functionalization for Enhanced Room‑Temperature Trace NO_(2) Sensing

In this study,precise control over the thickness and termination of Ti3C2TX MXene flakes is achieved to enhance their electrical properties,environmental stability,and gas-sensing performance.Utilizing a hybrid method involving high-pressure processing,stirring,and immiscible solutions,sub-100 nm MXene flake thickness is achieved within the MXene film on the Si-wafer.Functionalization control is achieved by defunctionalizing MXene at 650℃ under vacuum and H2 gas in a CVD furnace,followed by refunctionalization with iodine and bromine vaporization from a bubbler attached to the CVD.Notably,the introduction of iodine,which has a larger atomic size,lower electronegativity,reduce shielding effect,and lower hydrophilicity(contact angle:99°),profoundly affecting MXene.It improves the surface area(36.2 cm^(2) g^(-1)),oxidation stability in aqueous/ambient environments(21 days/80 days),and film conductivity(749 S m^(-1)).Additionally,it significantly enhances the gas-sensing performance,including the sensitivity(0.1119Ωppm^(-1)),response(0.2% and 23%to 50 ppb and 200 ppm NO_(2)),and response/recovery times(90/100 s).The reduced shielding effect of the–I-terminals and the metallic characteristics of MXene enhance the selectivity of I-MXene toward NO2.This approach paves the way for the development of stable and high-performance gas-sensing two-dimensional materials with promising prospects for future studies.

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.

Transplantation of fibrin-thrombin encapsulated human induced neural stem cells promotes functional recovery of spinal cord injury rats through modulation of the microenvironment

Recent studies have mostly focused on engraftment of cells at the lesioned spinal cord,with the expectation that differentiated neurons facilitate recovery.Only a few studies have attempted to use transplanted cells and/or biomaterials as major modulators of the spinal cord injury microenvironment.Here,we aimed to investigate the role of microenvironment modulation by cell graft on functional recovery after spinal cord injury.Induced neural stem cells reprogrammed from human peripheral blood mononuclear cells,and/or thrombin plus fibrinogen,were transplanted into the lesion site of an immunosuppressed rat spinal cord injury model.Basso,Beattie and Bresnahan score,electrophysiological function,and immunofluorescence/histological analyses showed that transplantation facilitates motor and electrophysiological function,reduces lesion volume,and promotes axonal neurofilament expression at the lesion core.Examination of the graft and niche components revealed that although the graft only survived for a relatively short period(up to 15 days),it still had a crucial impact on the microenvironment.Altogether,induced neural stem cells and human fibrin reduced the number of infiltrated immune cells,biased microglia towards a regenerative M2 phenotype,and changed the cytokine expression profile at the lesion site.Graft-induced changes of the microenvironment during the acute and subacute stages might have disrupted the inflammatory cascade chain reactions,which may have exerted a long-term impact on the functional recovery of spinal cord injury rats.

Functional microfluidics:theory,microfabrication,and applications

Microfluidic devices are composed of microchannels with a diameter ranging from ten to a few hundred micrometers.Thus,quite a small(10-9–10-18l)amount of liquid can be manipulated by such a precise system.In the past three decades,significant progress in materials science,microfabrication,and various applications has boosted the development of promising functional microfluidic devices.In this review,the recent progress on novel microfluidic devices with various functions and applications is presented.First,the theory and numerical methods for studying the performance of microfluidic devices are briefly introduced.Then,materials and fabrication methods of functional microfluidic devices are summarized.Next,the recent significant advances in applications of microfluidic devices are highlighted,including heat sinks,clean water production,chemical reactions,sensors,biomedicine,capillaric circuits,wearable electronic devices,and microrobotics.Finally,perspectives on the challenges and future developments of functional microfluidic devices are presented.This review aims to inspire researchers from various fields engineering,materials,chemistry,mathematics,physics,and more—to collaborate and drive forward the development and applications of functional microfluidic devices,specifically for achieving carbon neutrality.

Deep brain implantable microelectrode arrays for detection and functional localization of the subthalamic nucleus in rats with Parkinson’s disease

The subthalamic nucleus(STN)is considered the best target for deep brain stimulation treatments of Parkinson’s disease(PD).It is difficult to localize the STN due to its small size and deep location.Multichannel microelectrode arrays(MEAs)can rapidly and precisely locate the STN,which is important for precise stimulation.In this paper,16-channel MEAs modified with multiwalled carbon nanotube/poly(3,4-ethylenedioxythiophene):poly(styrene sulfonate)(MWCNT/PEDOT:PSS)nanocomposites were designed and fabricated,and the accurate and rapid identification of the STN in PD rats was performed using detection sites distributed at different brain depths.These results showed that nuclei in 6-hydroxydopamine hydrobromide(6-OHDA)-lesioned brains discharged more intensely than those in unlesioned brains.In addition,the MEA simultaneously acquired neural signals from both the STN and the upper or lower boundary nuclei of the STN.Moreover,higher values of spike firing rate,spike amplitude,local field potential(LFP)power,and beta oscillations were detected in the STN of the 6-OHDA-lesioned brain,and may therefore be biomarkers of STN localization.Compared with the STNs of unlesioned brains,the power spectral density of spikes and LFPs synchronously decreased in the delta band and increased in the beta band of 6-OHDA-lesioned brains.This may be a cause of sleep and motor disorders associated with PD.Overall,this work describes a new cellular-level localization and detection method and provides a tool for future studies of deep brain nuclei.

Combined Promoting Effects of Specific Organic Functional Groups and Alumina Surface Characteristics for the Design of a Highly Efficient NiMo/Al_(2)O_(3) Hydrodesulfurization Catalyst

To prepare a highly efficient NiMo/Al_(2)O_(3) hydrodesulfurization catalyst,the combined effects of specific organic functional groups and alumina surface characteristics were investigated.First,the correlation between the surface characteristics of four different alumina and the existing Mo species states was established.It was found that the Mo equilibrium adsorption capacity can be used as a specific descriptor to quantitatively evaluate the changes in surface characteristics of different alumina.A lower Mo equilibrium adsorption capacity for alumina means weaker metal-support interaction and the loaded Mo species are easier to transform into MoS2.However,the Mo-O-Al bonds still exist at the metal-support interface.The introduction of cationic surfactant hecadecyl trimethyl ammonium bromide(CTAB)can further improve Mo species dispersion through electrostatic attraction with Mo anions and interaction of its alkyl chain with the alumina surface;meanwhile,the introduction of ethylenediamine tetraacetic acid(EDTA)can complex with Ni ions to enhance the Ni-promoting effect on Mo.Therefore,the NiMo catalyst designed using alumina with lower Mo equilibrium adsorption capacity and the simultaneous addition of EDTA and CTAB exhibits the highest hydrodesulfurization activity for 4,6-dimethyl dibenzothiophene because of its proper metal-support interaction and more well-dispersed Ni-Mo-S active phases.

Greatly enhanced corrosion/wear resistances of epoxy coating for Mg alloy through a synergistic effect between functionalized graphene and insulated blocking layer

The poor corrosion and wear resistances of Mg alloys seriously limit their potential applications in various industries.The conventional epoxy coating easily forms many intrinsic defects during the solidification process,which cannot provide sufficient protection.In the current study,we design a double-layer epoxy composite coating on Mg alloy with enhanced anti-corrosion/wear properties,via the spin-assisted assembly technique.The outer layer is functionalized graphene(FG)in waterborne epoxy resin(WEP)and the inner layer is Ce-based conversion(Ce)film.The FG sheets can be homogeneously dispersed within the epoxy matrix to fill the intrinsic defects and improve the barrier capability.The Ce film connects the outer layer with the substrate,showing the transition effect.The corrosion rate of Ce/WEP/FG composite coating is 2131 times lower than that of bare Mg alloy,and the wear rate is decreased by~90%.The improved corrosion resistance is attributed to the labyrinth effect(hindering the penetration of corrosive medium)and the obstruction of galvanic coupling behavior.The synergistic effect derived from the FG sheet and blocking layer exhibits great potential in realizing the improvement of multi-functional integration,which will open up a new avenue for the development of novel composite protection coatings of Mg alloys.

Structural and functional connectivity of the whole brain and subnetworks in individuals with mild traumatic brain injury:predictors of patient prognosis

Patients with mild traumatic brain injury have a diverse clinical presentation,and the underlying pathophysiology remains poorly understood.Magnetic resonance imaging is a non-invasive technique that has been widely utilized to investigate neuro biological markers after mild traumatic brain injury.This approach has emerged as a promising tool for investigating the pathogenesis of mild traumatic brain injury.G raph theory is a quantitative method of analyzing complex networks that has been widely used to study changes in brain structure and function.However,most previous mild traumatic brain injury studies using graph theory have focused on specific populations,with limited exploration of simultaneous abnormalities in structural and functional connectivity.Given that mild traumatic brain injury is the most common type of traumatic brain injury encounte red in clinical practice,further investigation of the patient characteristics and evolution of structural and functional connectivity is critical.In the present study,we explored whether abnormal structural and functional connectivity in the acute phase could serve as indicators of longitudinal changes in imaging data and cognitive function in patients with mild traumatic brain injury.In this longitudinal study,we enrolled 46 patients with mild traumatic brain injury who were assessed within 2 wee ks of injury,as well as 36 healthy controls.Resting-state functional magnetic resonance imaging and diffusion-weighted imaging data were acquired for graph theoretical network analysis.In the acute phase,patients with mild traumatic brain injury demonstrated reduced structural connectivity in the dorsal attention network.More than 3 months of followup data revealed signs of recovery in structural and functional connectivity,as well as cognitive function,in 22 out of the 46 patients.Furthermore,better cognitive function was associated with more efficient networks.Finally,our data indicated that small-worldness in the acute stage could serve as a predictor of longitudinal changes in connectivity in patients with mild traumatic brain injury.These findings highlight the importance of integrating structural and functional connectivity in unde rstanding the occurrence and evolution of mild traumatic brain injury.Additionally,exploratory analysis based on subnetworks could serve a predictive function in the prognosis of patients with mild traumatic brain injury.

Association of DNA methylation/demethylation with the functional outcome of stroke in a hyperinflammatory state

Inflammation is closely related to stroke prognosis, and high inflammation status leads to poor functional outcome in stroke. DNA methylation is involved in the pathogenesis and prognosis of stroke. However, the effect of DNA methylation on stroke at high levels of inflammation is unclear. In this study, we constructed a hyperinflammatory cerebral ischemia mouse model and investigated the effect of hypomethylation and hypermethylation on the functional outcome. We constructed a mouse model of transient middle cerebral artery occlusion and treated the mice with lipopolysaccharide to induce a hyperinflammatory state. To investigate the effect of DNA methylation on stroke, we used small molecule inhibitors to restrain the function of key DNA methylation and demethylation enzymes. 2,3,5-Triphenyltetrazolium chloride staining, neurological function scores, neurobehavioral tests, enzyme-linked immunosorbent assay, quantitative reverse transcription PCR and western blot assay were used to evaluate the effects after stroke in mice. We assessed changes in the global methylation status by measuring DNA 5-mc and DNA 5-hmc levels in peripheral blood after the use of the inhibitor. In the group treated with the DNA methylation inhibitor, brain tissue 2,3,5-triphenyltetrazolium chloride staining showed an increase in infarct volume, which was accompanied by a decrease in neurological scores and worsening of neurobehavioral performance. The levels of inflammatory factors interleukin 6 and interleukin-1 beta in ischemic brain tissue and plasma were elevated, indicating increased inflammation. Related inflammatory pathway exploration showed significant overactivation of nuclear factor kappa B. These results suggested that inhibiting DNA methylation led to poor functional outcome in mice with high inflammation following stroke. Further, the effects were reversed by inhibition of DNA demethylation. Our findings suggest that DNA methylation regulates the inflammatory response in stroke and has an important role in the functional outcome of hyperinflammatory stroke.

Ruxolitinib improves the inflammatory microenvironment,restores glutamate homeostasis,and promotes functional recovery after spinal cord injury

The inflammatory microenvironment and neurotoxicity can hinder neuronal regeneration and functional recovery after spinal cord injury.Ruxolitinib,a JAK-STAT inhibitor,exhibits effectiveness in autoimmune diseases,arthritis,and managing inflammatory cytokine storms.Although studies have shown the neuroprotective potential of ruxolitinib in neurological trauma,the exact mechanism by which it enhances functional recovery after spinal cord injury,particularly its effect on astrocytes,remains unclear.To address this gap,we established a mouse model of T10 spinal cord contusion and found that ruxolitinib effectively improved hindlimb motor function and reduced the area of spinal cord injury.Transcriptome sequencing analysis showed that ruxolitinib alleviated inflammation and immune response after spinal cord injury,restored EAAT2 expression,reduced glutamate levels,and alleviated excitatory toxicity.Furthermore,ruxolitinib inhibited the phosphorylation of JAK2 and STAT3 in the injured spinal cord and decreased the phosphorylation level of nuclear factor kappa-B and the expression of inflammatory factors interleukin-1β,interleukin-6,and tumor necrosis factor-α.Additionally,in glutamate-induced excitotoxicity astrocytes,ruxolitinib restored EAAT2 expression and increased glutamate uptake by inhibiting the activation of STAT3,thereby reducing glutamate-induced neurotoxicity,calcium influx,oxidative stress,and cell apoptosis,and increasing the complexity of dendritic branching.Collectively,these results indicate that ruxolitinib restores glutamate homeostasis by rescuing the expression of EAAT2 in astrocytes,reduces neurotoxicity,and effectively alleviates inflammatory and immune responses after spinal cord injury,thereby promoting functional recovery after spinal cord injury.