Stable pairs on nodal K3 fibrations

We study Pandharipande-Thomas's stable pair theory on $K3$ fibrations over curves with possibly nodal fibers. We describe stable pair invariants of the fiberwise irreducible curve classes in terms of Kawai-Yoshioka's formula for the Euler characteristics of moduli spaces of stable pairs on $K3$ surfaces and Noether-Lefschetz numbers of the fibration. Moreover, we investigate the relation of these invariants with the perverse (non-commutative) stable pair invariants of the $K3$ fibration. In the case that the $K3$ fibration is a projective Calabi-Yau threefold, by means of wall-crossing techniques, we write the stable pair invariants in terms of the generalized Donaldson-Thomas invariants of 2-dimensional Gieseker semistable sheaves supported on the fibers.Comment: Published versio

Quenching of phase coherence in quasi-one dimensional ring crystals

The comparison of the single-particle (SP) dynamics between the whisker and ring NbSe$_3$ crystals provides new insight into the phase transition properties in quasi-one-dimensional charge density wave (CDW) systems.Comment: 9 pages, 4 figure

Pump- and Probe-polarization Analyses of Ultrafast Carrier Dynamics in Organic Superconductors

We investigated photo-excited carrier relaxation dynamics in the strongly correlated organic superconductors kappa-(BEDT-TTF)(2)Cu(NCS)(2) and kappa-(BEDT-TTF)(2)Cu[N(CN)(2)]Br, using different polarizations of pump and probe pulses. Below the glasslike transition temperature (T (g)) anisotropic responses for probe polarization were observed in both compounds. Decomposing the data into anisotropic and isotropic components, we found the anisotropic component shows no pump polarization dependence, meaning that dissipative excitation process was dominant for the anisotropic carrier relaxation. This behavior indicates that the appearance of anisotropic responses can be associated with spatial symmetry breaking due to structural change of BEDT-TTF molecules

Gopakumar-Vafa invariants via vanishing cycles

In this paper, we propose an ansatz for defining Gopakumar-Vafa invariants of Calabi-Yau threefolds, using perverse sheaves of vanishing cycles. Our proposal is a modification of a recent approach of Kiem-Li, which is itself based on earlier ideas of Hosono-Saito-Takahashi. We conjecture that these invariants are equivalent to other curve-counting theories such as Gromov-Witten theory and Pandharipande-Thomas theory. Our main theorem is that, for local surfaces, our invariants agree with PT invariants for irreducible one-cycles. We also give a counter-example to the Kiem-Li conjectures, where our invariants match the predicted answer. Finally, we give examples where our invariant matches the expected answer in cases where the cycle is non-reduced, non-planar, or non-primitive.Comment: 63 pages, many improvements of the exposition following referee comments, final version to appear in Inventione

Toda Lattice Solutions of Differential-Difference Equations for Dissipative Systems

In a certain class of differential-difference equations for dissipative systems, we show that hyperbolic tangent model is the only the nonlinear system of equations which can admit some particular solutions of the Toda lattice. We give one parameter family of exact solutions, which include as special cases the Toda lattice solutions as well as the Whitham's solutions in the Newell's model. Our solutions can be used to describe temporal-spatial density patterns observed in the optimal velocity model for traffic flow.Comment: Latex, 13 pages, 1 figur

A 2-year follow-up of a study to compare the efficacy of lateral wedged insoles with subtalar strapping and in-shoe lateral wedged insoles in patients with varus deformity osteoarthritis of the knee

SummaryObjectiveThis study was conducted in order to assess the effect of wearing a lateral wedged insole with a subtalar strap for 2 years in patients with osteoarthritis varus deformity of the knee (knee OA).DesignThe setting was an outpatient clinic. The efficacies of the strapped insole and a traditional shoe insert wedged insole (the inserted insole), as a positive control, were compared at the baseline and after 2 years of treatment. Randomization was performed according to birth date. The 61 female outpatients with knee OA who completed a prior 6-month study were asked to wear their respective insoles continuously as treatment during the course of the 2-year study. The femorotibial angle (FTA) was assessed by standing radiographs obtained while the subjects were barefoot and the Lequesne index of the knee OA at 2 years was compared with those at baseline in each insole group.ResultsThere were 61 patients in the original study, but 13 patients (21.3%) did not want to wear the insole continuously and five (8.2%) withdrew for other reasons. The 42 patients who completed the 2-year study were evaluated. At the 2-year assessment, participants wearing the subtalar strapped insole (n=21) demonstrated significantly decreased FTA (P=0.015), and significantly improved Lequesne index (P=0.031) in comparison with their baseline assessments. These significant differences were not found in the group with the traditional shoe inserted wedged insole (n=21).ConclusionOnly those participants using the subtalar strapped insole demonstrated significant change in the FTA in comparison with the baseline assessments. If the insole with a subtalar strap maintains FTA for more than 2 years, it may restrict the progression of degenerative articular cartilage lesions of knee OA

A comparison of intra-articular hyaluronan injection accuracy rates between three approaches based on radiographic severity of knee osteoarthritis

SummaryObjectiveTo compare the accuracy rates of intra-articular hyaluronic acid (HA) injections for osteoarthritis (OA) of the knee between the modified Waddell approach (an anteromedial approach with manipulative ankle traction at 30° of knee flexion), an anteromedial approach with the subjects seated (hereinafter the seated anteromedial approach) and a lateral patellar approach based on the Kellgren–Lawrence (K–L) radiographic grade (II, III and IV).DesignsFifty patients with knee OA received HA injections through the three approaches. The accuracy rates were confirmed with a single radiograph after injections of a mixture of radiographic contrast medium.ResultsIn the K–L grade IV cases (n=11), the accuracy rates through the modified Waddell approach (11 out of 11, 100%) were significantly higher than those through the seated anteromedial approach (six out of 11, 55%) and the lateral patellar approach (six out of 11, 55%) (P=0.035). No significant differences were detected in the accuracy rates of the participants classified as grade II (n=21) or III (n=18) cases between the modified Waddell approach (86% and 78%, respectively), the seated anteromedial approach (71% and 56%, respectively) and the lateral patellar approach (86% and 61%, respectively) (P>0.05).ConclusionAlthough previous studies have been conducted on the accuracy of needle placement into the intra-articular space of the knee, no evaluations were performed with the results categorized by radiographic severity. This study highlighted the need for clinicians to change the approach employed for HA injections, according to the severity of knee OA

Influence of concomitant heeled footwear when wearing a lateral wedged insole for medial compartment osteoarthritis of the knee

SummaryObjectiveTo compare the influence of concomitant heeled footwear when wearing a lateral wedged insole for medial compartment of osteoarthritis (OA) of the knee, between everyday walking shoes for outdoor use and socks or flat footwear without a heel for indoor use.DesignA total of 227 outpatients were prospectively randomized and treated with a neutral wedged insole inserted into shoes (placebo with shoes; n=45), a wedged insole inserted into shoes (inserted insole with shoes; n=45), a sock-type ankle supporter with a wedged insole when wearing socks or flat footwear (inserted insole without shoes; n=46), a subtalar strapped insole when wearing shoes (strapped insole with shoes; n=45), and the strapped insole with socks or flat footwear (strapped insole without shoes; n=46). The Lequesne index of knee OA at week 12 was compared with the baseline in each treatment group.ResultsTwenty patients withdrew from the study, and the 207 patients who completed the 12-week study were evaluated. At the final assessment, participants wearing the inserted insole without shoes (P=0.003), the strapped insole with shoes (P<0.0001), and the strapped insole without shoes (P<0.0001) demonstrated significantly improved Lequesne index scores in comparison with their baseline assessments. No significant differences were found in the placebo (P=0.16) or the inserted insole with shoes (P=0.2) groups.ConclusionConcomitant heeled footwear may decrease the efficacy of an inserted lateral wedged insole. The optimal usage of a lateral wedged insole for knee OA would be the combination with socks or flat footwear without heels

On the Equivalence of Different Lax Pairs for the Kac-van Moerbeke Hierarchy

We give a simple algebraic proof that the two different Lax pairs for the Kac-van Moerbeke hierarchy, constructed from Jacobi respectively super-symmetric Dirac-type difference operators, give rise to the same hierarchy of evolution equations. As a byproduct we obtain some new recursions for computing these equations.Comment: 8 page