Hyperbolic Schwarz map for the hypergeometric differential equation

The Schwarz map of the hypergeometric differential equation is studied since the beginning of the last century. Its target is the complex projective line, the 2-sphere. This paper introduces the hyperbolic Schwarz map, whose target is the hyperbolic 3-space. This map can be considered to be a lifting to the 3-space of the Schwarz map. This paper studies the singularities of this map, and visualize its image when the monodromy group is a finite group or a typical Fuchsian group. General cases will be treated in a forthcoming paper.Comment: 16 pages, 8 figure

Derived Schwarz map of the hypergeometric differential equation and a parallel family of flat fronts

In the previous paper (math.CA/0609196) we defined a map, called the hyperbolic Schwarz map, from the one-dimensional projective space to the three-dimensional hyperbolic space by use of solutions of the hypergeometric differential equation, and thus obtained closed flat surfaces belonging to the class of flat fronts. We continue the study of such flat fronts in this paper. First, we introduce the notion of derived Schwarz maps of the hypergeometric differential equation and, second, we construct a parallel family of flat fronts connecting the classical Schwarz map and the derived Schwarz map.Comment: 15 pages, 12 figure

Analysis of potential muscular determinants of the preferred walk-run transition speed in human gait

textThe spontaneous transition from walking to running as walking speed increases is an intriguing neuromotor phenomenon that consistently occurs near 2 m/s in humans. Despite investigations of various metabolic and biomechanical factors, the determinants of the transition have remained elusive. However, no study has investigated the potential influence of intrinsic muscle properties and fiber-tendon interactions as potential determinants. The overall objective of this research was to use a forward dynamical simulation framework in three studies to identify the potential influence of these muscular determinants on the preferred walk-run transition speed (PTS). In the first study, individual muscle force production was examined as walking speed increased to assess the influence of intrinsic muscle properties on the PTS. The simulation data showed that of all the major lower-extremity muscle groups examined, the ankle plantar flexors were the only muscles to show a decrease in force production, despite an increase in activation, as walking speed approached the PTS. The force reduction was attributed to adverse contractile conditions. Considering the importance of the plantar flexors to providing body support and forward progression, the impaired force generation was deemed an important determinant of the PTS. In the second study, individual muscle contributions to body support and forward progression in walking and running at the PTS were quantified to clarify differences in muscle function between the two gait modes. The most distinctive difference was the reduced soleus contribution to forward progression in running. All other muscle groups performed similarly between the two gait modes. In the third study, individual muscle fiber and tendon mechanical work was quantified to examine whether there existed an energetic advantage during walking and running above and below the PTS. The total muscle fiber work was found to be higher in running than walking below the PTS, and higher in walking than running above the PTS. In addition, tendon elasticity utilization was lower in running below the PTS than in running above the PTS. These results highlight the advantages of each gait mode and suggest why walking below the PTS and running above the PTS are the preferred gaits.Mechanical Engineerin

Individual Muscle Contributions to the Axial Knee Joint Contact Force During Normal Walking

Muscles are significant contributors to the high joint forces developed in the knee during human walking. Not only do muscles contribute to the knee joint forces by acting to compress the joint, but they also develop joint forces indirectly through their contributions to the ground reaction forces via dynamic coupling. Thus, muscles can have significant contributions to forces at joints they do not span. However, few studies have investigated how the major lower-limb muscles contribute to the knee joint contact forces during walking. The goal of this study was to use a muscle-actuated forward dynamics simulation of walking to identify how individual muscles contribute to the axial tibio-femoral joint force. The simulation results showed that the vastii muscles are the primary contributors to the axial joint force in early stance while the gastrocnemius is the primary contributor in late stance. The tibio-femoral joint force generated by these muscles was at times greater than the muscle forces themselves. Muscles that do not cross the knee joint (e.g., the gluteus maximus and soleus) also have significant contributions to the tibio-femoral joint force through their contributions to the ground reaction forces. Further, small changes in walking kinematics (e.g., knee flexion angle) can have a significant effect on the magnitude of the knee joint forces. Thus, altering walking mechanics and muscle coordination patterns to utilize muscle groups that perform the same biomechanical function, yet contribute less to the knee joint forces may be an effective way to reduce knee joint loading during walking

False-Positive Mediastinal Lymphadenopathy on 18F-Fluorodeoxyglucose Positron Emission Tomography and Computed Tomography after Rectal Cancer Resection: A Case Report of Thoracoscopic Surgery in the Prone Position

18F-fluorodeoxyglucose (FDG) positron emission tomography and computed tomography (integrated FDG PET/CT) has been used to diagnose recurrence and differentiate postoperative changes from lymph node metastasis in colorectal cancer, although its accuracy is questionable. We report a prone thoracoscopic surgery for a rectal cancer patient in which false-positive mediastinal lymph nodes were found on FDG-PET/CT. A 60-year-old man underwent a laparoscopic high anterior resection and D3 lymph node dissection for rectal cancer. The histopathological diagnosis was moderately differentiated adenocarcinoma of the rectum, stage IIIB (pT3N1M0), necessitating oral fluoropyrimidine agent S-1. After the primary surgery, a solitary mediastinal lymph node measuring 30 mm in diameter was detected, and abnormal accumulation was confirmed by FDG-PET/CT (SUVmax, 11.7). Thoracoscopic resection was performed in the prone position, but histopathological results showed no metastasis. He was subsequently diagnosed with reactive lymphadenitis. The patient was discharged on postoperative day 4 in good condition and is alive without recurrence 12 months after surgery. PET/CT is useful for the detection of colorectal cancer recurrence; however, it does have a high false-positive rate for mediastinal lymph nodes. There is a limit to its diagnostic accuracy, and one must determine the indication for surgical treatment carefully. Surgery in the prone position is a useful and minimally invasive approach to the mediastinum and allows aggressive resection to be performed

Modeling photometric variations due to a global inhomogeneity on an obliquely rotating star: application to lightcurves of white dwarfs

We develop a general framework to compute photometric variations induced by the oblique rotation of a star with an axisymmetric inhomogeneous surface. We apply the framework to compute lightcurves of white dwarfs adopting two simple models of their surface inhomogeneity. Depending on the surface model and the location of the observer, the resulting lightcurve exhibits a departure from a purely sinusoidal curve that are observed for a fraction of white dwarfs. As a specific example, we fit our model to the observed phase-folded lightcurve of a fast-spinning white dwarf ZTF J190132.9+145808.7 (with the rotation period of 419s). We find that the size and obliquity angle of the spot responsible for the photometric variation are \dts \approx 60^\circ and \thetaS \approx 60^\circ or $90^\circ$, respectively, implying an interesting constraint on the surface distribution of the magnetic field on white dwarfs.Comment: 25 pages, 9 figures, accepted for publication in PAS

One-Step Holographic Photoalignment for Twisted Nematic Liquid Crystal Gratings

Liquid crystal gratings, in which liquid crystal molecules are periodically aligned, are fabricated by highly efficient and practical one-step holographic photoalignment method using a photocrosslinkable polymer liquid crystal (PCLC). This method is an innovative fabrication technique for liquid crystal grating containing a twisted nematic alignment, which does not require a conventional complex fabrication process. In this chapter, three types of liquid crystal gratings with twisted nematic alignment are fabricated. Periodic director distributions of these liquid crystal gratings are analyzed based on the elastic continuum theory and observed experimentally using a polarized light optical microscope. Furthermore, the polarization diffraction properties were measured by illumination with a visible laser beam. The resultant liquid crystal gratings exhibit various polarization diffraction properties depending on the director distributions and the polarization states of the incident beams. These polarization diffraction properties are well explained by theoretical analysis based on Jones calculus. These resultant liquid crystal gratings exhibit great potential for application as a diffractive optical element that can simultaneously control the various parameters of the light wave, such as amplitude, polarization states, and propagation direction

Lattice quantum chromodynamics (QCD) studies on decuplet baryons as meson-baryon bound states in the HAL QCD method

We study decuplet baryons from meson–baryon interactions in lattice quantum chromodynamics (QCD), in particular, Δ and Ω baryons from P-wave I = 3/2 Nπ and I = 0 $Xi bar{K}$ interactions, respectively. Interaction potentials are calculated in the HAL QCD method using 3-quark-type source operators at mπ ≈ 410 MeV and mK ≈ 635 MeV, where Δ as well as Ω baryons are stable. We use the conventional stochastic estimate of all-to-all propagators combined with the all-mode averaging to reduce statistical fluctuations. We have found that the $Xi bar{K}$ system has a weaker attraction than the Nπ system while the binding energy from the threshold is larger for Ω than Δ. This suggests that an inequality $m_{N}+m_{pi }-m_{Delta }lt m_{Xi }+m_{bar{K}}-m_{Omega }$ comes mainly from a smaller spatial size of a $Xi bar{K}$ bound state due to a larger reduced mass, rather than its interaction. Root-mean-square distances of bound states in both systems are small, indicating that Δ and Ω are tightly bound states and thus can be regarded qualitatively as composite states of three quarks. Results of binding energies agree with those obtained from temporal two-point functions within large systematic errors, which arise dominantly from the lattice artifact at short distances

New Paradigms of Radiotherapy for Bone Metastasis

Proper care of patients with bone metastasis requires interdisciplinary treatments. Radiotherapy (RT) plays a central role in the management of painful bone metastasis. External beam RT can provide rapid successful palliation of painful bone metastasis in 50–80% of patients, is associated with very few adverse effects and leads to complete pain relief at the treated site in up to one‐third of patients. Intensity‐modulated RT (IMRT) or stereotactic body RT (SBRT) enables the delivery of higher doses to the target tumor while minimizing the dose to adjacent organs. Reirradiation using IMRT or SBRT is a valuable option for the management of bone metastases. A multidisciplinary team, especially one consisting of a spinal surgeon and rehabilitation physician, is particularly useful for treating patients with spinal bone metastases characterized by spinal instability. Rehabilitation intervention which increases the physical activity level and prevents deconditioning is important. Future developments in surgical procedures and RT will likely improve the management protocols for bone metastases and technology to reduce metal artifacts in radiation planning might improve the efficacy and safety of combination therapy