Singular solutions, repeated roots and completeness for higher-spin chains

We investigate the completeness of the solutions of the Bethe equations for the integrable spin-s isotropic (XXX) spin chain with periodic boundary conditions. Solutions containing the exact string i s, i (s-1), ..., -i(s-1), -is are singular. For s>1/2, there exist also "strange" solutions with repeated roots, which nevertheless are physical (i.e., correspond to eigenstates of the Hamiltonian). We derive conditions for the singular solutions and the solutions with repeated roots to be physical. We formulate a conjecture for the number of solutions with pairwise distinct roots in terms of the numbers of singular and strange solutions. Using homotopy continuation, we solve the Bethe equations numerically for s=1 and s=3/2 up to 8 sites, and find some support for the conjecture. We also exhibit several examples of strange solutions.Comment: 17 pages; many tables provided as supplemental material; v2: minor change

Counting solutions of the Bethe equations of the quantum group invariant open XXZ chain at roots of unity

We consider the sl(2)_q-invariant open spin-1/2 XXZ quantum spin chain of finite length N. For the case that q is a root of unity, we propose a formula for the number of admissible solutions of the Bethe ansatz equations in terms of dimensions of irreducible representations of the Temperley-Lieb algebra; and a formula for the degeneracies of the transfer matrix eigenvalues in terms of dimensions of tilting sl(2)_q-modules. These formulas include corrections that appear if two or more tilting modules are spectrum-degenerate. For the XX case (q=exp(i pi/2)), we give explicit formulas for the number of admissible solutions and degeneracies. We also consider the cases of generic q and the isotropic (q->1) limit. Numerical solutions of the Bethe equations up to N=8 are presented. Our results are consistent with the Bethe ansatz solution being complete.Comment: 34 pages; v2: reference added; v3: two more references added and minor correction

FHF2 isoforms differentially regulate Nav1.6-mediated resurgent sodium currents in dorsal root ganglion neurons

Nav1.6 and Nav1.6-mediated resurgent currents have been implicated in several pain pathologies. However, our knowledge of how fast resurgent currents are modulated in neurons is limited. Our study explored the potential regulation of Nav1.6-mediated resurgent currents by isoforms of fibroblast growth factor homologous factor 2 (FHF2) in an effort to address the gap in our knowledge. FHF2 isoforms colocalize with Nav1.6 in peripheral sensory neurons. Cell line studies suggest that these proteins differentially regulate inactivation. In particular, FHF2A mediates long-term inactivation, a mechanism proposed to compete with the open-channel blocker mechanism that mediates resurgent currents. On the other hand, FHF2B lacks the ability to mediate long-term inactivation and may delay inactivation favoring open-channel block. Based on these observations, we hypothesized that FHF2A limits resurgent currents, whereas FHF2B enhances resurgent currents. Overall, our results suggest that FHF2A negatively regulates fast resurgent current by enhancing long-term inactivation and delaying recovery. In contrast, FHF2B positively regulated resurgent current and did not alter long-term inactivation. Chimeric constructs of FHF2A and Navβ4 (likely the endogenous open channel blocker in sensory neurons) exhibited differential effects on resurgent currents, suggesting that specific regions within FHF2A and Navβ4 have important regulatory functions. Our data also indicate that FHFAs and FHF2B isoform expression are differentially regulated in a radicular pain model and that associated neuronal hyperexcitability is substantially attenuated by a FHFA peptide. As such, these findings suggest that FHF2A and FHF2B regulate resurgent current in sensory neurons and may contribute to hyperexcitability associated with some pain pathologies

Highly localized interactions between sensory neurons and sprouting sympathetic fibers observed in a transgenic tyrosine hydroxylase reporter mouse

<p>Abstract</p> <p>Background</p> <p>Sprouting of sympathetic fibers into sensory ganglia occurs in many preclinical pain models, providing a possible anatomical substrate for sympathetically enhanced pain. However, the functional consequences of this sprouting have been controversial. We used a transgenic mouse in which sympathetic fibers expressed green fluorescent protein, observable in live tissue. Medium and large diameter lumbar sensory neurons with and without nearby sympathetic fibers were recorded in whole ganglion preparations using microelectrodes.</p> <p>Results</p> <p>After spinal nerve ligation, sympathetic sprouting was extensive by 3 days. Abnormal spontaneous activity increased to 15% and rheobase was reduced. Spontaneously active cells had Aαβ conduction velocities but were clustered near the medium/large cell boundary. Neurons with sympathetic basket formations had a dramatically higher incidence of spontaneous activity (71%) and had lower rheobase than cells with no sympathetic fibers nearby. Cells with lower density nearby fibers had intermediate phenotypes. Immunohistochemistry of sectioned ganglia showed that cells surrounded by sympathetic fibers were enriched in nociceptive markers TrkA, substance P, or CGRP. Spontaneous activity began before sympathetic sprouting was observed, but blocking sympathetic sprouting on day 3 by cutting the dorsal ramus in addition to the ventral ramus of the spinal nerve greatly reduced abnormal spontaneous activity.</p> <p>Conclusions</p> <p>The data suggest that early sympathetic sprouting into the sensory ganglia may have highly localized, excitatory effects. Quantitatively, neurons with sympathetic basket formations may account for more than half of the observed spontaneous activity, despite being relatively rare. Spontaneous activity in sensory neurons and sympathetic sprouting may be mutually re-enforcing.</p

Drop size modification in black liquor sprays from commercial nozzles using vibratory assist

"June 1995.""Submitted to Atomization and Sprays.

Transformational dynamics of BZO and BHO nanorods imposed by Y2O3 nanoparticles for improved isotropic pinning in YBa2Cu3O7−δ thin films

An elastic strain model was applied to evaluate the rigidity of the c-axis aligned one-dimensional artificial pinning centers (1D-APCs) in YBa2Cu3O7-δ matrix films. Higher rigidity was predicted for BaZrO3 1D-APCs than that of the BaHfO3 1D-APCs. This suggests a secondary APC doping of Y2O3 in the 1D-APC/YBa2Cu3O7-δ nanocomposite films would generate a stronger perturbation to the c-axis alignment of the BaHfO3 1D-APCs and therefore a more isotropic magnetic vortex pinning landscape. In order to experimentally confirm this, we have made a comparative study of the critical current density Jc (H, θ, T) of 2 vol.% BaZrO3 + 3 vol.%Y2O3 and 2 vol.%BaHfO3 + 3 vol.%Y2O3 double-doped (DD) YBa2Cu3O7-δ films deposited at their optimal growth conditions. A much enhanced isotropic pinning was observed in the BaHfO3 DD samples. For example, at 65 K and 9.0 T, the variation of the Jc across the entire θ range from θ=0 (H//c) to θ=90 degree (H//ab) is less than 18% for BaHfO3 DD films, in contrast to about 100% for the BaZrO3 DD counterpart. In addition, lower α values from the Jc(H) ∼ H-α fitting were observed in the BaHfO3 DD films in a large θ range away from the H//c-axis. Since the two samples have comparable Jc values at H//c-axis, the improved isotropic pinning in BaHfO3 DD films confirms the theoretically predicted higher tunability of the BaHfO3 1D-APCs in APC/YBa2Cu3O7-δ nanocomposite films

JNK1 phosphorylation of SCG10 determines microtubule dynamics and axodendritic length

c-Jun NH2-terminal kinases (JNKs) are essential during brain development, when they regulate morphogenic changes involving cell movement and migration. In the adult, JNK determines neuronal cytoarchitecture. To help uncover the molecular effectors for JNKs in these events, we affinity purified JNK-interacting proteins from brain. This revealed that the stathmin family microtubule-destabilizing proteins SCG10, SCLIP, RB3, and RB3′ interact tightly with JNK. Furthermore, SCG10 is also phosphorylated by JNK in vivo on sites that regulate its microtubule depolymerizing activity, serines 62 and 73. SCG10-S73 phosphorylation is significantly decreased in JNK1−/− cortex, indicating that JNK1 phosphorylates SCG10 in developing forebrain. JNK phosphorylation of SCG10 determines axodendritic length in cerebrocortical cultures, and JNK site–phosphorylated SCG10 colocalizes with active JNK in embryonic brain regions undergoing neurite elongation and migration. We demonstrate that inhibition of cytoplasmic JNK and expression of SCG10-62A/73A both inhibited fluorescent tubulin recovery after photobleaching. These data suggest that JNK1 is responsible for regulation of SCG10 depolymerizing activity and neurite elongation during brain development